update
This commit is contained in:
Morten Hjorth-Jensen
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4 [label="gini = 0.0\nsamples = 239\nvalue = [[239, 0]\n[0, 239]]", fillcolor="#e58139"] ;
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5 [label="mean texture <= 18.935\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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5 [label="mean radius <= 12.265\ngini = 0.444\nsamples = 3\nvalue = [[2, 1]\n[1, 2]]", fillcolor="#fdf6f0"] ;
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6 [label="gini = 0.0\nsamples = 1\nvalue = [[0, 1]\n[1, 0]]", fillcolor="#e58139"] ;
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@@ -22,7 +22,7 @@ edge [fontname="helvetica"] ;
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10 [label="gini = 0.0\nsamples = 3\nvalue = [[0, 3]\n[3, 0]]", fillcolor="#e58139"] ;
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11 [label="mean texture <= 16.22\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ;
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11 [label="area error <= 13.475\ngini = 0.278\nsamples = 6\nvalue = [[1, 5]\n[5, 1]]", fillcolor="#f4caac"] ;
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1 -> 11 ;
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12 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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@@ -30,11 +30,11 @@ edge [fontname="helvetica"] ;
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14 [label="worst texture <= 20.645\ngini = 0.202\nsamples = 167\nvalue = [[19, 148]\n[148, 19]]", fillcolor="#f0b68c"] ;
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0 -> 14 [labeldistance=2.5, labelangle=-45, headlabel="False"] ;
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15 [label="worst radius <= 17.74\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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15 [label="worst area <= 964.4\ngini = 0.375\nsamples = 16\nvalue = [[12, 4]\n[4, 12]]", fillcolor="#f9e3d4"] ;
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16 [label="gini = 0.0\nsamples = 11\nvalue = [[11, 0]\n[0, 11]]", fillcolor="#e58139"] ;
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17 [label="worst concave points <= 0.104\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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17 [label="worst texture <= 18.445\ngini = 0.32\nsamples = 5\nvalue = [[1, 4]\n[4, 1]]", fillcolor="#f6d5bd"] ;
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18 [label="gini = 0.0\nsamples = 1\nvalue = [[1, 0]\n[0, 1]]", fillcolor="#e58139"] ;
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@@ -42,7 +42,7 @@ edge [fontname="helvetica"] ;
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20 [label="mean concave points <= 0.049\ngini = 0.088\nsamples = 151\nvalue = [[7, 144]\n[144, 7]]", fillcolor="#ea985d"] ;
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21 [label="compactness error <= 0.016\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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21 [label="concave points error <= 0.01\ngini = 0.48\nsamples = 15\nvalue = [[6, 9]\n[9, 6]]", fillcolor="#ffffff"] ;
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22 [label="gini = 0.0\nsamples = 9\nvalue = [[0, 9]\n[9, 0]]", fillcolor="#e58139"] ;
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@@ -3,7 +3,9 @@
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{
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"cell_type": "markdown",
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"id": "4b4c06bc",
|
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"metadata": {},
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"metadata": {
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"editable": true
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},
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"source": [
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"<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
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"doconce format html exercisesweek41.do.txt -->\n",
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@@ -13,11 +15,13 @@
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{
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"cell_type": "markdown",
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"id": "bcb25e64",
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"metadata": {},
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"metadata": {
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"editable": true
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},
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"source": [
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"# Exercises week 42\n",
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"\n",
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"**October 14-18, 2024**\n",
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"**October 11-18, 2024**\n",
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"\n",
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"Date: **Deadline is Friday October 18 at midnight**\n"
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]
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@@ -25,13 +29,17 @@
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{
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"cell_type": "markdown",
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"id": "bb01f126",
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"metadata": {},
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"metadata": {
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"editable": true
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},
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"source": [
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"# Overarching aims of the exercises this week\n",
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"\n",
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"The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.\n",
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"\n",
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"This week, you will implement only the feed-forward pass. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes several checks along the way that you have implemented the pieces of the feed-forward pass correctly. If you have trouble running a notebook, or importing pytorch, you can run this notebook in google colab instead: (LINK TO COLAB), though we recommend that you set up VSCode and your python environment to run code like this locally.\n"
|
||||
"This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.\n",
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"\n",
|
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"If you have trouble running a notebook, you can run this notebook in google colab instead (https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true), an updated link will be provided on the course discord (you can also send an email to k.h.fredly@fys.uio.no if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.\n"
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]
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},
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{
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@@ -41,8 +49,33 @@
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"metadata": {},
|
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"outputs": [],
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"source": [
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"import autograd.numpy as np\n",
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"from autograd import grad"
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"import autograd.numpy as np # We need to use this numpy wrapper to make automatic differentiation work later\n",
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"from sklearn import datasets\n",
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"import matplotlib.pyplot as plt\n",
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"from sklearn.metrics import accuracy_score\n",
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"\n",
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"\n",
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"# Defining some activation functions\n",
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"def ReLU(z):\n",
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" return np.where(z > 0, z, 0)\n",
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"\n",
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"\n",
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"def sigmoid(z):\n",
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" return 1 / (1 + np.exp(-z))\n",
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"\n",
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"\n",
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"def softmax(z):\n",
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" \"\"\"Compute softmax values for each set of scores in the rows of the matrix z.\n",
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" Used with batched input data.\"\"\"\n",
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" e_z = np.exp(z - np.max(z, axis=0))\n",
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" return e_z / np.sum(e_z, axis=1)[:, np.newaxis]\n",
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"\n",
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"\n",
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"def softmax_vec(z):\n",
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" \"\"\"Compute softmax values for each set of scores in the vector z.\n",
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" Use this function when you use the activation function on one vector at a time\"\"\"\n",
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" e_z = np.exp(z - np.max(z))\n",
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" return e_z / np.sum(e_z)"
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]
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},
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{
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@@ -52,7 +85,7 @@
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"source": [
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"# Exercise 1\n",
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"\n",
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"Complete the following parts to compute the activation of the first layer.\n"
|
||||
"In this exercise you will compute the activation of the first layer. You only need to change the code in the cells right below an exercise, the rest works out of the box. Feel free to make changes and see how stuff works though!\n"
|
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]
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},
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{
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@@ -64,21 +97,24 @@
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"source": [
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"np.random.seed(2024)\n",
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"\n",
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"\n",
|
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"def ReLU(z):\n",
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" return np.where(z > 0, z, 0)\n",
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"\n",
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"\n",
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||||
"x = np.random.randn(2) # network input\n",
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"x = np.random.randn(2) # network input. This is a single input with two features\n",
|
||||
"W1 = np.random.randn(4, 2) # first layer weights"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "4ed2cf3d",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Given the shape of the first layer weight matrix, what is the input shape of the neural network? What is the output shape of the first layer?\n"
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]
|
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},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "edf7217b",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Define the bias of the first layer, `b1`with the correct shape\n"
|
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"**b)** Define the bias of the first layer, `b1`with the correct shape. (Run the next cell right after the previous to get the random generated values to line up with the test solution below)\n"
|
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]
|
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},
|
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{
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@@ -88,7 +124,7 @@
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"metadata": {},
|
||||
"outputs": [],
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"source": [
|
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"b1 = np.random.randn(4)"
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"b1 = ..."
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]
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},
|
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{
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@@ -96,7 +132,7 @@
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"id": "09e8d453",
|
||||
"metadata": {},
|
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"source": [
|
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"**b)** Compute the intermediary `z1` for the first layer\n"
|
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"**c)** Compute the intermediary `z1` for the first layer\n"
|
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]
|
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},
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{
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@@ -106,7 +142,7 @@
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"metadata": {},
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"outputs": [],
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"source": [
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"z1 = W1 @ x + b1"
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"z1 = ..."
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]
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},
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{
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@@ -114,7 +150,7 @@
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"id": "6f71374e",
|
||||
"metadata": {},
|
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"source": [
|
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"**c)** Compute the activation `a1` for the first layer using the ReLU activation function defined earlier.\n"
|
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"**d)** Compute the activation `a1` for the first layer using the ReLU activation function defined earlier.\n"
|
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]
|
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},
|
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{
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@@ -124,7 +160,7 @@
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"metadata": {},
|
||||
"outputs": [],
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"source": [
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"a1 = ReLU(z1)"
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"a1 = ..."
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]
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},
|
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{
|
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@@ -132,7 +168,7 @@
|
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"id": "088710c0",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Confirm that you got the correct activation with the test below.\n"
|
||||
"Confirm that you got the correct activation with the test below. Make sure that you define `b1` with the randn function right after you define `W1`.\n"
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]
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},
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{
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@@ -154,9 +190,11 @@
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"source": [
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"# Exercise 2\n",
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"\n",
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"Compute the activation of the second layer with an output of length 8 and ReLU activation.\n",
|
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"Now we will add a layer to the network with an output of length 8 and ReLU activation.\n",
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"\n",
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"**a)** Define the weight and bias of the second layer with the right shapes.\n"
|
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"**a)** What is the input of the second layer? What is its shape?\n",
|
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"\n",
|
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"**b)** Define the weight and bias of the second layer with the right shapes.\n"
|
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]
|
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},
|
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{
|
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@@ -166,8 +204,8 @@
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"metadata": {},
|
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"outputs": [],
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"source": [
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"W2 = np.random.randn(8, 4)\n",
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"b2 = np.random.randn(8)"
|
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"W2 = ...\n",
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"b2 = ..."
|
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]
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},
|
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{
|
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@@ -175,7 +213,7 @@
|
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"id": "5bd7d84b",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Compute intermediary `z2` and activation `a2` for the second layer.\n"
|
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"**c)** Compute the intermediary `z2` and activation `a2` for the second layer.\n"
|
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]
|
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},
|
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{
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@@ -185,8 +223,8 @@
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"metadata": {},
|
||||
"outputs": [],
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"source": [
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"z2 = W2 @ a1\n",
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"a2 = ReLU(z2)"
|
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"z2 = ...\n",
|
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"a2 = ..."
|
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]
|
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},
|
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{
|
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@@ -204,7 +242,9 @@
|
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"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
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"print(a2.shape == (8,))"
|
||||
"print(\n",
|
||||
" np.allclose(np.exp(len(a2)), 2980.9579870417283)\n",
|
||||
") # This should evaluate to True if a2 has the correct shape :)"
|
||||
]
|
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},
|
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{
|
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@@ -226,16 +266,16 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def create_layers(network_input_size, output_sizes):\n",
|
||||
"def create_layers(network_input_size, layer_output_sizes):\n",
|
||||
" layers = []\n",
|
||||
"\n",
|
||||
" i_size = network_input_size\n",
|
||||
" for output_size in output_sizes:\n",
|
||||
" W = np.random.rand(output_size, i_size)\n",
|
||||
" b = np.random.rand(output_size)\n",
|
||||
" for layer_output_size in layer_output_sizes:\n",
|
||||
" W = ...\n",
|
||||
" b = ...\n",
|
||||
" layers.append((W, b))\n",
|
||||
"\n",
|
||||
" i_size = output_size\n",
|
||||
" i_size = layer_output_size\n",
|
||||
" return layers"
|
||||
]
|
||||
},
|
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@@ -244,7 +284,7 @@
|
||||
"id": "bdc0cda2",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Comple the function below so that it evaluates the intermediate `z` and activation `a` for each layer, and returns the final activation `a`. This is the complete feed-forward pass, a full neural network!\n"
|
||||
"**b)** Comple the function below so that it evaluates the intermediary `z` and activation `a` for each layer, with ReLU actication, and returns the final activation `a`. This is the complete feed-forward pass, a full neural network!\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -254,11 +294,11 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def feed_forward(layers, input):\n",
|
||||
"def feed_forward_all_relu(layers, input):\n",
|
||||
" a = input\n",
|
||||
" for W, b in layers:\n",
|
||||
" z = W @ a + b\n",
|
||||
" a = ReLU(z)\n",
|
||||
" z = ...\n",
|
||||
" a = ...\n",
|
||||
" return a"
|
||||
]
|
||||
},
|
||||
@@ -276,14 +316,30 @@
|
||||
"id": "89a8f70d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
"source": [
|
||||
"input_size = ...\n",
|
||||
"layer_output_sizes = [...]\n",
|
||||
"\n",
|
||||
"x = np.random.rand(input_size)\n",
|
||||
"layers = ...\n",
|
||||
"predict = ...\n",
|
||||
"print(predict)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "0da7fd52",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**d)** Why is a neural network with no activation functions always mathematically equivelent to a neural network with only one layer?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "306d8b7c",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 4\n"
|
||||
"# Exercise 4 - Custom activation for each layer\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -291,29 +347,7 @@
|
||||
"id": "221c7b6c",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So far, every layer has used the same activation, ReLU. We often want to use other types of activation however, so we need to update our code to support multiple types of activation. Make sure that you have completed every previous exercise before trying this one.\n",
|
||||
"\n",
|
||||
"**a)** Make the `create_layers` function also accept a list of activation functions, which is used to add activation functions to each of the tuples in `layers`. Make new functions to not mess with the old ones.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "9df82312",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def create_layers_4(network_input_size, output_sizes, activation_funcs):\n",
|
||||
" layers = []\n",
|
||||
"\n",
|
||||
" i_size = network_input_size\n",
|
||||
" for output_size, activation in zip(output_sizes, activation_funcs):\n",
|
||||
" W = np.random.rand(output_size, i_size)\n",
|
||||
" b = np.random.rand(output_size)\n",
|
||||
" layers.append((W, b, activation))\n",
|
||||
"\n",
|
||||
" i_size = output_size\n",
|
||||
" return layers"
|
||||
"So far, every layer has used the same activation, ReLU. We often want to use other types of activation however, so we need to update our code to support multiple types of activation functions. Make sure that you have completed every previous exercise before trying this one.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -321,7 +355,7 @@
|
||||
"id": "10896d06",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Update the `feed_forward` function to support this change.\n"
|
||||
"**a)** Complete the `feed_forward` function which accepts a list of activation functions as an argument, and which evaluates these activation functions at each layer.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -331,11 +365,109 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def feed_forward_4(layers, input):\n",
|
||||
"def feed_forward(input, layers, activations):\n",
|
||||
" a = input\n",
|
||||
" for W, b, activation in layers:\n",
|
||||
" z = W @ a + b\n",
|
||||
" a = activation(z)\n",
|
||||
" for (W, b), activation in zip(layers, activations):\n",
|
||||
" z = ...\n",
|
||||
" a = ...\n",
|
||||
" return a"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "8f7df363",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Make a list with three activation functions(don't call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd's numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)\n",
|
||||
"\n",
|
||||
"Then evaluate a network with three layers and these activation functions.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "301b46dc",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"network_input_size = ...\n",
|
||||
"layer_output_sizes = [...]\n",
|
||||
"activations = [...]\n",
|
||||
"layers = ...\n",
|
||||
"\n",
|
||||
"x = np.random.randn(network_input_size)\n",
|
||||
"feed_forward(x, layers, activations)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a8d6c425",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 5 - Processing multiple inputs at once\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "0f4330a4",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"So far, the feed forward function has taken one input vector as an input. This vector then undergoes a linear transformation and then an element-wise non-linear operation for each layer. This approach of sending one vector in at a time is great for interpreting how the network transforms data with its linear and non-linear operations, but not the best for numerical efficiency. Now, we want to be able to send many inputs through the network at once. This will make the code a bit harder to understand, but it will make it faster, and more compact. It will be worth the trouble.\n",
|
||||
"\n",
|
||||
"To process multiple inputs at once, while still performing the same operations, you will only need to flip a couple things around.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "17023bb7",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Complete the function `create_layers_batch` so that the weight matrix is the transpose of what it was when you only sent in one input at a time.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "a241fd79",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def create_layers_batch(network_input_size, layer_output_sizes):\n",
|
||||
" layers = []\n",
|
||||
"\n",
|
||||
" i_size = network_input_size\n",
|
||||
" for layer_output_size in layer_output_sizes:\n",
|
||||
" W = ...\n",
|
||||
" b = ...\n",
|
||||
" layers.append((W, b))\n",
|
||||
"\n",
|
||||
" i_size = layer_output_size\n",
|
||||
" return layers"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a6349db6",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Make a matrix of inputs with the shape (number of features, number of inputs), you choose the number of inputs and features per input. Then complete the function `feed_forward_batch` so that you can process this matrix of inputs with only one matrix multiplication and one broadcasted vector addition per layer. (Hint: You will only need to swap two variable around from your previous implementation, but remember to test that you get the same results for equivelent inputs!)\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "425f3bcc",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"inputs = np.random.rand(1000, 4)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def feed_forward_batch(inputs, layers, activations):\n",
|
||||
" a = inputs\n",
|
||||
" for (W, b), activation in zip(layers, activations):\n",
|
||||
" z = ...\n",
|
||||
" a = ...\n",
|
||||
" return a"
|
||||
]
|
||||
},
|
||||
@@ -354,15 +486,29 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from scipy.special import softmax\n",
|
||||
"\n",
|
||||
"network_input_size = 4\n",
|
||||
"output_sizes = [12, 10, 3]\n",
|
||||
"activation_funcs = [ReLU, ReLU, softmax]\n",
|
||||
"layers = create_layers_4(network_input_size, output_sizes, activation_funcs)\n",
|
||||
"network_input_size = ...\n",
|
||||
"layer_output_sizes = [...]\n",
|
||||
"activations = [...]\n",
|
||||
"layers = create_layers_batch(network_input_size, layer_output_sizes)\n",
|
||||
"\n",
|
||||
"x = np.random.randn(network_input_size)\n",
|
||||
"predict = feed_forward_4(layers, x)"
|
||||
"feed_forward_batch(inputs, layers, activations)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "87999271",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"You should use this batched approach moving forward, as it will lead to much more compact code. However, remember that each input is still treated separately, and that you will need to keep in mind the transposed weight matrix and other details when implementing backpropagation.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "237eb782",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 6 - Predicting on real data\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -370,9 +516,9 @@
|
||||
"id": "54d5fde7",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The final exercise will hopefully be very simple if everything has worked so far. You will evaluate your neural network on the iris data set (https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html).\n",
|
||||
"You will now evaluate your neural network on the iris data set (https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html).\n",
|
||||
"\n",
|
||||
"This dataset contains data on 150 flowers of 3 different types which can be separated pretty well using the four features given for each flower, which includes the width and length of their leaves. You are not expected to do any training of the network or actual classification, unless you feel like it, in that case you can do exercise 5.\n"
|
||||
"This dataset contains data on 150 flowers of 3 different types which can be separated pretty well using the four features given for each flower, which includes the width and length of their leaves. You are will later train your network to actually make good predictions.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -382,10 +528,6 @@
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# Loading and plotting iris dataset\n",
|
||||
"from sklearn import datasets\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"iris = datasets.load_iris()\n",
|
||||
"\n",
|
||||
"_, ax = plt.subplots()\n",
|
||||
@@ -396,24 +538,91 @@
|
||||
")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "ed3e2fc9",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"inputs = iris.data\n",
|
||||
"\n",
|
||||
"# Since each prediction is a vector with a score for each of the three types of flowers,\n",
|
||||
"# we need to make each target a vector with a 1 for the correct flower and a 0 for the others.\n",
|
||||
"targets = np.zeros((len(iris.data), 3))\n",
|
||||
"for i, t in enumerate(iris.target):\n",
|
||||
" targets[i, t] = 1\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def accuracy(predictions, targets):\n",
|
||||
" one_hot_predictions = np.zeros(predictions.shape)\n",
|
||||
"\n",
|
||||
" for i, prediction in enumerate(predictions):\n",
|
||||
" one_hot_predictions[i, np.argmax(prediction)] = 1\n",
|
||||
" return accuracy_score(one_hot_predictions, targets)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "c528846f",
|
||||
"id": "0362c4a9",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**c)** Loop over the iris dataset(`iris.data`) and evaluate the network for each data point.\n"
|
||||
"**a)** What should the input size for the network be with this dataset? What should the output shape of the last layer be?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "bf62607e",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**b)** Create a network with two hidden layers, the first with sigmoid activation and the last with softmax, the first layer should have 8 \"nodes\", the second has the number of nodes you found in exercise a). Softmax returns a \"probability distribution\", in the sense that the numbers in the output are positive and add up to 1 and, their magnitude are in some sense relative to their magnitude before going through the softmax function. Remember to use the batched version of the create_layers and feed forward functions.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "2efc507d",
|
||||
"id": "5366d4ae",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# No need to change this cell! Just make sure it works!\n",
|
||||
"for x in iris.data:\n",
|
||||
" prediction = feed_forward_4(layers, x)"
|
||||
"...\n",
|
||||
"layers = ..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "c528846f",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**c)** Evaluate your model on the entire iris dataset! For later purposes, we will split the data into train and test sets, and compute gradients on smaller batches of the training data. But for now, evaluate the network on the whole thing at once.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "6c783105",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"predictions = feed_forward_batch(inputs, layers, activations)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "01a3caa8",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**d)** Compute the accuracy of your model using the accuracy function defined above. Recreate your model a couple times and see how the accuracy changes.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "a2612b82",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print(accuracy(predictions, targets))"
|
||||
]
|
||||
},
|
||||
{
|
||||
@@ -421,31 +630,126 @@
|
||||
"id": "334560b6",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Exercise 5 (Very optional and very hard :)\n"
|
||||
"# Exercise 6 - Training on real data\n",
|
||||
"\n",
|
||||
"To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "ea0a8fe0",
|
||||
"id": "700cabe4",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** Make the iris target values into one-hot vectors.\n",
|
||||
"The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is \"most certain\" on the correct target.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "56bef776",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"from autograd import grad\n",
|
||||
"\n",
|
||||
"**b)** Define the cross-entropy loss function to evaluate the performance of your network on the data set.\n",
|
||||
"\n",
|
||||
"**c)** Use the autograd package to take the gradient of the cross entropy wrt. the weights and biases of the network.\n",
|
||||
"def cost(input, layers, activations, target):\n",
|
||||
" predict = feed_forward_batch(input, layers, activations)\n",
|
||||
" return cross_entropy(predict, target)\n",
|
||||
"\n",
|
||||
"**d)** Use gradient descent of some sort to optimize the parameters.\n",
|
||||
"\n",
|
||||
"**e)** Evaluate the accuracy of the network.\n",
|
||||
"def cross_entropy(predict, target):\n",
|
||||
" return np.sum(-target * np.log(predict))\n",
|
||||
"\n",
|
||||
"**e)** Show off how you did in a group session!\n"
|
||||
"\n",
|
||||
"gradient_func = grad(\n",
|
||||
" cross_entropy, 1\n",
|
||||
") # Taking the gradient wrt. the second input to the cost function"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "7b1b74bc",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**a)** What shape should the gradient of the cost function wrt. weights and biases be?\n",
|
||||
"\n",
|
||||
"**b)** Use the `gradient_func` function to take the gradient of the cross entropy wrt. the weights and biases of the network. Check the shapes of what's inside. What does the `grad` func from autograd actually do?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "841c9e87",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"layers_grad = gradient_func(inputs, layers, activations, targets) # Don't change this"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "adc9e9be",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**c)** Finish the `train_network` function.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "6e4d38d3",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def train_network(\n",
|
||||
" inputs, layers, activations, targets, learning_rate=0.001, epochs=100\n",
|
||||
"):\n",
|
||||
" for i in range(epochs):\n",
|
||||
" layers_grad = gradient_func(inputs, layers, activations, targets)\n",
|
||||
" for (W, b), (W_g, b_g) in zip(layers, layers_grad):\n",
|
||||
" W -= ...\n",
|
||||
" b -= ..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "2f65d663",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**e)** What do we call the gradient method used above?\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "7059dd8c",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**d)** Train your network and see how the accuracy changes! Make a plot if you want.\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "5027c7a5",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"..."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "3bc77016",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**e)** How high of an accuracy is it possible to acheive with a neural network on this dataset, if we use the whole thing as training data?\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3 (ipykernel)",
|
||||
"display_name": ".venv",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
@@ -459,7 +763,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
|
||||
"version": "3.12.7"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1056,13 +1066,13 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha:
|
||||
[1.94485679]
|
||||
[2.07549007]
|
||||
Coefficient beta :
|
||||
[[5.13059483]]
|
||||
Mean squared error: 0.32
|
||||
Variance score: 0.87
|
||||
[[5.14029264]]
|
||||
Mean squared error: 0.23
|
||||
Variance score: 0.89
|
||||
Mean squared log error: 0.01
|
||||
Mean absolute error: 0.45
|
||||
Mean absolute error: 0.38
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter1_19_1.png" src="_images/chapter1_19_1.png" />
|
||||
@@ -1162,7 +1172,7 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/chapter1_33_0.png" src="_images/chapter1_33_0.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.004999999999999996
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.004999999999999987
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1373,7 +1383,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1707,7 +1717,7 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.19166666666666668
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1716,7 +1726,7 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1725,7 +1735,7 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1734,7 +1744,7 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1743,7 +1753,7 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1752,7 +1762,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1761,191 +1771,34 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57122/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">8</span><span class="p">],</span> <span class="n">line</span> <span class="mi">11</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">lmbd</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">lmbd_vals</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">dnn</span> <span class="o">=</span> <span class="n">NeuralNetwork</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train_onehot</span><span class="p">,</span> <span class="n">eta</span><span class="o">=</span><span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="o">=</span><span class="n">lmbd</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="n">epochs</span><span class="p">,</span> <span class="n">batch_size</span><span class="o">=</span><span class="n">batch_size</span><span class="p">,</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">10</span> <span class="n">n_hidden_neurons</span><span class="o">=</span><span class="n">n_hidden_neurons</span><span class="p">,</span> <span class="n">n_categories</span><span class="o">=</span><span class="n">n_categories</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">11</span> <span class="n">dnn</span><span class="o">.</span><span class="n">train</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="n">DNN_numpy</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dnn</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">15</span> <span class="n">test_predict</span> <span class="o">=</span> <span class="n">dnn</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 98,</span> in <span class="ni">NeuralNetwork.train</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">95</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">X_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">96</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Y_data_full</span><span class="p">[</span><span class="n">chosen_datapoints</span><span class="p">]</span>
|
||||
<span class="ne">---> </span><span class="mi">98</span> <span class="bp">self</span><span class="o">.</span><span class="n">feed_forward</span><span class="p">()</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">99</span> <span class="bp">self</span><span class="o">.</span><span class="n">backpropagation</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">Cell In[6], line 38,</span> in <span class="ni">NeuralNetwork.feed_forward</span><span class="nt">(self)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">36</span> <span class="k">def</span> <span class="nf">feed_forward</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">37</span> <span class="c1"># feed-forward for training</span>
|
||||
<span class="ne">---> </span><span class="mi">38</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">X_data</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_weights</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">hidden_bias</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">39</span> <span class="bp">self</span><span class="o">.</span><span class="n">a_h</span> <span class="o">=</span> <span class="n">sigmoid</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">z_h</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">41</span> <span class="bp">self</span><span class="o">.</span><span class="n">z_o</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a_h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_weights</span><span class="p">)</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">output_bias</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1991,22 +1844,6 @@ Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22411/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter10_59_1.png" src="_images/chapter10_59_1.png" />
|
||||
<img alt="_images/chapter10_59_2.png" src="_images/chapter10_59_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="scikit-learn-implementation">
|
||||
@@ -2042,333 +1879,6 @@ performance overall.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.18333333333333332
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.18611111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.13055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.24444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.23333333333333334
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.12777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.1527777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9111111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.8305555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8888888888888888
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8944444444444445
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.975
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9777777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.001
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.
|
||||
warnings.warn(
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9861111111111112
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.9888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.01
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.9722222222222222
|
||||
|
||||
Learning rate = 0.01
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.9527777777777777
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.9027777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.8583333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.9055555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.8805555555555555
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.8722222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.1
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.8666666666666667
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 1e-05
|
||||
Accuracy score on test set: 0.17222222222222222
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.0001
|
||||
Accuracy score on test set: 0.11666666666666667
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
@@ -2412,10 +1922,6 @@ Accuracy score on test set: 0.09444444444444444
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/chapter10_63_0.png" src="_images/chapter10_63_0.png" />
|
||||
<img alt="_images/chapter10_63_1.png" src="_images/chapter10_63_1.png" />
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
|
||||
@@ -2454,14 +1960,6 @@ and/or if you use <strong>anaconda</strong>, just write (or install from the gra
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span> <span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">12</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
|
||||
<span class="n">conda</span> <span class="n">create</span> <span class="o">-</span><span class="n">n</span> <span class="n">tf</span> <span class="n">tensorflow</span>
|
||||
<span class="o">^</span>
|
||||
<span class="ne">SyntaxError</span>: invalid syntax
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>To install the current release of GPU TensorFlow</p>
|
||||
<div class="cell docutils container">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -2662,6 +2672,43 @@ Using TensorFlow results in a much better execution time. Try it!</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:60,</span> in <span class="ni">jacobian</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">50</span> <span class="nd">@unary_to_nary</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">51</span> <span class="k">def</span> <span class="nf">jacobian</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">52</span><span class="w"> </span><span class="sd">"""</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">53</span><span class="sd"> Returns a function which computes the Jacobian of `fun` with respect to</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">54</span><span class="sd"> positional argument number `argnum`, which must be a scalar or array. Unlike</span>
|
||||
<span class="sd"> (...)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">58</span><span class="sd"> (out1, out2, ...) then the Jacobian has shape (out1, out2, ..., in1, in2, ...).</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">59</span><span class="sd"> """</span>
|
||||
<span class="ne">---> </span><span class="mi">60</span> <span class="n">vjp</span><span class="p">,</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">_make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">61</span> <span class="n">ans_vspace</span> <span class="o">=</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="n">jacobian_shape</span> <span class="o">=</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10,</span> in <span class="ni">make_vjp</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">def</span> <span class="nf">make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_node</span> <span class="o">=</span> <span class="n">VJPNode</span><span class="o">.</span><span class="n">new_root</span><span class="p">()</span>
|
||||
<span class="ne">---> </span><span class="mi">10</span> <span class="n">end_value</span><span class="p">,</span> <span class="n">end_node</span> <span class="o">=</span> <span class="n">trace</span><span class="p">(</span><span class="n">start_node</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">end_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">zeros</span><span class="p">()</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10,</span> in <span class="ni">trace</span><span class="nt">(start_node, fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="k">with</span> <span class="n">trace_stack</span><span class="o">.</span><span class="n">new_trace</span><span class="p">()</span> <span class="k">as</span> <span class="n">t</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">start_box</span> <span class="o">=</span> <span class="n">new_box</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">start_node</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">10</span> <span class="n">end_box</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="n">start_box</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">11</span> <span class="k">if</span> <span class="n">isbox</span><span class="p">(</span><span class="n">end_box</span><span class="p">)</span> <span class="ow">and</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_trace</span> <span class="o">==</span> <span class="n">start_box</span><span class="o">.</span><span class="n">_trace</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">12</span> <span class="k">return</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_value</span><span class="p">,</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_node</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15,</span> in <span class="ni">unary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f</span><span class="nt">(x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">13</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">14</span> <span class="n">subargs</span> <span class="o">=</span> <span class="n">subvals</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">argnum</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
|
||||
<span class="ne">---> </span><span class="mi">15</span> <span class="k">return</span> <span class="n">fun</span><span class="p">(</span><span class="o">*</span><span class="n">subargs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.<locals>.nary_operator.<locals>.nary_f</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">19</span> <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:64,</span> in <span class="ni">jacobian</span><span class="nt">(fun, x)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="n">jacobian_shape</span> <span class="o">=</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">63</span> <span class="n">grads</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">vjp</span><span class="p">,</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">standard_basis</span><span class="p">())</span>
|
||||
@@ -2695,43 +2742,58 @@ Using TensorFlow results in a much better execution time. Try it!</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">22</span> <span class="k">for</span> <span class="n">parent</span><span class="p">,</span> <span class="n">ingrad</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">parents</span><span class="p">,</span> <span class="n">ingrads</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">23</span> <span class="n">outgrads</span><span class="p">[</span><span class="n">parent</span><span class="p">]</span> <span class="o">=</span> <span class="n">add_outgrads</span><span class="p">(</span><span class="n">outgrads</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">parent</span><span class="p">),</span> <span class="n">ingrad</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:78,</span> in <span class="ni">defvjp.<locals>.vjp_argnums.<locals>.<lambda></span><span class="nt">(g)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">76</span> <span class="n">vjp_0</span> <span class="o">=</span> <span class="n">vjp_0_fun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">77</span> <span class="n">vjp_1</span> <span class="o">=</span> <span class="n">vjp_1_fun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">78</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="p">(</span><span class="n">vjp_0</span><span class="p">(</span><span class="n">g</span><span class="p">),</span> <span class="n">vjp_1</span><span class="p">(</span><span class="n">g</span><span class="p">))</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">79</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">80</span> <span class="n">vjps</span> <span class="o">=</span> <span class="p">[</span><span class="n">vjps_dict</span><span class="p">[</span><span class="n">argnum</span><span class="p">](</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">argnum</span> <span class="ow">in</span> <span class="n">argnums</span><span class="p">]</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67,</span> in <span class="ni">defvjp.<locals>.vjp_argnums.<locals>.<lambda></span><span class="nt">(g)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">64</span> <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">65</span> <span class="s2">"VJP of </span><span class="si">{}</span><span class="s2"> wrt argnum 0 not defined"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun</span><span class="o">.</span><span class="vm">__name__</span><span class="p">))</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">66</span> <span class="n">vjp</span> <span class="o">=</span> <span class="n">vjpfun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">67</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="p">(</span><span class="n">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">),)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">68</span> <span class="k">elif</span> <span class="n">L</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">69</span> <span class="n">argnum_0</span><span class="p">,</span> <span class="n">argnum_1</span> <span class="o">=</span> <span class="n">argnums</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:660,</span> in <span class="ni">unbroadcast_f.<locals>.<lambda></span><span class="nt">(g)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">658</span> <span class="k">def</span> <span class="nf">unbroadcast_f</span><span class="p">(</span><span class="n">target</span><span class="p">,</span> <span class="n">f</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">659</span> <span class="n">target_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">target</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">660</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">unbroadcast</span><span class="p">(</span><span class="n">f</span><span class="p">(</span><span class="n">g</span><span class="p">),</span> <span class="n">target_meta</span><span class="p">)</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423,</span> in <span class="ni">matmul_vjp_1.<locals>.<lambda></span><span class="nt">(g)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">421</span> <span class="n">A_ndim</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">422</span> <span class="n">B_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">423</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">matmul_adjoint_1</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">A_ndim</span><span class="p">,</span> <span class="n">B_meta</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:34,</span> in <span class="ni"><lambda></span><span class="nt">(g)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">30</span> <span class="c1"># ----- Binary ufuncs -----</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">32</span> <span class="n">defvjp</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">add</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">g</span><span class="p">),</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">33</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">g</span><span class="p">))</span>
|
||||
<span class="ne">---> </span><span class="mi">34</span> <span class="n">defvjp</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">multiply</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">y</span> <span class="o">*</span> <span class="n">g</span><span class="p">),</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">35</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">x</span> <span class="o">*</span> <span class="n">g</span><span class="p">))</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">36</span> <span class="n">defvjp</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">subtract</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">g</span><span class="p">),</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">37</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="o">-</span><span class="n">g</span><span class="p">))</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">38</span> <span class="n">defvjp</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">divide</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">g</span> <span class="o">/</span> <span class="n">y</span><span class="p">),</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">39</span> <span class="k">lambda</span> <span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">:</span> <span class="n">unbroadcast_f</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="o">-</span> <span class="n">g</span> <span class="o">*</span> <span class="n">x</span> <span class="o">/</span> <span class="n">y</span><span class="o">**</span><span class="mi">2</span><span class="p">))</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:413,</span> in <span class="ni">matmul_adjoint_1</span><span class="nt">(A, G, A_ndim, B_meta)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">411</span> <span class="k">if</span> <span class="n">B_is_vec</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">412</span> <span class="n">result</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">413</span> <span class="k">return</span> <span class="n">unbroadcast</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">B_meta</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_boxes.py:27,</span> in <span class="ni">ArrayBox.__mul__</span><span class="nt">(self, other)</span>
|
||||
<span class="ne">---> </span><span class="mi">27</span> <span class="k">def</span> <span class="fm">__mul__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">):</span> <span class="k">return</span> <span class="n">anp</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">other</span><span class="p">)</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:653,</span> in <span class="ni">unbroadcast</span><span class="nt">(x, target_meta, broadcast_idx)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">651</span> <span class="k">for</span> <span class="n">axis</span><span class="p">,</span> <span class="n">size</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">target_shape</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">652</span> <span class="k">if</span> <span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<span class="ne">--> </span><span class="mi">653</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">654</span> <span class="k">if</span> <span class="n">anp</span><span class="o">.</span><span class="n">iscomplexobj</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">target_iscomplex</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">655</span> <span class="n">x</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:44,</span> in <span class="ni">primitive.<locals>.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">42</span> <span class="n">parents</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">box</span><span class="o">.</span><span class="n">_node</span> <span class="k">for</span> <span class="n">_</span> <span class="p">,</span> <span class="n">box</span> <span class="ow">in</span> <span class="n">boxed_args</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">43</span> <span class="n">argnums</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">argnum</span> <span class="k">for</span> <span class="n">argnum</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">boxed_args</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">44</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">f_wrapped</span><span class="p">(</span><span class="o">*</span><span class="n">argvals</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">45</span> <span class="n">node</span> <span class="o">=</span> <span class="n">node_constructor</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">f_wrapped</span><span class="p">,</span> <span class="n">argvals</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">,</span> <span class="n">argnums</span><span class="p">,</span> <span class="n">parents</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">46</span> <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48,</span> in <span class="ni">primitive.<locals>.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45,</span> in <span class="ni">primitive.<locals>.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">43</span> <span class="n">argnums</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">argnum</span> <span class="k">for</span> <span class="n">argnum</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">boxed_args</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">44</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">f_wrapped</span><span class="p">(</span><span class="o">*</span><span class="n">argvals</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="ne">---> </span><span class="mi">45</span> <span class="n">node</span> <span class="o">=</span> <span class="n">node_constructor</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">f_wrapped</span><span class="p">,</span> <span class="n">argvals</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">,</span> <span class="n">argnums</span><span class="p">,</span> <span class="n">parents</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">46</span> <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">47</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="ne">---> </span><span class="mi">48</span> <span class="k">return</span> <span class="n">f_raw</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36,</span> in <span class="ni">VJPNode.__init__</span><span class="nt">(self, value, fun, args, kwargs, parent_argnums, parents)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">33</span> <span class="n">fun_name</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="s1">'__name__'</span><span class="p">,</span> <span class="n">fun</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">34</span> <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">"VJP of </span><span class="si">{}</span><span class="s2"> wrt argnums </span><span class="si">{}</span><span class="s2"> not defined"</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">35</span> <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun_name</span><span class="p">,</span> <span class="n">parent_argnums</span><span class="p">))</span>
|
||||
<span class="ne">---> </span><span class="mi">36</span> <span class="bp">self</span><span class="o">.</span><span class="n">vjp</span> <span class="o">=</span> <span class="n">vjpmaker</span><span class="p">(</span><span class="n">parent_argnums</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:66,</span> in <span class="ni">defvjp.<locals>.vjp_argnums</span><span class="nt">(argnums, ans, args, kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">63</span> <span class="k">except</span> <span class="ne">KeyError</span><span class="p">:</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">64</span> <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">65</span> <span class="s2">"VJP of </span><span class="si">{}</span><span class="s2"> wrt argnum 0 not defined"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun</span><span class="o">.</span><span class="vm">__name__</span><span class="p">))</span>
|
||||
<span class="ne">---> </span><span class="mi">66</span> <span class="n">vjp</span> <span class="o">=</span> <span class="n">vjpfun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">67</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="p">(</span><span class="n">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">),)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">68</span> <span class="k">elif</span> <span class="n">L</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:297,</span> in <span class="ni">grad_np_sum</span><span class="nt">(ans, x, axis, keepdims, dtype)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">294</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="n">broadcast_axes</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">295</span> <span class="n">defvjp</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">broadcast_to</span><span class="p">,</span> <span class="n">grad_broadcast_to</span><span class="p">)</span>
|
||||
<span class="ne">--> </span><span class="mi">297</span> <span class="k">def</span> <span class="nf">grad_np_sum</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">298</span> <span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">anp</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">299</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">repeat_to_match_shape</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="p">,</span> <span class="n">axis</span><span class="p">,</span> <span class="n">keepdims</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
|
||||
<span class="ne">KeyboardInterrupt</span>:
|
||||
</pre></div>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1235,12 +1245,12 @@ labels = (n_inputs) = (1797,)
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.layers</span> <span class="kn">import</span> <span class="n">Input</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">3</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.models</span> <span class="kn">import</span> <span class="n">Sequential</span> <span class="c1">#This allows appending layers to existing models</span>
|
||||
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">443</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">443</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">444</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">445</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">440</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">438</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">439</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">440</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/framework/load_library.py:151,</span> in <span class="ni">load_library</span><span class="nt">(library_location)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">148</span> <span class="n">kernel_libraries</span> <span class="o">=</span> <span class="p">[</span><span class="n">library_location</span><span class="p">]</span>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -647,12 +657,12 @@ systems such as automatic translation and speech-to-text.</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">tensorflow.keras</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">models</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.layers</span> <span class="kn">import</span> <span class="n">Input</span>
|
||||
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">443</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">443</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">444</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">445</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">440</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">438</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">439</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">440</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/framework/load_library.py:151,</span> in <span class="ni">load_library</span><span class="nt">(library_location)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">148</span> <span class="n">kernel_libraries</span> <span class="o">=</span> <span class="p">[</span><span class="n">library_location</span><span class="p">]</span>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1305,10 +1315,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.009134699065945493
|
||||
4.0244965108017645
|
||||
[[0.85613835 2.50655379]
|
||||
[2.50655379 8.3404509 ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.04718566894028431
|
||||
4.11080997912276
|
||||
[[ 1.10517643 3.48455788]
|
||||
[ 3.48455788 12.00216162]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1345,10 +1355,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07971187802560528
|
||||
1.800782161095708
|
||||
[[1. 0.59411814]
|
||||
[0.59411814 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07836997022107646
|
||||
1.1378267322316808
|
||||
[[1. 0.63980097]
|
||||
[0.63980097 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1378,30 +1388,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.81395716 1.89155934]
|
||||
[-1.34726166 -4.13453411]
|
||||
[-0.46229544 -2.34061974]
|
||||
[ 0.24429334 1.4051634 ]
|
||||
[ 0.41971814 1.6405671 ]
|
||||
[ 2.02456235 5.03973227]
|
||||
[-1.97311824 -4.72521196]
|
||||
[ 0.10738656 0.24578123]
|
||||
[-0.52702419 -2.34023682]
|
||||
[ 0.69978197 3.31779928]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.34931214 3.06139439]
|
||||
[-0.44476964 -2.60794187]
|
||||
[ 0.02225493 0.16388664]
|
||||
[-1.91193672 -3.82324216]
|
||||
[-0.2044881 -1.56027537]
|
||||
[-1.15572395 -3.25982474]
|
||||
[ 0.94217756 1.49888671]
|
||||
[ 0.28472162 2.92474572]
|
||||
[ 2.38943 7.14118216]
|
||||
[-1.27097785 -3.5388115 ]]
|
||||
0 1
|
||||
0 0.813957 1.891559
|
||||
1 -1.347262 -4.134534
|
||||
2 -0.462295 -2.340620
|
||||
3 0.244293 1.405163
|
||||
4 0.419718 1.640567
|
||||
5 2.024562 5.039732
|
||||
6 -1.973118 -4.725212
|
||||
7 0.107387 0.245781
|
||||
8 -0.527024 -2.340237
|
||||
9 0.699782 3.317799
|
||||
0 1.349312 3.061394
|
||||
1 -0.444770 -2.607942
|
||||
2 0.022255 0.163887
|
||||
3 -1.911937 -3.823242
|
||||
4 -0.204488 -1.560275
|
||||
5 -1.155724 -3.259825
|
||||
6 0.942178 1.498887
|
||||
7 0.284722 2.924746
|
||||
8 2.389430 7.141182
|
||||
9 -1.270978 -3.538811
|
||||
0 1
|
||||
0 1.000000 0.969413
|
||||
1 0.969413 1.000000
|
||||
0 1.000000 0.950873
|
||||
1 0.950873 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1458,37 +1468,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.092746 0.090302 0.090561 0.088058 0.085463 0.081530 0.078898
|
||||
2 0.0 0.090302 0.088694 0.089052 0.086797 0.084423 0.080286 0.077782
|
||||
3 0.0 0.090561 0.089052 0.095106 0.092533 0.089858 0.089404 0.086489
|
||||
4 0.0 0.088058 0.086797 0.092533 0.090114 0.087585 0.086913 0.084127
|
||||
5 0.0 0.085463 0.084423 0.089858 0.087585 0.085197 0.084340 0.081681
|
||||
6 0.0 0.081530 0.080286 0.089404 0.086913 0.084340 0.086471 0.083596
|
||||
7 0.0 0.078898 0.077782 0.086489 0.084127 0.081681 0.083596 0.080849
|
||||
8 0.0 0.076334 0.075334 0.083645 0.081405 0.079080 0.080793 0.078170
|
||||
9 0.0 0.073841 0.072946 0.080875 0.078753 0.076543 0.078067 0.075562
|
||||
10 0.0 0.072973 0.071789 0.082361 0.079982 0.077541 0.081296 0.078544
|
||||
11 0.0 0.070485 0.069391 0.079518 0.077254 0.074928 0.078454 0.075823
|
||||
12 0.0 0.068088 0.067077 0.076777 0.074622 0.072404 0.075712 0.073198
|
||||
13 0.0 0.065778 0.064845 0.074134 0.072083 0.069970 0.073071 0.070667
|
||||
14 0.0 0.063554 0.062693 0.071588 0.069637 0.067623 0.070527 0.068229
|
||||
1 0.0 0.074334 0.080585 0.077061 0.078751 0.080220 0.070657 0.071406
|
||||
2 0.0 0.080585 0.088425 0.082009 0.084289 0.086338 0.074009 0.075052
|
||||
3 0.0 0.077061 0.082009 0.085147 0.086339 0.087297 0.081324 0.081796
|
||||
4 0.0 0.078751 0.084289 0.086339 0.087789 0.089007 0.081926 0.082537
|
||||
5 0.0 0.080220 0.086338 0.087297 0.089007 0.090492 0.082307 0.083061
|
||||
6 0.0 0.070657 0.074009 0.081324 0.081926 0.082307 0.079874 0.080032
|
||||
7 0.0 0.071406 0.075052 0.081796 0.082537 0.083061 0.080032 0.080271
|
||||
8 0.0 0.072148 0.076101 0.082240 0.083128 0.083801 0.080150 0.080474
|
||||
9 0.0 0.072902 0.077180 0.082670 0.083714 0.084548 0.080237 0.080651
|
||||
10 0.0 0.063646 0.065859 0.075320 0.075498 0.075472 0.075478 0.075409
|
||||
11 0.0 0.064071 0.066452 0.075576 0.075838 0.075897 0.075542 0.075525
|
||||
12 0.0 0.064514 0.067074 0.075838 0.076189 0.076340 0.075602 0.075639
|
||||
13 0.0 0.064980 0.067731 0.076108 0.076555 0.076803 0.075658 0.075753
|
||||
14 0.0 0.065472 0.068429 0.076389 0.076938 0.077292 0.075711 0.075868
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.076334 0.073841 0.072973 0.070485 0.068088 0.065778 0.063554
|
||||
2 0.075334 0.072946 0.071789 0.069391 0.067077 0.064845 0.062693
|
||||
3 0.083645 0.080875 0.082361 0.079518 0.076777 0.074134 0.071588
|
||||
4 0.081405 0.078753 0.079982 0.077254 0.074622 0.072083 0.069637
|
||||
5 0.079080 0.076543 0.077541 0.074928 0.072404 0.069970 0.067623
|
||||
6 0.080793 0.078067 0.081296 0.078454 0.075712 0.073071 0.070527
|
||||
7 0.078170 0.075562 0.078544 0.075823 0.073198 0.070667 0.068229
|
||||
8 0.075609 0.073115 0.075864 0.073260 0.070747 0.068324 0.065989
|
||||
9 0.073115 0.070730 0.073260 0.070769 0.068364 0.066044 0.063809
|
||||
10 0.075864 0.073260 0.077608 0.074866 0.072223 0.069676 0.067224
|
||||
11 0.073260 0.070769 0.074866 0.072241 0.069711 0.067273 0.064924
|
||||
12 0.070747 0.068364 0.072223 0.069711 0.067288 0.064954 0.062705
|
||||
13 0.068324 0.066044 0.069676 0.067273 0.064954 0.062719 0.060565
|
||||
14 0.065989 0.063809 0.067224 0.064924 0.062705 0.060565 0.058503
|
||||
1 0.072148 0.072902 0.063646 0.064071 0.064514 0.064980 0.065472
|
||||
2 0.076101 0.077180 0.065859 0.066452 0.067074 0.067731 0.068429
|
||||
3 0.082240 0.082670 0.075320 0.075576 0.075838 0.076108 0.076389
|
||||
4 0.083128 0.083714 0.075498 0.075838 0.076189 0.076555 0.076938
|
||||
5 0.083801 0.084548 0.075472 0.075897 0.076340 0.076803 0.077292
|
||||
6 0.080150 0.080237 0.075478 0.075542 0.075602 0.075658 0.075711
|
||||
7 0.080474 0.080651 0.075409 0.075525 0.075639 0.075753 0.075868
|
||||
8 0.080766 0.081038 0.075293 0.075463 0.075634 0.075809 0.075988
|
||||
9 0.081038 0.081411 0.075136 0.075363 0.075595 0.075834 0.076082
|
||||
10 0.075293 0.075136 0.072406 0.072329 0.072240 0.072140 0.072028
|
||||
11 0.075463 0.075363 0.072329 0.072286 0.072234 0.072173 0.072101
|
||||
12 0.075634 0.075595 0.072240 0.072234 0.072220 0.072199 0.072171
|
||||
13 0.075809 0.075834 0.072140 0.072173 0.072199 0.072221 0.072238
|
||||
14 0.075988 0.076082 0.072028 0.072101 0.072171 0.072238 0.072303
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1969,11 +1979,13 @@ We select values of the hyperparameter <span class="math notranslate nohighlight
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[2. 2.]
|
||||
Training MSE for OLS
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Training MSE for OLS
|
||||
3.0
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter2_252_1.png" src="_images/chapter2_252_1.png" />
|
||||
<img alt="_images/chapter2_252_2.png" src="_images/chapter2_252_2.png" />
|
||||
</div>
|
||||
</div>
|
||||
<p>We see here that we reach a plateau for the Ridge results. Writing out the coefficients <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>, we observe that they are getting smaller and smaller and our error stabilizes since the predicted values of <span class="math notranslate nohighlight">\(\tilde{\boldsymbol{y}}\)</span> approach zero.</p>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -859,10 +869,10 @@ number <span class="math notranslate nohighlight">\(i\)</span> is left out. Usin
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.146141 sec
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.154751 sec
|
||||
Jackknife Statistics :
|
||||
original bias std. error
|
||||
100.139 100.129 0.148776
|
||||
99.9896 99.9796 0.149524
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1081,7 +1091,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
99.989 15.1792 99.9878 0.152149
|
||||
100.307 14.9693 100.309 0.149416
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1288,7 +1298,9 @@ Error: 0.08426840630693411
|
||||
Bias^2: 0.0796891867672603
|
||||
Var: 0.004579219539673834
|
||||
0.08426840630693411 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
|
||||
Polynomial degree: 2
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 2
|
||||
Error: 0.10398646080125035
|
||||
Bias^2: 0.1007711427354898
|
||||
Var: 0.0032153180657605116
|
||||
@@ -1315,7 +1327,9 @@ Error: 0.037813671417389005
|
||||
Bias^2: 0.033657685071527665
|
||||
Var: 0.00415598634586135
|
||||
0.037813671417389005 >= 0.033657685071527665 + 0.00415598634586135 = 0.03781367141738902
|
||||
Polynomial degree: 7
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 7
|
||||
Error: 0.02760977349102253
|
||||
Bias^2: 0.022999498260366312
|
||||
Var: 0.004610275230656212
|
||||
@@ -1342,21 +1356,21 @@ Error: 0.07160048164233104
|
||||
Bias^2: 0.014436800088904942
|
||||
Var: 0.05716368155342608
|
||||
0.07160048164233104 >= 0.014436800088904942 + 0.05716368155342608 = 0.07160048164233102
|
||||
Polynomial degree: 12
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 12
|
||||
Error: 0.11547777218872497
|
||||
Bias^2: 0.01628578269596628
|
||||
Var: 0.09919198949275869
|
||||
0.11547777218872497 >= 0.01628578269596628 + 0.09919198949275869 = 0.11547777218872497
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
|
||||
Polynomial degree: 13
|
||||
Error: 0.22842468702219465
|
||||
Bias^2: 0.01975416527185249
|
||||
Var: 0.20867052175034223
|
||||
0.22842468702219465 >= 0.01975416527185249 + 0.20867052175034223 = 0.2284246870221947
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter3_66_4.png" src="_images/chapter3_66_4.png" />
|
||||
<img alt="_images/chapter3_66_6.png" src="_images/chapter3_66_6.png" />
|
||||
</div>
|
||||
</div>
|
||||
<p>The bias-variance tradeoff summarizes the fundamental tension in
|
||||
@@ -1647,12 +1661,12 @@ Mean squared error on test data: 877.21517262
|
||||
Degree of polynomial: 23
|
||||
Mean squared error on training data: 0.00085892
|
||||
Mean squared error on test data: 5567.04664255
|
||||
Degree of polynomial: 24
|
||||
Mean squared error on training data: 0.00084707
|
||||
Mean squared error on test data: 1325.26124692
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 24
|
||||
Mean squared error on training data: 0.00084707
|
||||
Mean squared error on test data: 1325.26124692
|
||||
Degree of polynomial: 25
|
||||
Mean squared error on training data: 0.00079125
|
||||
Mean squared error on test data: 129012.83870189
|
||||
Degree of polynomial: 26
|
||||
@@ -1661,19 +1675,19 @@ Mean squared error on test data: 18388.59354079
|
||||
Degree of polynomial: 27
|
||||
Mean squared error on training data: 0.00069123
|
||||
Mean squared error on test data: 2351.97979891
|
||||
Degree of polynomial: 28
|
||||
Mean squared error on training data: 0.00062592
|
||||
Mean squared error on test data: 3983.63037846
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 28
|
||||
Mean squared error on training data: 0.00062592
|
||||
Mean squared error on test data: 3983.63037846
|
||||
Degree of polynomial: 29
|
||||
Mean squared error on training data: 0.00060704
|
||||
Mean squared error on test data: 3262.26814548
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -1907,7 +1921,7 @@ cross-validation (LOOCV).</p>
|
||||
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|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2796,7 +2810,7 @@ linear system as an equation would reduce this down to
|
||||
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|
||||
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||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/4162706317.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2940,7 +2954,7 @@ with the form utilized in linear regression, viz.</p>
|
||||
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|
||||
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||||
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/3777801602.py:7: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
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|
||||
</pre></div>
|
||||
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||||
@@ -2980,7 +2994,7 @@ cost function is given by</p>
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||||
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||||
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||||
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/438060758.py:10: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
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|
||||
@@ -3015,7 +3029,7 @@ cost function is given by</p>
|
||||
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|
||||
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||||
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|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22458/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
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||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57183/3544313922.py:9: UserWarning: set_ticklabels() should only be used with a fixed number of ticks, i.e. after set_ticks() or using a FixedLocator.
|
||||
cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
|
||||
</pre></div>
|
||||
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||||
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|
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Week 41 Neural networks and constructing a neural network code
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||||
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||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2nd degree coefficients:
|
||||
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|
||||
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|
||||
second power: -5.234332597247826e-05
|
||||
zero power: -0.22158725223474995
|
||||
first power: 0.24121476598003452
|
||||
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|
||||
</pre></div>
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||||
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@@ -741,10 +751,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
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||||
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||||
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||||
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|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.012423940191689783
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||||
4.101008878523571
|
||||
[[0.89527291 2.65532045]
|
||||
[2.65532045 8.81987609]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.1001408041761458
|
||||
4.2807716628772665
|
||||
[[ 1.15654145 3.54867722]
|
||||
[ 3.54867722 11.70485195]]
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||||
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|
||||
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||||
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||||
@@ -784,10 +794,10 @@ a more brute force way. Here we scale the mean values for each column of the des
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||||
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||||
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||||
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|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08705631913312815
|
||||
1.7026908764394864
|
||||
[[1. 0.65870313]
|
||||
[0.65870313 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.09543871010617433
|
||||
1.6888043337746685
|
||||
[[1. 0.7167077]
|
||||
[0.7167077 1. ]]
|
||||
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|
||||
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||||
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||||
@@ -816,30 +826,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
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|
||||
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|
||||
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|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-1.7755649 -4.56778296]
|
||||
[-0.81015037 -2.80072356]
|
||||
[ 0.73628249 1.95206335]
|
||||
[ 0.97366347 1.61130099]
|
||||
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|
||||
[ 0.36881837 0.56037913]
|
||||
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|
||||
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|
||||
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|
||||
[ 1.60116388 6.52211567]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.20575734 0.01384583]
|
||||
[-0.89876098 -3.04065686]
|
||||
[-0.76289128 -3.17080691]
|
||||
[-0.0334136 0.16124569]
|
||||
[ 2.73970542 9.28885103]
|
||||
[ 0.75413023 2.98474769]
|
||||
[-1.87894459 -5.48121459]
|
||||
[-1.26814205 -2.4848097 ]
|
||||
[ 0.18114057 -0.9889962 ]
|
||||
[ 1.37293361 2.71779401]]
|
||||
0 1
|
||||
0 -1.775565 -4.567783
|
||||
1 -0.810150 -2.800724
|
||||
2 0.736282 1.952063
|
||||
3 0.973663 1.611301
|
||||
4 0.727132 1.979656
|
||||
5 0.368818 0.560379
|
||||
6 -1.331631 -2.593912
|
||||
7 -0.689539 -1.582987
|
||||
8 0.199824 -1.080110
|
||||
9 1.601164 6.522116
|
||||
0 1
|
||||
0 1.00000 0.94335
|
||||
1 0.94335 1.00000
|
||||
0 -0.205757 0.013846
|
||||
1 -0.898761 -3.040657
|
||||
2 -0.762891 -3.170807
|
||||
3 -0.033414 0.161246
|
||||
4 2.739705 9.288851
|
||||
5 0.754130 2.984748
|
||||
6 -1.878945 -5.481215
|
||||
7 -1.268142 -2.484810
|
||||
8 0.181141 -0.988996
|
||||
9 1.372934 2.717794
|
||||
0 1
|
||||
0 1.000000 0.970965
|
||||
1 0.970965 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -896,37 +906,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.088650 0.084209 0.092689 0.091653 0.090476 0.085764 0.085378
|
||||
2 0.0 0.084209 0.080559 0.088599 0.087876 0.087020 0.082478 0.082249
|
||||
3 0.0 0.092689 0.088599 0.102209 0.101292 0.100209 0.097667 0.097380
|
||||
4 0.0 0.091653 0.087876 0.101292 0.100523 0.099588 0.097017 0.096811
|
||||
5 0.0 0.090476 0.087020 0.100209 0.099588 0.098803 0.096203 0.096078
|
||||
6 0.0 0.085764 0.082478 0.097667 0.097017 0.096203 0.095425 0.095278
|
||||
7 0.0 0.085378 0.082249 0.097380 0.096811 0.096078 0.095278 0.095178
|
||||
8 0.0 0.084976 0.082002 0.097060 0.096570 0.095915 0.095090 0.095037
|
||||
9 0.0 0.084550 0.081730 0.096700 0.096287 0.095710 0.094857 0.094849
|
||||
10 0.0 0.077672 0.075070 0.090429 0.090002 0.089421 0.089826 0.089786
|
||||
11 0.0 0.077490 0.074976 0.090319 0.089940 0.089408 0.089800 0.089790
|
||||
12 0.0 0.077310 0.074882 0.090204 0.089872 0.089386 0.089763 0.089783
|
||||
13 0.0 0.077131 0.074787 0.090081 0.089795 0.089354 0.089714 0.089763
|
||||
14 0.0 0.076951 0.074688 0.089949 0.089708 0.089311 0.089653 0.089730
|
||||
1 0.0 0.090565 0.089065 0.093226 0.091674 0.090154 0.086287 0.084847
|
||||
2 0.0 0.089065 0.087946 0.092421 0.091068 0.089735 0.085988 0.084674
|
||||
3 0.0 0.093226 0.092421 0.102147 0.100816 0.099494 0.098144 0.096731
|
||||
4 0.0 0.091674 0.091068 0.100816 0.099622 0.098431 0.097115 0.095803
|
||||
5 0.0 0.090154 0.089735 0.099494 0.098431 0.097365 0.096077 0.094862
|
||||
6 0.0 0.086287 0.085988 0.098144 0.097115 0.096077 0.096630 0.095395
|
||||
7 0.0 0.084847 0.084674 0.096731 0.095803 0.094862 0.095395 0.094243
|
||||
8 0.0 0.083459 0.083405 0.095358 0.094527 0.093680 0.094189 0.093115
|
||||
9 0.0 0.082121 0.082180 0.094027 0.093288 0.092530 0.093011 0.092013
|
||||
10 0.0 0.078708 0.078711 0.091732 0.090935 0.090118 0.091871 0.090804
|
||||
11 0.0 0.077431 0.077523 0.090387 0.089668 0.088926 0.090626 0.089626
|
||||
12 0.0 0.076203 0.076378 0.089086 0.088441 0.087772 0.089417 0.088481
|
||||
13 0.0 0.075021 0.075274 0.087828 0.087255 0.086655 0.088242 0.087369
|
||||
14 0.0 0.073883 0.074212 0.086611 0.086107 0.085573 0.087102 0.086289
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.084976 0.084550 0.077672 0.077490 0.077310 0.077131 0.076951
|
||||
2 0.082002 0.081730 0.075070 0.074976 0.074882 0.074787 0.074688
|
||||
3 0.097060 0.096700 0.090429 0.090319 0.090204 0.090081 0.089949
|
||||
4 0.096570 0.096287 0.090002 0.089940 0.089872 0.089795 0.089708
|
||||
5 0.095915 0.095710 0.089421 0.089408 0.089386 0.089354 0.089311
|
||||
6 0.095090 0.094857 0.089826 0.089800 0.089763 0.089714 0.089653
|
||||
7 0.095037 0.094849 0.089786 0.089790 0.089783 0.089763 0.089730
|
||||
8 0.094941 0.094797 0.089704 0.089738 0.089760 0.089769 0.089763
|
||||
9 0.094797 0.094697 0.089576 0.089639 0.089690 0.089726 0.089748
|
||||
10 0.089704 0.089576 0.085655 0.085690 0.085712 0.085722 0.085716
|
||||
11 0.089738 0.089639 0.085690 0.085747 0.085790 0.085819 0.085833
|
||||
12 0.089760 0.089690 0.085712 0.085790 0.085853 0.085902 0.085935
|
||||
13 0.089769 0.089726 0.085722 0.085819 0.085902 0.085970 0.086021
|
||||
14 0.089763 0.089748 0.085716 0.085833 0.085935 0.086021 0.086092
|
||||
1 0.083459 0.082121 0.078708 0.077431 0.076203 0.075021 0.073883
|
||||
2 0.083405 0.082180 0.078711 0.077523 0.076378 0.075274 0.074212
|
||||
3 0.095358 0.094027 0.091732 0.090387 0.089086 0.087828 0.086611
|
||||
4 0.094527 0.093288 0.090935 0.089668 0.088441 0.087255 0.086107
|
||||
5 0.093680 0.092530 0.090118 0.088926 0.087772 0.086655 0.085573
|
||||
6 0.094189 0.093011 0.091871 0.090626 0.089417 0.088242 0.087102
|
||||
7 0.093115 0.092013 0.090804 0.089626 0.088481 0.087369 0.086289
|
||||
8 0.092064 0.091034 0.089755 0.088642 0.087560 0.086508 0.085486
|
||||
9 0.091034 0.090075 0.088726 0.087675 0.086653 0.085659 0.084694
|
||||
10 0.089755 0.088726 0.088455 0.087327 0.086227 0.085155 0.084112
|
||||
11 0.088642 0.087675 0.087327 0.086256 0.085212 0.084195 0.083203
|
||||
12 0.087560 0.086653 0.086227 0.085212 0.084222 0.083257 0.082316
|
||||
13 0.086508 0.085659 0.085155 0.084195 0.083257 0.082342 0.081450
|
||||
14 0.085486 0.084694 0.084112 0.083203 0.082316 0.081450 0.080605
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1115,10 +1125,12 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
|
||||
0 3.914672 1.954823
|
||||
1 1.954823 1.963858
|
||||
[[3.91467223 1.95482298]
|
||||
[1.95482298 1.96385798]]
|
||||
0 4.114499 2.071143
|
||||
1 2.071143 2.061388
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.11449851 2.07114326]
|
||||
[2.07114326 2.0613875 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1145,8 +1157,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
|
||||
[[3.91467223 1.95482298]
|
||||
[1.95482298 1.96385798]]
|
||||
[[4.11449851 2.07114326]
|
||||
[2.07114326 2.0613875 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
|
||||
@@ -1206,16 +1218,16 @@ questions.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
|
||||
5.123928000581825
|
||||
0.7546022135629743
|
||||
5.399533503407795
|
||||
0.776352510835556
|
||||
First eigenvector
|
||||
[0.85043503 0.5260801 ]
|
||||
[0.84973247 0.52721412]
|
||||
Second eigenvector
|
||||
[-0.5260801 0.85043503]
|
||||
[-0.52721412 0.84973247]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
|
||||
[0.85043503 0.5260801 ]
|
||||
[-0.84973247 -0.52721412]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -600,12 +610,12 @@ Gaussian distribution.</p>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">6</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">image</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">7</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">443</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">443</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">444</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">445</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">440</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">438</span> <span class="n">_plugin_dir</span> <span class="o">=</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">_s</span><span class="p">,</span> <span class="s1">'tensorflow-plugins'</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">439</span> <span class="k">if</span> <span class="n">_os</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">exists</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">):</span>
|
||||
<span class="ne">--> </span><span class="mi">440</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">441</span> <span class="c1"># Load Pluggable Device Library</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">442</span> <span class="n">_ll</span><span class="o">.</span><span class="n">load_pluggable_device_library</span><span class="p">(</span><span class="n">_plugin_dir</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/framework/load_library.py:151,</span> in <span class="ni">load_library</span><span class="nt">(library_location)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">148</span> <span class="n">kernel_libraries</span> <span class="o">=</span> <span class="p">[</span><span class="n">library_location</span><span class="p">]</span>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -321,6 +321,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -804,15 +804,15 @@ regression.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.04881585]
|
||||
[2.96745096]]
|
||||
Eigenvalues of Hessian Matrix:[0.37175588 4.15690073]
|
||||
[[4.1729993]
|
||||
[3.0170097]]
|
||||
Eigenvalues of Hessian Matrix:[0.28192769 4.68753434]
|
||||
theta from own gd
|
||||
[[4.04881585]
|
||||
[2.96745096]]
|
||||
[[4.1729993]
|
||||
[3.0170097]]
|
||||
theta from own sdg
|
||||
[[4.04015455]
|
||||
[2.95745651]]
|
||||
[[4.14043884]
|
||||
[2.99071523]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_5_1.png" src="_images/exercisesweek41_5_1.png" />
|
||||
@@ -934,14 +934,14 @@ first example shows results with ordinary leats squares.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.37007195]
|
||||
[3.48441798]]
|
||||
Eigenvalues of Hessian Matrix:[0.32411274 4.30450049]
|
||||
[[4.03696458]
|
||||
[3.0324793 ]]
|
||||
Eigenvalues of Hessian Matrix:[0.30959659 4.4150026 ]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[3.37007195]
|
||||
[3.48441798]]
|
||||
[[4.03696458]
|
||||
[3.0324793 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_16_2.png" src="_images/exercisesweek41_16_2.png" />
|
||||
@@ -1012,73 +1012,73 @@ Eigenvalues of Hessian Matrix:[0.32411274 4.30450049]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.]
|
||||
[3.]]
|
||||
Eigenvalues of Hessian Matrix:[0.27227895 4.125757 ]
|
||||
0 [-11.75978215] [-12.89770892]
|
||||
1 [-0.06807123] [0.06136823]
|
||||
2 [-0.06357887] [0.05731824]
|
||||
3 [-0.05938299] [0.05353553]
|
||||
4 [-0.05546402] [0.05000245]
|
||||
5 [-0.05180367] [0.04670255]
|
||||
6 [-0.04838489] [0.04362042]
|
||||
7 [-0.04519174] [0.04074169]
|
||||
8 [-0.04220931] [0.03805295]
|
||||
9 [-0.03942371] [0.03554165]
|
||||
10 [-0.03682195] [0.03319608]
|
||||
11 [-0.03439189] [0.03100531]
|
||||
12 [-0.0321222] [0.02895911]
|
||||
13 [-0.0300023] [0.02704796]
|
||||
14 [-0.0280223] [0.02526293]
|
||||
15 [-0.02617297] [0.02359571]
|
||||
16 [-0.02444569] [0.02203851]
|
||||
17 [-0.0228324] [0.02058408]
|
||||
18 [-0.02132557] [0.01922564]
|
||||
19 [-0.01991819] [0.01795684]
|
||||
20 [-0.0186037] [0.01677178]
|
||||
21 [-0.01737595] [0.01566493]
|
||||
22 [-0.01622922] [0.01463112]
|
||||
23 [-0.01515818] [0.01366555]
|
||||
24 [-0.01415781] [0.01276369]
|
||||
25 [-0.01322347] [0.01192135]
|
||||
26 [-0.01235079] [0.0111346]
|
||||
27 [-0.0115357] [0.01039977]
|
||||
28 [-0.0107744] [0.00971344]
|
||||
29 [-0.01006335] [0.0090724]
|
||||
Eigenvalues of Hessian Matrix:[0.23469347 4.90407685]
|
||||
0 [-18.02987043] [-22.42501752]
|
||||
1 [-0.32329897] [0.25206371]
|
||||
2 [-0.30782691] [0.24000075]
|
||||
3 [-0.2930953] [0.22851508]
|
||||
4 [-0.27906869] [0.21757908]
|
||||
5 [-0.26571335] [0.20716644]
|
||||
6 [-0.25299716] [0.19725211]
|
||||
7 [-0.24088952] [0.18781225]
|
||||
8 [-0.22936132] [0.17882416]
|
||||
9 [-0.21838482] [0.17026621]
|
||||
10 [-0.20793362] [0.16211781]
|
||||
11 [-0.19798258] [0.15435937]
|
||||
12 [-0.18850776] [0.14697222]
|
||||
13 [-0.17948638] [0.1399386]
|
||||
14 [-0.17089674] [0.13324158]
|
||||
15 [-0.16271817] [0.12686507]
|
||||
16 [-0.15493099] [0.12079371]
|
||||
17 [-0.14751649] [0.11501291]
|
||||
18 [-0.14045682] [0.10950876]
|
||||
19 [-0.13373501] [0.10426802]
|
||||
20 [-0.12733488] [0.09927808]
|
||||
21 [-0.12124104] [0.09452695]
|
||||
22 [-0.11543883] [0.09000319]
|
||||
23 [-0.10991429] [0.08569593]
|
||||
24 [-0.10465415] [0.08159479]
|
||||
25 [-0.09964573] [0.07768993]
|
||||
26 [-0.094877] [0.07397193]
|
||||
27 [-0.09033649] [0.07043187]
|
||||
28 [-0.08601328] [0.06706123]
|
||||
29 [-0.08189696] [0.06385189]
|
||||
theta from own gd
|
||||
[[3.96547946]
|
||||
[3.03112129]]
|
||||
0 [-0.00939922] [0.00847367]
|
||||
1 [-0.00877892] [0.00791445]
|
||||
2 [-0.00801346] [0.00722437]
|
||||
3 [-0.00725498] [0.00654058]
|
||||
4 [-0.00654864] [0.00590379]
|
||||
5 [-0.00590456] [0.00532314]
|
||||
6 [-0.00532167] [0.00479764]
|
||||
7 [-0.0047956] [0.00432337]
|
||||
8 [-0.00432129] [0.00389577]
|
||||
9 [-0.00389382] [0.00351039]
|
||||
10 [-0.0035086] [0.00316311]
|
||||
11 [-0.00316149] [0.00285017]
|
||||
12 [-0.00284871] [0.0025682]
|
||||
13 [-0.00256688] [0.00231412]
|
||||
14 [-0.00231293] [0.00208517]
|
||||
15 [-0.0020841] [0.00187888]
|
||||
16 [-0.00187791] [0.00169299]
|
||||
17 [-0.00169212] [0.0015255]
|
||||
18 [-0.00152471] [0.00137458]
|
||||
19 [-0.00137387] [0.00123858]
|
||||
20 [-0.00123795] [0.00111605]
|
||||
21 [-0.00111547] [0.00100563]
|
||||
22 [-0.00100511] [0.00090614]
|
||||
23 [-0.00090567] [0.00081649]
|
||||
24 [-0.00081607] [0.00073571]
|
||||
25 [-0.00073534] [0.00066293]
|
||||
26 [-0.00066259] [0.00059734]
|
||||
27 [-0.00059703] [0.00053824]
|
||||
28 [-0.00053797] [0.00048499]
|
||||
29 [-0.00048474] [0.00043701]
|
||||
[[3.66774691]
|
||||
[3.25904489]]
|
||||
0 [-0.07797763] [0.06079614]
|
||||
1 [-0.07424587] [0.05788664]
|
||||
2 [-0.06957317] [0.05424351]
|
||||
3 [-0.06484181] [0.05055465]
|
||||
4 [-0.06031928] [0.04702861]
|
||||
5 [-0.05607583] [0.04372016]
|
||||
6 [-0.05211919] [0.04063532]
|
||||
7 [-0.04843794] [0.03776519]
|
||||
8 [-0.04501548] [0.03509683]
|
||||
9 [-0.04183444] [0.0326167]
|
||||
10 [-0.03887807] [0.03031173]
|
||||
11 [-0.03613058] [0.02816961]
|
||||
12 [-0.03357723] [0.02617887]
|
||||
13 [-0.03120433] [0.02432881]
|
||||
14 [-0.02899912] [0.02260949]
|
||||
15 [-0.02694975] [0.02101168]
|
||||
16 [-0.02504521] [0.01952679]
|
||||
17 [-0.02327527] [0.01814683]
|
||||
18 [-0.0216304] [0.01686439]
|
||||
19 [-0.02010178] [0.01567258]
|
||||
20 [-0.01868119] [0.014565]
|
||||
21 [-0.01736099] [0.01353569]
|
||||
22 [-0.01613409] [0.01257912]
|
||||
23 [-0.01499389] [0.01169016]
|
||||
24 [-0.01393427] [0.01086401]
|
||||
25 [-0.01294954] [0.01009625]
|
||||
26 [-0.01203439] [0.00938275]
|
||||
27 [-0.01118392] [0.00871967]
|
||||
28 [-0.01039355] [0.00810345]
|
||||
29 [-0.00965904] [0.00753078]
|
||||
theta from own gd wth momentum
|
||||
[[3.99839581]
|
||||
[3.00144622]]
|
||||
[[3.96175251]
|
||||
[3.02982009]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1131,17 +1131,17 @@ theta from own gd wth momentum
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.81818338]
|
||||
[3.12840176]]
|
||||
Eigenvalues of Hessian Matrix:[0.26024513 4.64291046]
|
||||
0 [-16.3824865] [-20.20867716]
|
||||
1 [9.71640303e-15] [1.05750493e-14]
|
||||
2 [-2.05998413e-17] [-2.11570114e-16]
|
||||
3 [6.96057795e-17] [1.90885733e-16]
|
||||
4 [6.96057795e-17] [1.90885733e-16]
|
||||
[[4.15451852]
|
||||
[2.83230774]]
|
||||
Eigenvalues of Hessian Matrix:[0.30616802 4.24299211]
|
||||
0 [-10.57502449] [-11.57610367]
|
||||
1 [-4.47905601e-15] [-4.07372439e-16]
|
||||
2 [-6.9388939e-16] [-7.21432413e-16]
|
||||
3 [-6.9388939e-16] [-7.21432413e-16]
|
||||
4 [-6.9388939e-16] [-7.21432413e-16]
|
||||
beta from own Newton code
|
||||
[[3.81818338]
|
||||
[3.12840176]]
|
||||
[[4.15451852]
|
||||
[2.83230774]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1230,18 +1230,20 @@ beta from own Newton code
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.6955259]
|
||||
[3.2809076]]
|
||||
Eigenvalues of Hessian Matrix:[0.31381731 4.50516278]
|
||||
theta from own gd
|
||||
[[3.6955259]
|
||||
[3.2809076]]
|
||||
[[4.04601419]
|
||||
[3.12204312]]
|
||||
Eigenvalues of Hessian Matrix:[0.33604208 4.45709724]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_22_1.png" src="_images/exercisesweek41_22_1.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.04601419]
|
||||
[3.12204312]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_22_2.png" src="_images/exercisesweek41_22_2.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[3.6805151 ]
|
||||
[3.33045013]]
|
||||
[[4.02781444]
|
||||
[3.13976073]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1323,15 +1325,15 @@ theta from own gd
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.98751068]
|
||||
[2.92901115]]
|
||||
Eigenvalues of Hessian Matrix:[0.28244905 4.61501312]
|
||||
[[3.96417888]
|
||||
[3.06634473]]
|
||||
Eigenvalues of Hessian Matrix:[0.32962444 4.18715465]
|
||||
theta from own gd
|
||||
[[3.98556236]
|
||||
[2.93059014]]
|
||||
[[3.9639885]
|
||||
[3.0665111]]
|
||||
theta from own sdg with momentum
|
||||
[[4.01133846]
|
||||
[2.92452609]]
|
||||
[[4.00842216]
|
||||
[3.14285244]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1406,9 +1408,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
|
||||
[[1.99974365]
|
||||
[3.0013839 ]
|
||||
[3.99861193]]
|
||||
[[1.99969895]
|
||||
[3.00167058]
|
||||
[3.99835872]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1490,9 +1492,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
|
||||
[[1.99757634]
|
||||
[2.9983289 ]
|
||||
[3.99759503]]
|
||||
[[1.99852187]
|
||||
[3.03868311]
|
||||
[3.95744254]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1578,9 +1580,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
|
||||
[[1.99993596]
|
||||
[3.00035483]
|
||||
[3.99963172]]
|
||||
[[1.99996471]
|
||||
[3.00026784]
|
||||
[3.99973141]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1653,7 +1655,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
return asarray(x, dtype=self.dtype)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x1360ef5e0>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x11892e7f0>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_39_2.png" src="_images/exercisesweek41_39_2.png" />
|
||||
@@ -1688,7 +1690,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x135f8b1f0>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x118995f70>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/exercisesweek41_41_1.png" src="_images/exercisesweek41_41_1.png" />
|
||||
|
||||
@@ -445,13 +445,23 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-4">
|
||||
Exercise 4
|
||||
<a class="reference internal nav-link" href="#exercise-4-custom-activation-for-each-layer">
|
||||
Exercise 4 - Custom activation for each layer
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-5-very-optional-and-very-hard">
|
||||
Exercise 5 (Very optional and very hard :)
|
||||
<a class="reference internal nav-link" href="#exercise-5-processing-multiple-inputs-at-once">
|
||||
Exercise 5 - Processing multiple inputs at once
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-6-predicting-on-real-data">
|
||||
Exercise 6 - Predicting on real data
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-6-training-on-real-data">
|
||||
Exercise 6 - Training on real data
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
@@ -500,13 +510,23 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-4">
|
||||
Exercise 4
|
||||
<a class="reference internal nav-link" href="#exercise-4-custom-activation-for-each-layer">
|
||||
Exercise 4 - Custom activation for each layer
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-5-very-optional-and-very-hard">
|
||||
Exercise 5 (Very optional and very hard :)
|
||||
<a class="reference internal nav-link" href="#exercise-5-processing-multiple-inputs-at-once">
|
||||
Exercise 5 - Processing multiple inputs at once
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-6-predicting-on-real-data">
|
||||
Exercise 6 - Predicting on real data
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h1 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#exercise-6-training-on-real-data">
|
||||
Exercise 6 - Training on real data
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
@@ -523,17 +543,43 @@ doconce format html exercisesweek41.do.txt -->
|
||||
<!-- dom:TITLE: Exercises week 41 -->
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-42">
|
||||
<h1>Exercises week 42<a class="headerlink" href="#exercises-week-42" title="Permalink to this headline">¶</a></h1>
|
||||
<p><strong>October 14-18, 2024</strong></p>
|
||||
<p><strong>October 11-18, 2024</strong></p>
|
||||
<p>Date: <strong>Deadline is Friday October 18 at midnight</strong></p>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="overarching-aims-of-the-exercises-this-week">
|
||||
<h1>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this headline">¶</a></h1>
|
||||
<p>The aim of the exercises this week is to get started with implementing a neural network. There are a lot of technical and finicky parts of implementing a neutal network, so take your time.</p>
|
||||
<p>This week, you will implement only the feed-forward pass. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes several checks along the way that you have implemented the pieces of the feed-forward pass correctly. If you have trouble running a notebook, or importing pytorch, you can run this notebook in google colab instead: (LINK TO COLAB), though we recommend that you set up VSCode and your python environment to run code like this locally.</p>
|
||||
<p>This week, you will implement only the feed-forward pass and updating the network parameters with simple gradient descent, the gradient will be computed using autograd using code we provide. Next week, you will implement backpropagation. We recommend that you do the exercises this week by editing and running this notebook file, as it includes some checks along the way that you have implemented the pieces of the feed-forward pass correctly, and running small parts of the code at a time will be important for understanding the methods.</p>
|
||||
<p>If you have trouble running a notebook, you can run this notebook in google colab instead (<a class="reference external" href="https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true">https://colab.research.google.com/drive/1OCQm1tlTWB6hZSf9I7gGUgW9M8SbVeQu#offline=true&sandboxMode=true</a>), an updated link will be provided on the course discord (you can also send an email to <a class="reference external" href="mailto:k.h.fredly%40fys.uio.no">k<span>.</span>h<span>.</span>fredly<span>@</span>fys<span>.</span>uio<span>.</span>no</a> if you encounter any trouble), though we recommend that you set up VSCode and your python environment to run code like this locally.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span> <span class="c1"># We need to use this numpy wrapper to make automatic differentiation work later</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
|
||||
|
||||
|
||||
<span class="c1"># Defining some activation functions</span>
|
||||
<span class="k">def</span> <span class="nf">ReLU</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">z</span> <span class="o">></span> <span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">sigmoid</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">z</span><span class="p">))</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">softmax</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
|
||||
<span class="w"> </span><span class="sd">"""Compute softmax values for each set of scores in the rows of the matrix z.</span>
|
||||
<span class="sd"> Used with batched input data."""</span>
|
||||
<span class="n">e_z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span>
|
||||
<span class="k">return</span> <span class="n">e_z</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">e_z</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">softmax_vec</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
|
||||
<span class="w"> </span><span class="sd">"""Compute softmax values for each set of scores in the vector z.</span>
|
||||
<span class="sd"> Use this function when you use the activation function on one vector at a time"""</span>
|
||||
<span class="n">e_z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">z</span><span class="p">))</span>
|
||||
<span class="k">return</span> <span class="n">e_z</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">e_z</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -541,47 +587,43 @@ doconce format html exercisesweek41.do.txt -->
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-1">
|
||||
<h1>Exercise 1<a class="headerlink" href="#exercise-1" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Complete the following parts to compute the activation of the first layer.</p>
|
||||
<p>In this exercise you will compute the activation of the first layer. You only need to change the code in the cells right below an exercise, the rest works out of the box. Feel free to make changes and see how stuff works though!</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">2024</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">ReLU</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">z</span> <span class="o">></span> <span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># network input</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># network input. This is a single input with two features</span>
|
||||
<span class="n">W1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="c1"># first layer weights</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>a)</strong> Define the bias of the first layer, <code class="docutils literal notranslate"><span class="pre">b1</span></code>with the correct shape</p>
|
||||
<p><strong>a)</strong> Given the shape of the first layer weight matrix, what is the input shape of the neural network? What is the output shape of the first layer?</p>
|
||||
<p><strong>b)</strong> Define the bias of the first layer, <code class="docutils literal notranslate"><span class="pre">b1</span></code>with the correct shape. (Run the next cell right after the previous to get the random generated values to line up with the test solution below)</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">b1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">b1</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>b)</strong> Compute the intermediary <code class="docutils literal notranslate"><span class="pre">z1</span></code> for the first layer</p>
|
||||
<p><strong>c)</strong> Compute the intermediary <code class="docutils literal notranslate"><span class="pre">z1</span></code> for the first layer</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">z1</span> <span class="o">=</span> <span class="n">W1</span> <span class="o">@</span> <span class="n">x</span> <span class="o">+</span> <span class="n">b1</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">z1</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>c)</strong> Compute the activation <code class="docutils literal notranslate"><span class="pre">a1</span></code> for the first layer using the ReLU activation function defined earlier.</p>
|
||||
<p><strong>d)</strong> Compute the activation <code class="docutils literal notranslate"><span class="pre">a1</span></code> for the first layer using the ReLU activation function defined earlier.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a1</span> <span class="o">=</span> <span class="n">ReLU</span><span class="p">(</span><span class="n">z1</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a1</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>Confirm that you got the correct activation with the test below.</p>
|
||||
<p>Confirm that you got the correct activation with the test below. Make sure that you define <code class="docutils literal notranslate"><span class="pre">b1</span></code> with the randn function right after you define <code class="docutils literal notranslate"><span class="pre">W1</span></code>.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">sol1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.60610368</span><span class="p">,</span> <span class="mf">4.0076268</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.56469864</span><span class="p">])</span>
|
||||
@@ -591,7 +633,41 @@ doconce format html exercisesweek41.do.txt -->
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">TypeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">6</span><span class="p">],</span> <span class="n">line</span> <span class="mi">3</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">1</span> <span class="n">sol1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.60610368</span><span class="p">,</span> <span class="mf">4.0076268</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.56469864</span><span class="p">])</span>
|
||||
<span class="ne">----> </span><span class="mi">3</span> <span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">a1</span><span class="p">,</span> <span class="n">sol1</span><span class="p">))</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48,</span> in <span class="ni">primitive.<locals>.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">46</span> <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">47</span> <span class="k">else</span><span class="p">:</span>
|
||||
<span class="ne">---> </span><span class="mi">48</span> <span class="k">return</span> <span class="n">f_raw</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File <__array_function__ internals>:180,</span> in <span class="ni">allclose</span><span class="nt">(*args, **kwargs)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/numeric.py:2251,</span> in <span class="ni">allclose</span><span class="nt">(a, b, rtol, atol, equal_nan)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2180</span> <span class="nd">@array_function_dispatch</span><span class="p">(</span><span class="n">_allclose_dispatcher</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2181</span> <span class="k">def</span> <span class="nf">allclose</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="mf">1.e-5</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1.e-8</span><span class="p">,</span> <span class="n">equal_nan</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2182</span><span class="w"> </span><span class="sd">"""</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2183</span><span class="sd"> Returns True if two arrays are element-wise equal within a tolerance.</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2184</span><span class="sd"> </span>
|
||||
<span class="sd"> (...)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2249</span><span class="sd"> </span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2250</span><span class="sd"> """</span>
|
||||
<span class="ne">-> </span><span class="mi">2251</span> <span class="n">res</span> <span class="o">=</span> <span class="nb">all</span><span class="p">(</span><span class="n">isclose</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">rtol</span><span class="o">=</span><span class="n">rtol</span><span class="p">,</span> <span class="n">atol</span><span class="o">=</span><span class="n">atol</span><span class="p">,</span> <span class="n">equal_nan</span><span class="o">=</span><span class="n">equal_nan</span><span class="p">))</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2252</span> <span class="k">return</span> <span class="nb">bool</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
|
||||
|
||||
<span class="nn">File <__array_function__ internals>:180,</span> in <span class="ni">isclose</span><span class="nt">(*args, **kwargs)</span>
|
||||
|
||||
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/numeric.py:2358,</span> in <span class="ni">isclose</span><span class="nt">(a, b, rtol, atol, equal_nan)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2355</span> <span class="n">dt</span> <span class="o">=</span> <span class="n">multiarray</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="mf">1.</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2356</span> <span class="n">y</span> <span class="o">=</span> <span class="n">asanyarray</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">dt</span><span class="p">)</span>
|
||||
<span class="ne">-> </span><span class="mi">2358</span> <span class="n">xfin</span> <span class="o">=</span> <span class="n">isfinite</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2359</span> <span class="n">yfin</span> <span class="o">=</span> <span class="n">isfinite</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">2360</span> <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="n">xfin</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">(</span><span class="n">yfin</span><span class="p">):</span>
|
||||
|
||||
<span class="ne">TypeError</span>: ufunc 'isfinite' not supported for the input types, and the inputs could not be safely coerced to any supported types according to the casting rule ''safe''
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -599,21 +675,22 @@ doconce format html exercisesweek41.do.txt -->
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-2">
|
||||
<h1>Exercise 2<a class="headerlink" href="#exercise-2" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Compute the activation of the second layer with an output of length 8 and ReLU activation.</p>
|
||||
<p><strong>a)</strong> Define the weight and bias of the second layer with the right shapes.</p>
|
||||
<p>Now we will add a layer to the network with an output of length 8 and ReLU activation.</p>
|
||||
<p><strong>a)</strong> What is the input of the second layer? What is its shape?</p>
|
||||
<p><strong>b)</strong> Define the weight and bias of the second layer with the right shapes.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">W2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||
<span class="n">b2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">8</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">W2</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">b2</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>b)</strong> Compute intermediary <code class="docutils literal notranslate"><span class="pre">z2</span></code> and activation <code class="docutils literal notranslate"><span class="pre">a2</span></code> for the second layer.</p>
|
||||
<p><strong>c)</strong> Compute the intermediary <code class="docutils literal notranslate"><span class="pre">z2</span></code> and activation <code class="docutils literal notranslate"><span class="pre">a2</span></code> for the second layer.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">z2</span> <span class="o">=</span> <span class="n">W2</span> <span class="o">@</span> <span class="n">a1</span>
|
||||
<span class="n">a2</span> <span class="o">=</span> <span class="n">ReLU</span><span class="p">(</span><span class="n">z2</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">z2</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">a2</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -621,12 +698,9 @@ doconce format html exercisesweek41.do.txt -->
|
||||
<p>Confirm that you got the correct activation shape with the test below.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">a2</span><span class="o">.</span><span class="n">shape</span> <span class="o">==</span> <span class="p">(</span><span class="mi">8</span><span class="p">,))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span>
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">allclose</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">a2</span><span class="p">)),</span> <span class="mf">2980.9579870417283</span><span class="p">)</span>
|
||||
<span class="p">)</span> <span class="c1"># This should evaluate to True if a2 has the correct shape :)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -638,65 +712,115 @@ doconce format html exercisesweek41.do.txt -->
|
||||
<p><strong>a)</strong> Complete the function below so that it returns a list <code class="docutils literal notranslate"><span class="pre">layers</span></code> of weight and bias tuples <code class="docutils literal notranslate"><span class="pre">(W,</span> <span class="pre">b)</span></code> for each layer, in order, with the correct shapes that we can use later as our network parameters.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">output_sizes</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">network_input_size</span>
|
||||
<span class="k">for</span> <span class="n">output_size</span> <span class="ow">in</span> <span class="n">output_sizes</span><span class="p">:</span>
|
||||
<span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">output_size</span><span class="p">,</span> <span class="n">i_size</span><span class="p">)</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">output_size</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">layer_output_size</span> <span class="ow">in</span> <span class="n">layer_output_sizes</span><span class="p">:</span>
|
||||
<span class="n">W</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">layers</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span>
|
||||
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">output_size</span>
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">layer_output_size</span>
|
||||
<span class="k">return</span> <span class="n">layers</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>b)</strong> Comple the function below so that it evaluates the intermediate <code class="docutils literal notranslate"><span class="pre">z</span></code> and activation <code class="docutils literal notranslate"><span class="pre">a</span></code> for each layer, and returns the final activation <code class="docutils literal notranslate"><span class="pre">a</span></code>. This is the complete feed-forward pass, a full neural network!</p>
|
||||
<p><strong>b)</strong> Comple the function below so that it evaluates the intermediary <code class="docutils literal notranslate"><span class="pre">z</span></code> and activation <code class="docutils literal notranslate"><span class="pre">a</span></code> for each layer, with ReLU actication, and returns the final activation <code class="docutils literal notranslate"><span class="pre">a</span></code>. This is the complete feed-forward pass, a full neural network!</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward_all_relu</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="nb">input</span>
|
||||
<span class="k">for</span> <span class="n">W</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">layers</span><span class="p">:</span>
|
||||
<span class="n">z</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="n">ReLU</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
|
||||
<span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="k">return</span> <span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>c)</strong> Create a network with input size 8 and layers with output sizes 10, 16, 6, 2. Evaluate it and make sure that you get the correct size vectors along the way.</p>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-4">
|
||||
<h1>Exercise 4<a class="headerlink" href="#exercise-4" title="Permalink to this headline">¶</a></h1>
|
||||
<p>So far, every layer has used the same activation, ReLU. We often want to use other types of activation however, so we need to update our code to support multiple types of activation. Make sure that you have completed every previous exercise before trying this one.</p>
|
||||
<p><strong>a)</strong> Make the <code class="docutils literal notranslate"><span class="pre">create_layers</span></code> function also accept a list of activation functions, which is used to add activation functions to each of the tuples in <code class="docutils literal notranslate"><span class="pre">layers</span></code>. Make new functions to not mess with the old ones.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers_4</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">output_sizes</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">input_size</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">layer_output_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">input_size</span><span class="p">)</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">predict</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">predict</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>d)</strong> Why is a neural network with no activation functions always mathematically equivelent to a neural network with only one layer?</p>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-4-custom-activation-for-each-layer">
|
||||
<h1>Exercise 4 - Custom activation for each layer<a class="headerlink" href="#exercise-4-custom-activation-for-each-layer" title="Permalink to this headline">¶</a></h1>
|
||||
<p>So far, every layer has used the same activation, ReLU. We often want to use other types of activation however, so we need to update our code to support multiple types of activation functions. Make sure that you have completed every previous exercise before trying this one.</p>
|
||||
<p><strong>a)</strong> Complete the <code class="docutils literal notranslate"><span class="pre">feed_forward</span></code> function which accepts a list of activation functions as an argument, and which evaluates these activation functions at each layer.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">):</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="nb">input</span>
|
||||
<span class="k">for</span> <span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="n">activation</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">):</span>
|
||||
<span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="k">return</span> <span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>b)</strong> Make a list with three activation functions(don’t call them yet! you can make a list with function names as elements, and then call these elements of the list later), two ReLU and one sigmoid. (If you add other functions than the ones defined at the start of the notebook, make sure everything is defined using autograd’s numpy wrapper, like above, since we want to use automatic differentiation on all of these functions later.)</p>
|
||||
<p>Then evaluate a network with three layers and these activation functions.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">network_input_size</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">layer_output_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||
<span class="n">activations</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="o">...</span>
|
||||
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">)</span>
|
||||
<span class="n">feed_forward</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-5-processing-multiple-inputs-at-once">
|
||||
<h1>Exercise 5 - Processing multiple inputs at once<a class="headerlink" href="#exercise-5-processing-multiple-inputs-at-once" title="Permalink to this headline">¶</a></h1>
|
||||
<p>So far, the feed forward function has taken one input vector as an input. This vector then undergoes a linear transformation and then an element-wise non-linear operation for each layer. This approach of sending one vector in at a time is great for interpreting how the network transforms data with its linear and non-linear operations, but not the best for numerical efficiency. Now, we want to be able to send many inputs through the network at once. This will make the code a bit harder to understand, but it will make it faster, and more compact. It will be worth the trouble.</p>
|
||||
<p>To process multiple inputs at once, while still performing the same operations, you will only need to flip a couple things around.</p>
|
||||
<p><strong>a)</strong> Complete the function <code class="docutils literal notranslate"><span class="pre">create_layers_batch</span></code> so that the weight matrix is the transpose of what it was when you only sent in one input at a time.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers_batch</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">network_input_size</span>
|
||||
<span class="k">for</span> <span class="n">output_size</span><span class="p">,</span> <span class="n">activation</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">output_sizes</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
|
||||
<span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">output_size</span><span class="p">,</span> <span class="n">i_size</span><span class="p">)</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">output_size</span><span class="p">)</span>
|
||||
<span class="n">layers</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">activation</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">layer_output_size</span> <span class="ow">in</span> <span class="n">layer_output_sizes</span><span class="p">:</span>
|
||||
<span class="n">W</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">b</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">layers</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span>
|
||||
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">output_size</span>
|
||||
<span class="n">i_size</span> <span class="o">=</span> <span class="n">layer_output_size</span>
|
||||
<span class="k">return</span> <span class="n">layers</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>b)</strong> Update the <code class="docutils literal notranslate"><span class="pre">feed_forward</span></code> function to support this change.</p>
|
||||
<p><strong>b)</strong> Make a matrix of inputs with the shape (number of features, number of inputs), you choose the number of inputs and features per input. Then complete the function <code class="docutils literal notranslate"><span class="pre">feed_forward_batch</span></code> so that you can process this matrix of inputs with only one matrix multiplication and one broadcasted vector addition per layer. (Hint: You will only need to swap two variable around from your previous implementation, but remember to test that you get the same results for equivelent inputs!)</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward_4</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="nb">input</span>
|
||||
<span class="k">for</span> <span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">activation</span> <span class="ow">in</span> <span class="n">layers</span><span class="p">:</span>
|
||||
<span class="n">z</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="n">activation</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">inputs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">feed_forward_batch</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">):</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="n">inputs</span>
|
||||
<span class="k">for</span> <span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="n">activation</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">):</span>
|
||||
<span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">a</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="k">return</span> <span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -705,28 +829,26 @@ doconce format html exercisesweek41.do.txt -->
|
||||
<p><strong>c)</strong> Create and evaluate a neural network with 4 inputs and layers with output sizes 12, 10, 3 and activations ReLU, ReLU, softmax.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.special</span> <span class="kn">import</span> <span class="n">softmax</span>
|
||||
|
||||
<span class="n">network_input_size</span> <span class="o">=</span> <span class="mi">4</span>
|
||||
<span class="n">output_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="mi">12</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
|
||||
<span class="n">activation_funcs</span> <span class="o">=</span> <span class="p">[</span><span class="n">ReLU</span><span class="p">,</span> <span class="n">ReLU</span><span class="p">,</span> <span class="n">softmax</span><span class="p">]</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="n">create_layers_4</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">output_sizes</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">network_input_size</span> <span class="o">=</span> <span class="o">...</span>
|
||||
<span class="n">layer_output_sizes</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||
<span class="n">activations</span> <span class="o">=</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="n">create_layers_batch</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">)</span>
|
||||
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">)</span>
|
||||
<span class="n">predict</span> <span class="o">=</span> <span class="n">feed_forward_4</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="n">feed_forward_batch</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p>The final exercise will hopefully be very simple if everything has worked so far. You will evaluate your neural network on the iris data set (<a class="reference external" href="https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html">https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html</a>).</p>
|
||||
<p>This dataset contains data on 150 flowers of 3 different types which can be separated pretty well using the four features given for each flower, which includes the width and length of their leaves. You are not expected to do any training of the network or actual classification, unless you feel like it, in that case you can do exercise 5.</p>
|
||||
<p>You should use this batched approach moving forward, as it will lead to much more compact code. However, remember that each input is still treated separately, and that you will need to keep in mind the transposed weight matrix and other details when implementing backpropagation.</p>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-6-predicting-on-real-data">
|
||||
<h1>Exercise 6 - Predicting on real data<a class="headerlink" href="#exercise-6-predicting-on-real-data" title="Permalink to this headline">¶</a></h1>
|
||||
<p>You will now evaluate your neural network on the iris data set (<a class="reference external" href="https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html">https://scikit-learn.org/1.5/auto_examples/datasets/plot_iris_dataset.html</a>).</p>
|
||||
<p>This dataset contains data on 150 flowers of 3 different types which can be separated pretty well using the four features given for each flower, which includes the width and length of their leaves. You are will later train your network to actually make good predictions.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Loading and plotting iris dataset</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
|
||||
<span class="n">iris</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span><span class="p">()</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">iris</span> <span class="o">=</span> <span class="n">datasets</span><span class="o">.</span><span class="n">load_iris</span><span class="p">()</span>
|
||||
|
||||
<span class="n">_</span><span class="p">,</span> <span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
|
||||
<span class="n">scatter</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">)</span>
|
||||
@@ -737,29 +859,114 @@ doconce format html exercisesweek41.do.txt -->
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<img alt="_images/exercisesweek42_34_0.png" src="_images/exercisesweek42_34_0.png" />
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>c)</strong> Loop over the iris dataset(<code class="docutils literal notranslate"><span class="pre">iris.data</span></code>) and evaluate the network for each data point.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># No need to change this cell! Just make sure it works!</span>
|
||||
<span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">:</span>
|
||||
<span class="n">prediction</span> <span class="o">=</span> <span class="n">feed_forward_4</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">inputs</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>
|
||||
|
||||
<span class="c1"># Since each prediction is a vector with a score for each of the three types of flowers,</span>
|
||||
<span class="c1"># we need to make each target a vector with a 1 for the correct flower and a 0 for the others.</span>
|
||||
<span class="n">targets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">data</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">iris</span><span class="o">.</span><span class="n">target</span><span class="p">):</span>
|
||||
<span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">targets</span><span class="p">):</span>
|
||||
<span class="n">one_hot_predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">predictions</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">prediction</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">predictions</span><span class="p">):</span>
|
||||
<span class="n">one_hot_predictions</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">prediction</span><span class="p">)]</span> <span class="o">=</span> <span class="mi">1</span>
|
||||
<span class="k">return</span> <span class="n">accuracy_score</span><span class="p">(</span><span class="n">one_hot_predictions</span><span class="p">,</span> <span class="n">targets</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>a)</strong> What should the input size for the network be with this dataset? What should the output shape of the last layer be?</p>
|
||||
<p><strong>b)</strong> Create a network with two hidden layers, the first with sigmoid activation and the last with softmax, the first layer should have 8 “nodes”, the second has the number of nodes you found in exercise a). Softmax returns a “probability distribution”, in the sense that the numbers in the output are positive and add up to 1 and, their magnitude are in some sense relative to their magnitude before going through the softmax function. Remember to use the batched version of the create_layers and feed forward functions.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">...</span>
|
||||
<span class="n">layers</span> <span class="o">=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>c)</strong> Evaluate your model on the entire iris dataset! For later purposes, we will split the data into train and test sets, and compute gradients on smaller batches of the training data. But for now, evaluate the network on the whole thing at once.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">predictions</span> <span class="o">=</span> <span class="n">feed_forward_batch</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>d)</strong> Compute the accuracy of your model using the accuracy function defined above. Recreate your model a couple times and see how the accuracy changes.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">targets</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-5-very-optional-and-very-hard">
|
||||
<h1>Exercise 5 (Very optional and very hard :)<a class="headerlink" href="#exercise-5-very-optional-and-very-hard" title="Permalink to this headline">¶</a></h1>
|
||||
<p><strong>a)</strong> Make the iris target values into one-hot vectors.</p>
|
||||
<p><strong>b)</strong> Define the cross-entropy loss function to evaluate the performance of your network on the data set.</p>
|
||||
<p><strong>c)</strong> Use the autograd package to take the gradient of the cross entropy wrt. the weights and biases of the network.</p>
|
||||
<p><strong>d)</strong> Use gradient descent of some sort to optimize the parameters.</p>
|
||||
<p><strong>e)</strong> Evaluate the accuracy of the network.</p>
|
||||
<p><strong>e)</strong> Show off how you did in a group session!</p>
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="exercise-6-training-on-real-data">
|
||||
<h1>Exercise 6 - Training on real data<a class="headerlink" href="#exercise-6-training-on-real-data" title="Permalink to this headline">¶</a></h1>
|
||||
<p>To be able to actually do anything useful with your neural network, you need to train it. For this, we need a cost function and a way to take the gradient of the cost function wrt. the network parameters. The following exercises guide you through taking the gradient using autograd, and updating the network parameters using the gradient. Feel free to implement gradient methods like ADAM if you finish everything.</p>
|
||||
<p>The cross-entropy loss function can evaluate performance on classification tasks. It sees if your prediction is “most certain” on the correct target.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">cost</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
|
||||
<span class="n">predict</span> <span class="o">=</span> <span class="n">feed_forward_batch</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">cross_entropy</span><span class="p">(</span><span class="n">predict</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">cross_entropy</span><span class="p">(</span><span class="n">predict</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="n">target</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">predict</span><span class="p">))</span>
|
||||
|
||||
|
||||
<span class="n">gradient_func</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span>
|
||||
<span class="n">cross_entropy</span><span class="p">,</span> <span class="mi">1</span>
|
||||
<span class="p">)</span> <span class="c1"># Taking the gradient wrt. the second input to the cost function</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>a)</strong> What shape should the gradient of the cost function wrt. weights and biases be?</p>
|
||||
<p><strong>b)</strong> Use the <code class="docutils literal notranslate"><span class="pre">gradient_func</span></code> function to take the gradient of the cross entropy wrt. the weights and biases of the network. Check the shapes of what’s inside. What does the <code class="docutils literal notranslate"><span class="pre">grad</span></code> func from autograd actually do?</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">layers_grad</span> <span class="o">=</span> <span class="n">gradient_func</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">,</span> <span class="n">targets</span><span class="p">)</span> <span class="c1"># Don't change this</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>c)</strong> Finish the <code class="docutils literal notranslate"><span class="pre">train_network</span></code> function.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">train_network</span><span class="p">(</span>
|
||||
<span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">,</span> <span class="n">targets</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">100</span>
|
||||
<span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">epochs</span><span class="p">):</span>
|
||||
<span class="n">layers_grad</span> <span class="o">=</span> <span class="n">gradient_func</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activations</span><span class="p">,</span> <span class="n">targets</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="p">(</span><span class="n">W_g</span><span class="p">,</span> <span class="n">b_g</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">layers_grad</span><span class="p">):</span>
|
||||
<span class="n">W</span> <span class="o">-=</span> <span class="o">...</span>
|
||||
<span class="n">b</span> <span class="o">-=</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>e)</strong> What do we call the gradient method used above?</p>
|
||||
<p><strong>d)</strong> Train your network and see how the accuracy changes! Make a plot if you want.</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<p><strong>e)</strong> How high of an accuracy is it possible to acheive with a neural network on this dataset, if we use the whole thing as training data?</p>
|
||||
</div>
|
||||
|
||||
<script type="text/x-thebe-config">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -643,8 +653,8 @@ matrices and vectors.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 0.03563709 0.57852915 0.83220985 1.27108866 -0.3587467 -0.38713573
|
||||
-0.09584387 0.5223261 1.7663967 0.94027059]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.34851141 0.11232457 -0.59560497 0.79558423 -0.74632311 0.97068015
|
||||
1.45921927 0.39225935 -0.87171492 0.44129766]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -865,26 +875,36 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.79010601 0.87637891 0.68824222 0.4636751 0.50100007 0.22715479
|
||||
0.17865868 0.90903158 0.5736973 0.96961052]
|
||||
[0.57293306 0.96660465 0.65525178 0.52480767 0.70159137 0.30894285
|
||||
0.11675128 0.60321647 0.68281739 0.64952115]
|
||||
[0.21833102 0.74761815 0.52789388 0.27530242 0.69463406 0.89961861
|
||||
0.91864509 0.41794469 0.27403356 0.11416086]
|
||||
[0.77596142 0.20224027 0.68830164 0.50895251 0.83741078 0.71957514
|
||||
0.78945959 0.94466211 0.06443054 0.29474356]
|
||||
[0.39914635 0.22706777 0.23499891 0.9794096 0.33435637 0.28614301
|
||||
0.21641173 0.16925937 0.79086674 0.41259788]
|
||||
[0.70408202 0.57833531 0.01817739 0.64689773 0.71380438 0.69311221
|
||||
0.09930135 0.90168941 0.47308061 0.445128 ]
|
||||
[0.10100211 0.60575887 0.69824402 0.06423317 0.24582593 0.97235642
|
||||
0.21181534 0.72033728 0.77014839 0.13298019]
|
||||
[0.25816519 0.81826799 0.19336703 0.34098895 0.10688434 0.34134773
|
||||
0.21635399 0.57016227 0.69925648 0.01418766]
|
||||
[0.80374623 0.58202531 0.71460518 0.66363129 0.02553865 0.7204561
|
||||
0.34704885 0.52927353 0.02631244 0.02944974]
|
||||
[0.57080764 0.04516434 0.15388662 0.99458998 0.2765068 0.05148401
|
||||
0.82259916 0.05648118 0.14249052 0.96164155]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[6.95039348e-01 4.77602426e-01 4.58218587e-02 7.93416236e-01
|
||||
9.55643340e-01 7.98621772e-01 4.69806017e-01 1.11371176e-01
|
||||
6.52359414e-01 4.86833907e-01]
|
||||
[6.34549184e-01 4.06225028e-01 6.55208611e-01 1.10909182e-02
|
||||
6.45609936e-01 2.42839645e-01 2.14335140e-01 4.88477745e-01
|
||||
7.33046180e-01 3.04253288e-01]
|
||||
[9.24911588e-01 6.09812323e-01 3.17886464e-01 8.85018556e-01
|
||||
9.82435177e-01 9.43167881e-01 7.43951798e-01 7.31787864e-01
|
||||
4.80369722e-01 8.57475388e-01]
|
||||
[1.16436977e-01 8.00829346e-01 3.64493447e-01 4.94082113e-02
|
||||
5.68163369e-01 4.84993546e-03 2.34121963e-01 2.49849206e-01
|
||||
3.86274590e-01 8.78949699e-01]
|
||||
[4.91568958e-01 9.21047414e-02 7.84745063e-01 6.96054705e-01
|
||||
6.19052323e-02 8.28645331e-01 8.30191327e-01 2.48853875e-01
|
||||
7.24382159e-01 3.97218946e-01]
|
||||
[3.79942527e-01 1.36403018e-02 7.08949703e-02 5.98556486e-01
|
||||
5.10274274e-01 5.86030593e-01 8.96762953e-02 9.27993904e-01
|
||||
5.79873884e-01 4.12085937e-01]
|
||||
[4.75733813e-01 3.83164611e-01 9.64968814e-01 2.10369090e-01
|
||||
6.15338896e-04 5.29509520e-01 4.33492417e-01 9.06496916e-01
|
||||
1.39646454e-01 4.21846767e-01]
|
||||
[1.24848631e-01 9.48875568e-01 8.00598510e-01 4.10923006e-01
|
||||
9.72407267e-01 9.52121734e-01 1.56665044e-01 5.06276815e-01
|
||||
5.30196557e-01 8.40012736e-01]
|
||||
[3.25145374e-01 1.83317854e-01 7.66763324e-02 9.66707072e-01
|
||||
8.23006632e-01 4.30655251e-01 4.69811070e-02 8.72758060e-01
|
||||
6.59088350e-01 7.28365323e-01]
|
||||
[5.96282505e-01 9.69432059e-01 1.10687432e-01 9.36439409e-01
|
||||
1.82212861e-01 9.15905706e-01 4.35826030e-01 3.89219980e-01
|
||||
4.21786054e-01 4.13799037e-02]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -944,15 +964,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.22370461988004753
|
||||
4.592766658048914
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.7163835161938888
|
||||
[[ 1.11935351 3.19945294 3.19001247]
|
||||
[ 3.19945294 10.52074297 8.75737136]
|
||||
[ 3.19001247 8.75737136 16.29078236]]
|
||||
[23.51532469 0.10801706 4.3075371 ]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.11406297261341168
|
||||
4.669908227073521
|
||||
0.2806901924685401
|
||||
[[ 0.98292239 2.97664837 2.73565966]
|
||||
[ 2.97664837 10.21905519 8.21690241]
|
||||
[ 2.73565966 8.21690241 13.03354844]]
|
||||
[20.77597019 0.09165112 3.36790471]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -56,7 +56,7 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 2 on Machine Learning, deadline November 4 (Midnight)" href="project2.html" />
|
||||
<link rel="prev" title="Week 41 Neural networks and constructing a neural network code" href="week41.html" />
|
||||
<link rel="prev" title="Week 42 Constructing a Neural Network code with examples" href="week42.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1069,11 +1079,11 @@ of code developers and contributors keeps increasing.</p>
|
||||
|
||||
<!-- Previous / next buttons -->
|
||||
<div class='prev-next-area'>
|
||||
<a class='left-prev' id="prev-link" href="week41.html" title="previous page">
|
||||
<a class='left-prev' id="prev-link" href="week42.html" title="previous page">
|
||||
<i class="fas fa-angle-left"></i>
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">previous</p>
|
||||
<p class="prev-next-title">Week 41 Neural networks and constructing a neural network code</p>
|
||||
<p class="prev-next-title">Week 42 Constructing a Neural Network code with examples</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="project2.html" title="next page">
|
||||
|
||||
@@ -322,6 +322,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -321,6 +321,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
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|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
File diff suppressed because one or more lines are too long
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
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|
||||
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|
||||
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|
||||
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||||
Exercises week 42
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
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|
||||
</li>
|
||||
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|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1015,27 +1025,27 @@ uncorrelated.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>4.177786562639708
|
||||
[[ 8.02409835 11.56990537 11.96799937 6.11006373 8.01793972 4.09014451
|
||||
12.65476419 -4.31938579 13.04431557 14.12208052]
|
||||
[11.56990537 16.68258595 17.25659561 8.81006889 11.56102529 5.89755794
|
||||
18.2468382 -6.22809974 18.80853029 20.36255393]
|
||||
[11.96799937 17.25659561 17.85035562 9.11320323 11.95881375 6.10047943
|
||||
18.8746702 -6.44239442 19.45568883 21.06318287]
|
||||
[ 6.11006373 8.81006889 9.11320323 4.65259487 6.10537416 3.11449867
|
||||
9.63615006 -3.2890577 9.93277949 10.75345893]
|
||||
[ 8.01793972 11.56102529 11.95881375 6.10537416 8.01178583 4.08700526
|
||||
12.64505146 -4.31607059 13.03430385 14.1112416 ]
|
||||
[ 4.09014451 5.89755794 6.10047943 3.11449867 4.08700526 2.08487999
|
||||
6.45054585 -2.20173175 6.64911288 7.19848482]
|
||||
[12.65476419 18.2468382 18.8746702 9.63615006 12.64505146 6.45054585
|
||||
19.95776346 -6.81208109 20.57212292 22.27186049]
|
||||
[-4.31938579 -6.22809974 -6.44239442 -3.2890577 -4.31607059 -2.20173175
|
||||
-6.81208109 2.32513272 -7.02177725 -7.60193996]
|
||||
[13.04431557 18.80853029 19.45568883 9.93277949 13.03430385 6.64911288
|
||||
20.57212292 -7.02177725 21.20539421 22.95745476]
|
||||
[14.12208052 20.36255393 21.06318287 10.75345893 14.1112416 7.19848482
|
||||
22.27186049 -7.60193996 22.95745476 24.85427641]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>1.5715150087179857
|
||||
[[ 9.98938878 7.54804438 5.31210861 4.15563816 11.04286013 12.33871003
|
||||
5.34554342 14.48549903 6.87661362 7.26028795]
|
||||
[ 7.54804438 5.70334935 4.01386236 3.14002608 8.3440539 9.32320616
|
||||
4.0391259 10.94533329 5.19601208 5.4859188 ]
|
||||
[ 5.31210861 4.01386236 2.8248473 2.20986506 5.87231849 6.56141925
|
||||
2.8426271 7.70302827 3.65681217 3.86084064]
|
||||
[ 4.15563816 3.14002608 2.20986506 1.72876728 4.59388777 5.13296813
|
||||
2.22377412 6.02604362 2.86070736 3.02031789]
|
||||
[11.04286013 8.3440539 5.87231849 4.59388777 12.20742956 13.63993855
|
||||
5.9092793 16.01312585 7.60181469 8.02595095]
|
||||
[12.33871003 9.32320616 6.56141925 5.13296813 13.63993855 15.24054861
|
||||
6.60271731 17.89222305 8.49386718 8.96777468]
|
||||
[ 5.34554342 4.0391259 2.8426271 2.22377412 5.9092793 6.60271731
|
||||
2.8605188 7.7515117 3.67982841 3.88514106]
|
||||
[14.48549903 10.94533329 7.70302827 6.02604362 16.01312585 17.89222305
|
||||
7.7515117 21.00525734 9.97169918 10.52806096]
|
||||
[ 6.87661362 5.19601208 3.65681217 2.86070736 7.60181469 8.49386718
|
||||
3.67982841 9.97169918 4.73380463 4.99792291]
|
||||
[ 7.26028795 5.4859188 3.86084064 3.02031789 8.02595095 8.96777468
|
||||
3.88514106 10.52806096 4.99792291 5.27677742]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1303,15 +1313,15 @@ more practically oriented methods like the blocking technique.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.061772005077293704
|
||||
4.355734685106391
|
||||
-0.03692132794542241
|
||||
1.0765856870687196 10.882972378790114 11.598549916355722
|
||||
3.274394546800107 2.662153330760193 7.985725003240627
|
||||
[[ 1.07658569 3.27439455 2.66215333]
|
||||
[ 3.27439455 10.88297238 7.985725 ]
|
||||
[ 2.66215333 7.985725 11.59854992]]
|
||||
[20.15422927 0.07415258 3.32972613]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.05818561278267464
|
||||
3.8056560957923695
|
||||
0.06926151969326948
|
||||
1.1885906477601598 12.229598952352728 16.227738984674172
|
||||
3.6795562921258607 3.451702023099923 10.293665700387852
|
||||
[[ 1.18859065 3.67955629 3.45170202]
|
||||
[ 3.67955629 12.22959895 10.2936657 ]
|
||||
[ 3.45170202 10.2936657 16.22773898]]
|
||||
[25.73550536 0.06057711 3.84984612]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1641,7 +1651,7 @@ assumption for approximating <span class="math notranslate nohighlight">\(\sigma
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.0370757046153366 1.001106660107757
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.03974553487733608 1.0433282860079154
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/statistics_188_1.png" src="_images/statistics_188_1.png" />
|
||||
|
||||
@@ -321,6 +321,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -321,6 +321,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1703,8 +1713,8 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.51262599 0.63980912 -1.25680702 0.97680846 -1.33095972 -0.41396339
|
||||
-0.81478187 -0.6087346 2.11164003 -1.21061589]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.81737781 0.45847011 0.53332849 1.04937026 0.53235952 2.24033384
|
||||
-0.05605892 -0.02193078 -0.37343957 0.17849836]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1929,26 +1939,26 @@ lowercase letters for vectors and uppercase letters for matrices)</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.1169204 0.51615779 0.40961688 0.169299 0.08009874 0.67925887
|
||||
0.8475889 0.92080432 0.07712724 0.2863391 ]
|
||||
[0.36161658 0.84155431 0.70135856 0.1576057 0.04686491 0.67511113
|
||||
0.29593305 0.22946401 0.78385675 0.20527785]
|
||||
[0.66575697 0.37717637 0.52407775 0.55094784 0.68989446 0.30013135
|
||||
0.39991048 0.20300793 0.25294371 0.91433102]
|
||||
[0.05080769 0.92665802 0.77039278 0.13455019 0.89692576 0.09621323
|
||||
0.48511333 0.8529175 0.32738537 0.12206812]
|
||||
[0.98108401 0.73397147 0.62288579 0.66003032 0.18712313 0.63307537
|
||||
0.2032806 0.17418673 0.06061276 0.92991181]
|
||||
[0.53480404 0.69484973 0.09821823 0.93019783 0.34478594 0.18646225
|
||||
0.11861803 0.25646067 0.55225408 0.84907109]
|
||||
[0.50352245 0.92678221 0.27037635 0.9833205 0.84985833 0.82844656
|
||||
0.34112554 0.9306628 0.89155606 0.24149532]
|
||||
[0.37137157 0.65751456 0.63693246 0.25068519 0.75674251 0.43724406
|
||||
0.34131583 0.74180248 0.63801791 0.76426396]
|
||||
[0.2311959 0.77594586 0.52606333 0.54222783 0.86434639 0.72364915
|
||||
0.4008393 0.68827947 0.56408898 0.68640031]
|
||||
[0.90137794 0.02599188 0.40848657 0.94114646 0.67199457 0.02124568
|
||||
0.32717946 0.59030403 0.59188296 0.81707832]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.15586219 0.68891428 0.38675231 0.63546905 0.97286326 0.423102
|
||||
0.42841423 0.3478095 0.66130478 0.63443371]
|
||||
[0.88685415 0.82561703 0.56766321 0.43258818 0.99057275 0.40058341
|
||||
0.84581375 0.64630711 0.03266152 0.57599494]
|
||||
[0.10145028 0.9074157 0.39386718 0.12831838 0.46242424 0.09280524
|
||||
0.88415819 0.26443391 0.55095316 0.85897711]
|
||||
[0.69243548 0.33745439 0.14452065 0.29030256 0.8063779 0.60720029
|
||||
0.42914251 0.44895662 0.09310479 0.48442601]
|
||||
[0.95152814 0.83294718 0.11005335 0.8758851 0.19375828 0.73888203
|
||||
0.83203197 0.69203997 0.65147818 0.35195241]
|
||||
[0.21506004 0.24874378 0.31370028 0.9525328 0.71672791 0.05879106
|
||||
0.45007578 0.36388542 0.50937003 0.57854115]
|
||||
[0.80033616 0.45273617 0.18038547 0.49557088 0.36209091 0.44512218
|
||||
0.84078641 0.28924386 0.99166852 0.22896144]
|
||||
[0.77579275 0.83519517 0.40640797 0.66272614 0.18234499 0.97628064
|
||||
0.19808709 0.1280526 0.33700495 0.32114535]
|
||||
[0.95462534 0.72047148 0.24512233 0.18474924 0.69169665 0.68763036
|
||||
0.8861811 0.54193001 0.87830277 0.79251831]
|
||||
[0.13092444 0.41452482 0.40447213 0.89714357 0.25360039 0.80373997
|
||||
0.51279028 0.58161787 0.08742496 0.45104086]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2003,13 +2013,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.04372067685794603
|
||||
3.777112373675558
|
||||
-0.028188673105960467
|
||||
[[ 1.0680225 3.36841864 2.42592679]
|
||||
[ 3.36841864 11.49312535 7.50233673]
|
||||
[ 2.42592679 7.50233673 7.94272259]]
|
||||
[18.418656 0.05992237 2.02529207]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.0458524213754298
|
||||
3.614161296466206
|
||||
-0.22985907723809532
|
||||
[[0.72589774 2.09219464 1.64672839]
|
||||
[2.09219464 6.9187554 4.62198131]
|
||||
[1.64672839 4.62198131 6.70530438]]
|
||||
[12.05431945 0.07101262 2.22462544]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2234,7 +2244,7 @@ Name: Aragorn, dtype: object
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
|
||||
<span class="ne">AttributeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22556/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="nn">/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57294/1326197715.py</span> in <span class="ni">?</span><span class="nt">()</span>
|
||||
<span class="ne">----> </span><span class="mi">6</span> <span class="n">new_hobbit</span> <span class="o">=</span> <span class="p">{</span><span class="s1">'First Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Peregrin"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">7</span> <span class="s1">'Last Name'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Took"</span><span class="p">],</span>
|
||||
<span class="g g-Whitespace"> </span><span class="mi">8</span> <span class="s1">'Place of birth'</span><span class="p">:</span> <span class="p">[</span><span class="s2">"Shire"</span><span class="p">],</span>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1671,7 +1681,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9960887274532307
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9953466931203151
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1688,7 +1698,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.010148621093080332
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.010175219431920396
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1703,23 +1713,23 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.01006224 0.02667406 0.0272743 0.00100202 0.01480927 0.00410183
|
||||
0.02088307 0.02506901 0.00463124 0.00672505 0.0304378 0.00076521
|
||||
0.05364579 0.01232366 0.00969623 0.00677215 0.02239876 0.03858916
|
||||
0.00923474 0.00848739 0.01701429 0.07172932 0.08858739 0.04575775
|
||||
0.02988432 0.00988356 0.01546126 0.00033415 0.03201922 0.01425384
|
||||
0.00575681 0.01882218 0.05853984 0.00528252 0.03254614 0.03092729
|
||||
0.01094916 0.05696574 0.03412067 0.02444266 0.05749111 0.0689303
|
||||
0.00736737 0.02104639 0.00274212 0.00588836 0.05043958 0.01456865
|
||||
0.01813363 0.06019833 0.01078008 0.01059242 0.02369044 0.02692965
|
||||
0.00657601 0.01218403 0.03745816 0.05363722 0.00561212 0.03820746
|
||||
0.00988992 0.00774376 0.03426412 0.01323341 0.02387182 0.01151556
|
||||
0.01097287 0.07292363 0.02846506 0.04186033 0.00836649 0.00340452
|
||||
0.06200455 0.03246707 0.02987496 0.00355323 0.01740381 0.01196506
|
||||
0.02635861 0.07487128 0.08472879 0.0073544 0.01150437 0.00571884
|
||||
0.02025574 0.0014028 0.01512884 0.02146636 0.05097344 0.0284405
|
||||
0.06151386 0.00737863 0.04452918 0.03906948 0.01163942 0.07468007
|
||||
0.01647074 0.0096667 0.00369201 0.0168171 ]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.03699304 0.0218856 0.02021288 0.0334505 0.02960445 0.01369614
|
||||
0.00606112 0.01429853 0.01174937 0.02585059 0.02044223 0.00174884
|
||||
0.06133572 0.03159246 0.04435458 0.00125802 0.00100423 0.00230308
|
||||
0.01055384 0.02352843 0.06971862 0.01300036 0.00547332 0.05554795
|
||||
0.01142354 0.01181458 0.00148216 0.01419341 0.0305221 0.01272102
|
||||
0.01700746 0.01552039 0.01616657 0.10695771 0.00405576 0.02979087
|
||||
0.0529838 0.01420773 0.06220192 0.04104182 0.00653725 0.07170448
|
||||
0.00997215 0.02490769 0.02580654 0.01682317 0.03221473 0.01838531
|
||||
0.02028936 0.0064349 0.04323964 0.02705202 0.03692828 0.01975755
|
||||
0.05636265 0.02880987 0.05692207 0.04085864 0.01085261 0.01457889
|
||||
0.03418643 0.01919791 0.00101555 0.00636951 0.04217103 0.0476266
|
||||
0.01169528 0.04544327 0.00978267 0.04046984 0.0032882 0.02072876
|
||||
0.05526935 0.05461692 0.00877816 0.00724303 0.00045923 0.00059105
|
||||
0.00917881 0.04254787 0.08728977 0.04513394 0.01606644 0.08956994
|
||||
0.02687671 0.07449122 0.04497158 0.01713187 0.02553907 0.0397137
|
||||
0.03313193 0.00738299 0.01743124 0.02953975 0.01131825 0.0864086
|
||||
0.01925934 0.02439287 0.09331672 0.01721277]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1788,15 +1798,15 @@ but now splitting the data into a training set and a test set.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.97802245 0.57331229 2.49761526 3.47609206 -1.5187643 ]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.94735263 0.70175778 2.99348646 1.86611894 -0.45576546]
|
||||
Training R2
|
||||
0.995702810640425
|
||||
0.9959836634296064
|
||||
Training MSE
|
||||
0.007370297974992432
|
||||
0.0085274606925055
|
||||
Test R2
|
||||
0.9950019477819025
|
||||
0.992232777849821
|
||||
Test MSE
|
||||
0.009880124918446542
|
||||
0.010638334964957053
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1659,7 +1669,7 @@ theorem.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
|
||||
original bias std. error
|
||||
100.257 14.853 100.257 0.149111
|
||||
100.091 15.1529 100.089 0.15052
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1889,14 +1899,14 @@ Error: 0.06547790180152355
|
||||
Bias^2: 0.06208238634231949
|
||||
Var: 0.0033955154592040936
|
||||
0.06547790180152355 >= 0.06208238634231949 + 0.0033955154592040936 = 0.06547790180152359
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 4
|
||||
Polynomial degree: 4
|
||||
Error: 0.06844519414009445
|
||||
Bias^2: 0.06453579006728324
|
||||
Var: 0.003909404072811226
|
||||
0.06844519414009445 >= 0.06453579006728324 + 0.003909404072811226 = 0.06844519414009446
|
||||
Polynomial degree: 5
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
|
||||
Error: 0.05227921801205686
|
||||
Bias^2: 0.0481872773043029
|
||||
Var: 0.004091940707753939
|
||||
@@ -1916,9 +1926,7 @@ Error: 0.017355848195593347
|
||||
Bias^2: 0.010331721306655127
|
||||
Var: 0.007024126888938232
|
||||
0.017355848195593347 >= 0.010331721306655127 + 0.007024126888938232 = 0.01735584819559336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 9
|
||||
Polynomial degree: 9
|
||||
Error: 0.02660572763718093
|
||||
Bias^2: 0.010018312644137363
|
||||
Var: 0.016587414993043573
|
||||
@@ -1930,7 +1938,9 @@ Error: 0.021592704588025025
|
||||
Bias^2: 0.010516485576645508
|
||||
Var: 0.011076219011379514
|
||||
0.021592704588025025 >= 0.010516485576645508 + 0.011076219011379514 = 0.021592704588025022
|
||||
Polynomial degree: 11
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 11
|
||||
Error: 0.07160048164233104
|
||||
Bias^2: 0.014436800088904942
|
||||
Var: 0.05716368155342608
|
||||
@@ -2354,33 +2364,33 @@ Mean squared error on test data: 1184.60929685
|
||||
Degree of polynomial: 23
|
||||
Mean squared error on training data: 0.00089193
|
||||
Mean squared error on test data: 3892.17483760
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 24
|
||||
Degree of polynomial: 24
|
||||
Mean squared error on training data: 0.00083355
|
||||
Mean squared error on test data: 1332.46736215
|
||||
Degree of polynomial: 25
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 25
|
||||
Mean squared error on training data: 0.00079904
|
||||
Mean squared error on test data: 7577.76690383
|
||||
Degree of polynomial: 26
|
||||
Mean squared error on training data: 0.00075590
|
||||
Mean squared error on test data: 1079.36895644
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 27
|
||||
Degree of polynomial: 27
|
||||
Mean squared error on training data: 0.00068091
|
||||
Mean squared error on test data: 3207.25343155
|
||||
Degree of polynomial: 28
|
||||
Mean squared error on training data: 0.00063362
|
||||
Mean squared error on test data: 674.79633065
|
||||
Degree of polynomial: 29
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial: 29
|
||||
Mean squared error on training data: 0.00063866
|
||||
Mean squared error on test data: 3099.60342978
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22575/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57311/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(trainingerror), label='Training Error')
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22575/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57311/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(testerror), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -2465,7 +2475,7 @@ Mean squared error on test data: 3099.60342978
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22575/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57311/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
|
||||
plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')
|
||||
</pre></div>
|
||||
</div>
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1802,7 +1812,7 @@ which equals</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x12aaa0b20>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11ffa0ee0>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_82_1.png" src="_images/week39_82_1.png" />
|
||||
@@ -1860,7 +1870,7 @@ which equals</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x12b14fa90>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x12ccea880>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_90_1.png" src="_images/week39_90_1.png" />
|
||||
@@ -2154,11 +2164,11 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.29950088 4.27458376]
|
||||
[[3.66841959]
|
||||
[3.26280614]]
|
||||
[[3.66841959]
|
||||
[3.26280614]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.33433563 4.2051784 ]
|
||||
[[3.94121002]
|
||||
[3.08191754]]
|
||||
[[3.94121002]
|
||||
[3.08191754]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_153_1.png" src="_images/week39_153_1.png" />
|
||||
@@ -2189,9 +2199,9 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.06267057]
|
||||
[2.86868711]]
|
||||
[4.05285677] [2.86799623]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.91483251]
|
||||
[3.09848937]]
|
||||
[3.87616945] [3.07001431]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2291,11 +2301,11 @@ minimum of this function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.24719968 4.31175179]
|
||||
[[4.07235641]
|
||||
[3.05476114]]
|
||||
[[4.06908518]
|
||||
[3.05761244]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Hessian Matrix:[0.26638638 4.40906565]
|
||||
[[4.26969649]
|
||||
[2.78617455]]
|
||||
[[4.26953857]
|
||||
[2.78630865]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_166_1.png" src="_images/week39_166_1.png" />
|
||||
@@ -3871,11 +3881,13 @@ Eigenvalues of Hessian Matrix:[0.29860173 3.8931686 ]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[4.0586484]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.0586484]
|
||||
[3.0718316]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week39_269_2.png" src="_images/week39_269_2.png" />
|
||||
<img alt="_images/week39_269_3.png" src="_images/week39_269_3.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[4.02496085]
|
||||
[3.12081773]]
|
||||
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -1304,17 +1314,17 @@ We summarize some of these here for the methods we hvae studied in project one,
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Parameters for OLS using gradient descent
|
||||
[[4.26604611]
|
||||
[2.29234681]
|
||||
[5.33329216]]
|
||||
[[3.8184887 ]
|
||||
[3.47851966]
|
||||
[4.77551387]]
|
||||
Parameters for Ridge using gradient descent
|
||||
[[3.6161104 ]
|
||||
[3.78762558]
|
||||
[4.65410649]]
|
||||
[[3.92021197]
|
||||
[3.11388017]
|
||||
[4.9458396 ]]
|
||||
Parameters for Lasso using gradient descent
|
||||
[[4.24335376]
|
||||
[2.36219301]
|
||||
[5.29669411]]
|
||||
[[3.87323528]
|
||||
[3.3008836 ]
|
||||
[4.86284277]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1366,11 +1376,11 @@ Parameters for Lasso using gradient descent
|
||||
[[4.]
|
||||
[3.]
|
||||
[5.]]
|
||||
0 [-26.28886314] [-34.64721597]
|
||||
1 [-1.83231208e-13] [-1.80848093e-13]
|
||||
2 [6.92779167e-16] [1.22835717e-15]
|
||||
3 [-1.3500312e-15] [-1.8110093e-15]
|
||||
4 [7.46069873e-16] [9.30442002e-16]
|
||||
0 [-31.91417133] [-44.48017159]
|
||||
1 [3.48805429e-13] [4.67477123e-13]
|
||||
2 [6.75015599e-16] [1.30675215e-15]
|
||||
3 [-1.17239551e-15] [-1.78477759e-15]
|
||||
4 [6.75015599e-16] [1.30675215e-15]
|
||||
beta from own Newton code
|
||||
[[4.]
|
||||
[3.]
|
||||
@@ -1712,15 +1722,15 @@ function.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.36014743]
|
||||
[2.76030841]]
|
||||
Eigenvalues of Hessian Matrix:[0.36278226 3.73204357]
|
||||
[[3.90300704]
|
||||
[3.16913489]]
|
||||
Eigenvalues of Hessian Matrix:[0.2964378 4.12443871]
|
||||
theta from own gd
|
||||
[[4.36014743]
|
||||
[2.76030841]]
|
||||
[[3.90300704]
|
||||
[3.16913489]]
|
||||
theta from own sdg
|
||||
[[4.34582863]
|
||||
[2.81684805]]
|
||||
[[3.93272428]
|
||||
[3.16328315]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_34_1.png" src="_images/week40_34_1.png" />
|
||||
@@ -2434,12 +2444,12 @@ first example shows results with ordinary leats squares.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.85068028]
|
||||
[3.09808149]]
|
||||
Eigenvalues of Hessian Matrix:[0.31897935 3.95770298]
|
||||
[[4.13791264]
|
||||
[2.92552059]]
|
||||
Eigenvalues of Hessian Matrix:[0.27874136 4.16226023]
|
||||
theta from own gd
|
||||
[[3.85068028]
|
||||
[3.09808149]]
|
||||
[[4.13791264]
|
||||
[2.92552059]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_100_1.png" src="_images/week40_100_1.png" />
|
||||
@@ -2508,77 +2518,75 @@ theta from own gd
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.]
|
||||
[[4.]
|
||||
[3.]]
|
||||
Eigenvalues of Hessian Matrix:[0.35713539 3.88632765]
|
||||
0 [-9.01615836] [-9.6932681]
|
||||
1 [0.01454469] [-0.01357366]
|
||||
2 [0.0132081] [-0.0123263]
|
||||
3 [0.01199434] [-0.01119357]
|
||||
4 [0.01089212] [-0.01016493]
|
||||
5 [0.00989118] [-0.00923082]
|
||||
6 [0.00898223] [-0.00838255]
|
||||
7 [0.0081568] [-0.00761224]
|
||||
8 [0.00740723] [-0.00691271]
|
||||
9 [0.00672654] [-0.00627746]
|
||||
10 [0.0061084] [-0.00570059]
|
||||
11 [0.00554707] [-0.00517673]
|
||||
12 [0.00503732] [-0.00470102]
|
||||
13 [0.00457441] [-0.00426902]
|
||||
14 [0.00415405] [-0.00387671]
|
||||
15 [0.00377231] [-0.00352046]
|
||||
16 [0.00342565] [-0.00319695]
|
||||
17 [0.00311085] [-0.00290316]
|
||||
18 [0.00282498] [-0.00263638]
|
||||
19 [0.00256537] [-0.0023941]
|
||||
20 [0.00232963] [-0.0021741]
|
||||
21 [0.00211555] [-0.00197431]
|
||||
22 [0.00192114] [-0.00179288]
|
||||
23 [0.00174459] [-0.00162812]
|
||||
24 [0.00158427] [-0.0014785]
|
||||
25 [0.00143869] [-0.00134264]
|
||||
26 [0.00130648] [-0.00121925]
|
||||
27 [0.00118642] [-0.00110721]
|
||||
28 [0.00107739] [-0.00100546]
|
||||
29 [0.00097839] [-0.00091307]
|
||||
Eigenvalues of Hessian Matrix:[0.32606365 3.80499859]
|
||||
0 [-10.98955596] [-10.8332972]
|
||||
1 [-0.26421616] [0.25444295]
|
||||
2 [-0.24157456] [0.23263884]
|
||||
3 [-0.22087319] [0.2127032]
|
||||
4 [-0.20194579] [0.19447592]
|
||||
5 [-0.18464035] [0.1778106]
|
||||
6 [-0.16881787] [0.16257339]
|
||||
7 [-0.15435127] [0.1486419]
|
||||
8 [-0.14112437] [0.13590426]
|
||||
9 [-0.12903093] [0.12425815]
|
||||
10 [-0.11797382] [0.11361003]
|
||||
11 [-0.10786423] [0.10387439]
|
||||
12 [-0.09862097] [0.09497303]
|
||||
13 [-0.09016979] [0.08683446]
|
||||
14 [-0.08244283] [0.07939331]
|
||||
15 [-0.07537801] [0.07258982]
|
||||
16 [-0.06891861] [0.06636934]
|
||||
17 [-0.06301273] [0.06068192]
|
||||
18 [-0.05761295] [0.05548187]
|
||||
19 [-0.05267589] [0.05072744]
|
||||
20 [-0.04816191] [0.04638043]
|
||||
21 [-0.04403475] [0.04240593]
|
||||
22 [-0.04026126] [0.03877201]
|
||||
23 [-0.03681113] [0.0354495]
|
||||
24 [-0.03365665] [0.03241171]
|
||||
25 [-0.0307725] [0.02963424]
|
||||
26 [-0.02813549] [0.02709478]
|
||||
27 [-0.02572446] [0.02477293]
|
||||
28 [-0.02352005] [0.02265005]
|
||||
29 [-0.02150453] [0.02070909]
|
||||
theta from own gd
|
||||
[[4.00248779]
|
||||
[2.9976783 ]]
|
||||
0 [0.00088848] [-0.00082916]
|
||||
1 [0.00080683] [-0.00075296]
|
||||
2 [0.00070819] [-0.00066091]
|
||||
3 [0.00061352] [-0.00057256]
|
||||
4 [0.00052874] [-0.00049344]
|
||||
5 [0.00045472] [-0.00042436]
|
||||
6 [0.00039072] [-0.00036464]
|
||||
7 [0.00033562] [-0.00031321]
|
||||
8 [0.00028825] [-0.000269]
|
||||
9 [0.00024755] [-0.00023102]
|
||||
10 [0.00021259] [-0.0001984]
|
||||
11 [0.00018256] [-0.00017038]
|
||||
12 [0.00015678] [-0.00014631]
|
||||
13 [0.00013464] [-0.00012565]
|
||||
14 [0.00011562] [-0.0001079]
|
||||
15 [9.92929225e-05] [-9.26639089e-05]
|
||||
16 [8.52694246e-05] [-7.95766504e-05]
|
||||
17 [7.32265127e-05] [-6.83377498e-05]
|
||||
18 [6.28844641e-05] [-5.86861591e-05]
|
||||
19 [5.40030606e-05] [-5.03976976e-05]
|
||||
20 [4.63760101e-05] [-4.32798457e-05]
|
||||
21 [3.98261559e-05] [-3.71672742e-05]
|
||||
22 [3.42013616e-05] [-3.19180036e-05]
|
||||
23 [2.93709777e-05] [-2.74101067e-05]
|
||||
24 [2.52228066e-05] [-2.35388766e-05]
|
||||
25 [2.1660497e-05] [-2.02143946e-05]
|
||||
26 [1.86013055e-05] [-1.73594414e-05]
|
||||
27 [1.59741748e-05] [-1.49077038e-05]
|
||||
28 [1.37180834e-05] [-1.2802234e-05]
|
||||
29 [1.17806281e-05] [-1.09941275e-05]
|
||||
[[3.93969971]
|
||||
[3.05806981]]
|
||||
0 [-0.01966173] [0.01893445]
|
||||
1 [-0.01797685] [0.0173119]
|
||||
2 [-0.01593089] [0.01534161]
|
||||
3 [-0.01395192] [0.01343585]
|
||||
4 [-0.01216264] [0.01171276]
|
||||
5 [-0.0105836] [0.01019212]
|
||||
6 [-0.00920294] [0.00886253]
|
||||
7 [-0.00800011] [0.00770419]
|
||||
8 [-0.00695371] [0.00669649]
|
||||
9 [-0.0060439] [0.00582034]
|
||||
10 [-0.00525303] [0.00505872]
|
||||
11 [-0.00456562] [0.00439674]
|
||||
12 [-0.00396815] [0.00382137]
|
||||
13 [-0.00344887] [0.0033213]
|
||||
14 [-0.00299754] [0.00288666]
|
||||
15 [-0.00260527] [0.0025089]
|
||||
16 [-0.00226433] [0.00218058]
|
||||
17 [-0.00196801] [0.00189522]
|
||||
18 [-0.00171047] [0.0016472]
|
||||
19 [-0.00148663] [0.00143164]
|
||||
20 [-0.00129209] [0.00124429]
|
||||
21 [-0.001123] [0.00108146]
|
||||
22 [-0.00097604] [0.00093994]
|
||||
23 [-0.00084831] [0.00081693]
|
||||
24 [-0.0007373] [0.00071003]
|
||||
25 [-0.00064081] [0.00061711]
|
||||
26 [-0.00055695] [0.00053635]
|
||||
27 [-0.00048407] [0.00046616]
|
||||
28 [-0.00042072] [0.00040516]
|
||||
29 [-0.00036566] [0.00035214]
|
||||
theta from own gd wth momentum
|
||||
[[4.00002833]
|
||||
[2.99997356]]
|
||||
[[3.99902531]
|
||||
[3.00093864]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2667,20 +2675,18 @@ theta from own gd wth momentum
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[3.91650453]
|
||||
[2.94495682]]
|
||||
Eigenvalues of Hessian Matrix:[0.34862407 4.10453899]
|
||||
[[4.11762444]
|
||||
[3.04098313]]
|
||||
Eigenvalues of Hessian Matrix:[0.29738252 4.51279273]
|
||||
theta from own gd
|
||||
[[4.11762444]
|
||||
[3.04098313]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own gd
|
||||
[[3.91650453]
|
||||
[2.94495682]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_104_2.png" src="_images/week40_104_2.png" />
|
||||
<img alt="_images/week40_104_1.png" src="_images/week40_104_1.png" />
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg
|
||||
[[3.8901199 ]
|
||||
[2.92458892]]
|
||||
[[4.07058967]
|
||||
[3.024004 ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2762,15 +2768,17 @@ Eigenvalues of Hessian Matrix:[0.34862407 4.10453899]
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
|
||||
[[4.05785974]
|
||||
[2.95842106]]
|
||||
Eigenvalues of Hessian Matrix:[0.29678339 4.37215356]
|
||||
[[4.4252885 ]
|
||||
[2.70944365]]
|
||||
Eigenvalues of Hessian Matrix:[0.28973035 4.32089655]
|
||||
theta from own gd
|
||||
[[4.05738629]
|
||||
[2.95882223]]
|
||||
theta from own sdg with momentum
|
||||
[[4.07489511]
|
||||
[2.90281987]]
|
||||
[[4.42394588]
|
||||
[2.71059619]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own sdg with momentum
|
||||
[[4.44845593]
|
||||
[2.72577807]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2839,9 +2847,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own AdaGrad
|
||||
[[1.99994537]
|
||||
[3.00034209]
|
||||
[3.99966798]]
|
||||
[[2.00036797]
|
||||
[2.99817613]
|
||||
[4.00177485]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2917,9 +2925,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own RMSprop
|
||||
[[1.99975636]
|
||||
[3.00348281]
|
||||
[3.99607299]]
|
||||
[[2.00119865]
|
||||
[3.01346635]
|
||||
[3.99284588]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -2999,9 +3007,9 @@ theta from own sdg with momentum
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>theta from own ADAM
|
||||
[[2.00002276]
|
||||
[2.99985884]
|
||||
[4.00009004]]
|
||||
[[1.99997244]
|
||||
[3.00018876]
|
||||
[3.99983332]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -3122,7 +3130,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
return asarray(x, dtype=self.dtype)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x11bcee130>]
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[<matplotlib.lines.Line2D at 0x10cc52cd0>]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_120_2.png" src="_images/week40_120_2.png" />
|
||||
@@ -3157,7 +3165,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x11bdd4640>
|
||||
<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span><matplotlib.collections.PathCollection at 0x10fcfaeb0>
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/week40_122_1.png" src="_images/week40_122_1.png" />
|
||||
|
||||
@@ -55,7 +55,7 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 1 on Machine Learning, deadline October 7 (midnight), 2024" href="project1.html" />
|
||||
<link rel="next" title="Exercises week 42" href="exercisesweek42.html" />
|
||||
<link rel="prev" title="Exercises week 41" href="exercisesweek41.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
@@ -323,6 +323,16 @@ const thebe_selector_output = ".output, .cell_output"
|
||||
Week 41 Neural networks and constructing a neural network code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="exercisesweek42.html">
|
||||
Exercises week 42
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="week42.html">
|
||||
Week 42 Constructing a Neural Network code with examples
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
@@ -3610,10 +3620,10 @@ features).</p>
|
||||
<p class="prev-next-title">Exercises week 41</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="project1.html" title="next page">
|
||||
<a class='right-next' id="next-link" href="exercisesweek42.html" title="next page">
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">next</p>
|
||||
<p class="prev-next-title">Project 1 on Machine Learning, deadline October 7 (midnight), 2024</p>
|
||||
<p class="prev-next-title">Exercises week 42</p>
|
||||
</div>
|
||||
<i class="fas fa-angle-right"></i>
|
||||
</a>
|
||||
|
||||
@@ -3378,7 +3378,7 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3714,7 +3714,7 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.19166666666666668
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3723,7 +3723,7 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3732,7 +3732,7 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3741,7 +3741,7 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3750,7 +3750,7 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3759,7 +3759,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.08611111111111111
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3768,7 +3768,7 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3777,11 +3777,11 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.09166666666666666
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3790,11 +3790,11 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3803,11 +3803,11 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3816,11 +3816,11 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3829,11 +3829,11 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3842,7 +3842,7 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3851,11 +3851,11 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.10555555555555556
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3864,11 +3864,11 @@ Lambda = 10.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3877,11 +3877,11 @@ Lambda = 1e-05
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3890,11 +3890,11 @@ Lambda = 0.0001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3903,11 +3903,11 @@ Lambda = 0.001
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3916,11 +3916,11 @@ Lambda = 0.01
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3929,11 +3929,11 @@ Lambda = 0.1
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3942,11 +3942,11 @@ Lambda = 1.0
|
||||
Accuracy score on test set: 0.07777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:43: RuntimeWarning: overflow encountered in exp
|
||||
exp_term = np.exp(self.z_o)
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
|
||||
self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -3999,15 +3999,15 @@ Accuracy score on test set: 0.07777777777777778
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_55841/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_57345/953065564.py:4: RuntimeWarning: overflow encountered in exp
|
||||
return 1/(1 + np.exp(-x))
|
||||
</pre></div>
|
||||
</div>
|
||||
@@ -4324,18 +4324,17 @@ Accuracy score on test set: 0.10555555555555556
|
||||
Learning rate = 1.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.17777777777777778
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.08333333333333333
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1.0
|
||||
Lambda = 1.0
|
||||
Accuracy score on test set: 0.08888888888888889
|
||||
|
||||
Learning rate = 1.0
|
||||
Lambda = 10.0
|
||||
Accuracy score on test set: 0.09444444444444444
|
||||
|
||||
@@ -4355,9 +4354,8 @@ Accuracy score on test set: 0.10555555555555556
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.01
|
||||
Accuracy score on test set: 0.1388888888888889
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 10.0
|
||||
|
||||
Learning rate = 10.0
|
||||
Lambda = 0.1
|
||||
Accuracy score on test set: 0.11388888888888889
|
||||
</pre></div>
|
||||
|
||||
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File diff suppressed because one or more lines are too long
@@ -2989,17 +2989,24 @@
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"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:81\u001b[0m, in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 79\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhessian\u001b[39m(fun, x):\n\u001b[1;32m 80\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mReturns a function that computes the exact Hessian.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m---> 81\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:60\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 50\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m 51\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mjacobian\u001b[39m(fun, x):\n\u001b[1;32m 52\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m 53\u001b[0m \u001b[38;5;124;03m Returns a function which computes the Jacobian of `fun` with respect to\u001b[39;00m\n\u001b[1;32m 54\u001b[0m \u001b[38;5;124;03m positional argument number `argnum`, which must be a scalar or array. Unlike\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 58\u001b[0m \u001b[38;5;124;03m (out1, out2, ...) then the Jacobian has shape (out1, out2, ..., in1, in2, ...).\u001b[39;00m\n\u001b[1;32m 59\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m---> 60\u001b[0m vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 61\u001b[0m ans_vspace \u001b[38;5;241m=\u001b[39m vspace(ans)\n\u001b[1;32m 62\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m 9\u001b[0m start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m end_value, end_node \u001b[38;5;241m=\u001b[39m \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m 9\u001b[0m start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 11\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m 12\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 14\u001b[0m subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 19\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:64\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 62\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m 63\u001b[0m grads \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(vjp, ans_vspace\u001b[38;5;241m.\u001b[39mstandard_basis())\n\u001b[0;32m---> 64\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mreshape(\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgrads\u001b[49m\u001b[43m)\u001b[49m, jacobian_shape)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m 84\u001b[0m \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m 85\u001b[0m \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m 86\u001b[0m \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m 89\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m 90\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp.<locals>.vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m 20\u001b[0m outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 22\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m 23\u001b[0m outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:78\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 76\u001b[0m vjp_0 \u001b[38;5;241m=\u001b[39m vjp_0_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m 77\u001b[0m vjp_1 \u001b[38;5;241m=\u001b[39m vjp_1_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 78\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp_0\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m, vjp_1(g))\n\u001b[1;32m 79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 80\u001b[0m vjps \u001b[38;5;241m=\u001b[39m [vjps_dict[argnum](ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs) \u001b[38;5;28;01mfor\u001b[39;00m argnum \u001b[38;5;129;01min\u001b[39;00m argnums]\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:660\u001b[0m, in \u001b[0;36munbroadcast_f.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 658\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21munbroadcast_f\u001b[39m(target, f):\n\u001b[1;32m 659\u001b[0m target_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(target)\n\u001b[0;32m--> 660\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: unbroadcast(\u001b[43mf\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m, target_meta)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:34\u001b[0m, in \u001b[0;36m<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 30\u001b[0m \u001b[38;5;66;03m# ----- Binary ufuncs -----\u001b[39;00m\n\u001b[1;32m 32\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39madd, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: g),\n\u001b[1;32m 33\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: g))\n\u001b[0;32m---> 34\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mmultiply, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43my\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m),\n\u001b[1;32m 35\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: x \u001b[38;5;241m*\u001b[39m g))\n\u001b[1;32m 36\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39msubtract, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: g),\n\u001b[1;32m 37\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[38;5;241m-\u001b[39mg))\n\u001b[1;32m 38\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mdivide, \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(x, \u001b[38;5;28;01mlambda\u001b[39;00m g: g \u001b[38;5;241m/\u001b[39m y),\n\u001b[1;32m 39\u001b[0m \u001b[38;5;28;01mlambda\u001b[39;00m ans, x, y : unbroadcast_f(y, \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[38;5;241m-\u001b[39m g \u001b[38;5;241m*\u001b[39m x \u001b[38;5;241m/\u001b[39m y\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m2\u001b[39m))\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_boxes.py:27\u001b[0m, in \u001b[0;36mArrayBox.__mul__\u001b[0;34m(self, other)\u001b[0m\n\u001b[0;32m---> 27\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m__mul__\u001b[39m(\u001b[38;5;28mself\u001b[39m, other): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmultiply\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mother\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:44\u001b[0m, in \u001b[0;36mprimitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 42\u001b[0m parents \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(box\u001b[38;5;241m.\u001b[39m_node \u001b[38;5;28;01mfor\u001b[39;00m _ , box \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[1;32m 43\u001b[0m argnums \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(argnum \u001b[38;5;28;01mfor\u001b[39;00m argnum, _ \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[0;32m---> 44\u001b[0m ans \u001b[38;5;241m=\u001b[39m \u001b[43mf_wrapped\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 45\u001b[0m node \u001b[38;5;241m=\u001b[39m node_constructor(ans, f_wrapped, argvals, kwargs, argnums, parents)\n\u001b[1;32m 46\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:48\u001b[0m, in \u001b[0;36mprimitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 46\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m 47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 48\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 64\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m 65\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m 66\u001b[0m vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m 68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m 69\u001b[0m argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423\u001b[0m, in \u001b[0;36mmatmul_vjp_1.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 421\u001b[0m A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[1;32m 422\u001b[0m B_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(B)\n\u001b[0;32m--> 423\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43mmatmul_adjoint_1\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mA_ndim\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mB_meta\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:413\u001b[0m, in \u001b[0;36mmatmul_adjoint_1\u001b[0;34m(A, G, A_ndim, B_meta)\u001b[0m\n\u001b[1;32m 411\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m B_is_vec:\n\u001b[1;32m 412\u001b[0m result \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msqueeze(result, anp\u001b[38;5;241m.\u001b[39mndim(G) \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n\u001b[0;32m--> 413\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munbroadcast\u001b[49m\u001b[43m(\u001b[49m\u001b[43mresult\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mB_meta\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:653\u001b[0m, in \u001b[0;36munbroadcast\u001b[0;34m(x, target_meta, broadcast_idx)\u001b[0m\n\u001b[1;32m 651\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m axis, size \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(target_shape):\n\u001b[1;32m 652\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m size \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[0;32m--> 653\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msum\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43maxis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43maxis\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkeepdims\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m 654\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m anp\u001b[38;5;241m.\u001b[39miscomplexobj(x) \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m target_iscomplex:\n\u001b[1;32m 655\u001b[0m x \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mreal(x)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45\u001b[0m, in \u001b[0;36mprimitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 43\u001b[0m argnums \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(argnum \u001b[38;5;28;01mfor\u001b[39;00m argnum, _ \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[1;32m 44\u001b[0m ans \u001b[38;5;241m=\u001b[39m f_wrapped(\u001b[38;5;241m*\u001b[39margvals, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 45\u001b[0m node \u001b[38;5;241m=\u001b[39m \u001b[43mnode_constructor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf_wrapped\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mparents\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 46\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m 47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36\u001b[0m, in \u001b[0;36mVJPNode.__init__\u001b[0;34m(self, value, fun, args, kwargs, parent_argnums, parents)\u001b[0m\n\u001b[1;32m 33\u001b[0m fun_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(fun, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m__name__\u001b[39m\u001b[38;5;124m'\u001b[39m, fun)\n\u001b[1;32m 34\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 35\u001b[0m \u001b[38;5;241m.\u001b[39mformat(fun_name, parent_argnums))\n\u001b[0;32m---> 36\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvjp \u001b[38;5;241m=\u001b[39m \u001b[43mvjpmaker\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparent_argnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:66\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m:\n\u001b[1;32m 64\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m 65\u001b[0m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[0;32m---> 66\u001b[0m vjp \u001b[38;5;241m=\u001b[39m \u001b[43mvjpfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 67\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (vjp(g),)\n\u001b[1;32m 68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:297\u001b[0m, in \u001b[0;36mgrad_np_sum\u001b[0;34m(ans, x, axis, keepdims, dtype)\u001b[0m\n\u001b[1;32m 294\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: anp\u001b[38;5;241m.\u001b[39msum(g, axis\u001b[38;5;241m=\u001b[39mbroadcast_axes, keepdims\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[1;32m 295\u001b[0m defvjp(anp\u001b[38;5;241m.\u001b[39mbroadcast_to, grad_broadcast_to)\n\u001b[0;32m--> 297\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad_np_sum\u001b[39m(ans, x, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, keepdims\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m, dtype\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m 298\u001b[0m shape, dtype \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mshape(x), anp\u001b[38;5;241m.\u001b[39mresult_type(x)\n\u001b[1;32m 299\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: repeat_to_match_shape(g, shape, dtype, axis, keepdims)[\u001b[38;5;241m0\u001b[39m]\n",
|
||||
"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
|
||||
]
|
||||
}
|
||||
@@ -3638,7 +3645,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
|
||||
"version": "3.9.15"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@@ -1305,7 +1305,7 @@
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mNotFoundError\u001b[0m Traceback (most recent call last)",
|
||||
"Cell \u001b[0;32mIn[4], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m datasets, layers, models\n\u001b[1;32m 2\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlayers\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Input\n\u001b[1;32m 3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmodels\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Sequential \u001b[38;5;66;03m#This allows appending layers to existing models\u001b[39;00m\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:443\u001b[0m\n\u001b[1;32m 441\u001b[0m _plugin_dir \u001b[38;5;241m=\u001b[39m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mjoin(_s, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtensorflow-plugins\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 442\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mexists(_plugin_dir):\n\u001b[0;32m--> 443\u001b[0m \u001b[43m_ll\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mload_library\u001b[49m\u001b[43m(\u001b[49m\u001b[43m_plugin_dir\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 444\u001b[0m \u001b[38;5;66;03m# Load Pluggable Device Library\u001b[39;00m\n\u001b[1;32m 445\u001b[0m _ll\u001b[38;5;241m.\u001b[39mload_pluggable_device_library(_plugin_dir)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:440\u001b[0m\n\u001b[1;32m 438\u001b[0m _plugin_dir \u001b[38;5;241m=\u001b[39m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mjoin(_s, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtensorflow-plugins\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 439\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mexists(_plugin_dir):\n\u001b[0;32m--> 440\u001b[0m \u001b[43m_ll\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mload_library\u001b[49m\u001b[43m(\u001b[49m\u001b[43m_plugin_dir\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 441\u001b[0m \u001b[38;5;66;03m# Load Pluggable Device Library\u001b[39;00m\n\u001b[1;32m 442\u001b[0m _ll\u001b[38;5;241m.\u001b[39mload_pluggable_device_library(_plugin_dir)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/framework/load_library.py:151\u001b[0m, in \u001b[0;36mload_library\u001b[0;34m(library_location)\u001b[0m\n\u001b[1;32m 148\u001b[0m kernel_libraries \u001b[38;5;241m=\u001b[39m [library_location]\n\u001b[1;32m 150\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m lib \u001b[38;5;129;01min\u001b[39;00m kernel_libraries:\n\u001b[0;32m--> 151\u001b[0m \u001b[43mpy_tf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mTF_LoadLibrary\u001b[49m\u001b[43m(\u001b[49m\u001b[43mlib\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 153\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 154\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mOSError\u001b[39;00m(\n\u001b[1;32m 155\u001b[0m errno\u001b[38;5;241m.\u001b[39mENOENT,\n\u001b[1;32m 156\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mThe file or folder to load kernel libraries from does not exist.\u001b[39m\u001b[38;5;124m'\u001b[39m,\n\u001b[1;32m 157\u001b[0m library_location)\n",
|
||||
"\u001b[0;31mNotFoundError\u001b[0m: dlopen(/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow-plugins/libmetal_plugin.dylib, 0x0006): symbol not found in flat namespace '_TF_GetInputPropertiesList'"
|
||||
]
|
||||
@@ -1649,7 +1649,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
|
||||
"version": "3.9.15"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@@ -67,7 +67,7 @@
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mNotFoundError\u001b[0m Traceback (most recent call last)",
|
||||
"Cell \u001b[0;32mIn[1], line 7\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n\u001b[0;32m----> 7\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mtf\u001b[39;00m\n\u001b[1;32m 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m datasets, layers, models\n\u001b[1;32m 9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlayers\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Input\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:443\u001b[0m\n\u001b[1;32m 441\u001b[0m _plugin_dir \u001b[38;5;241m=\u001b[39m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mjoin(_s, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtensorflow-plugins\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 442\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mexists(_plugin_dir):\n\u001b[0;32m--> 443\u001b[0m \u001b[43m_ll\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mload_library\u001b[49m\u001b[43m(\u001b[49m\u001b[43m_plugin_dir\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 444\u001b[0m \u001b[38;5;66;03m# Load Pluggable Device Library\u001b[39;00m\n\u001b[1;32m 445\u001b[0m _ll\u001b[38;5;241m.\u001b[39mload_pluggable_device_library(_plugin_dir)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:440\u001b[0m\n\u001b[1;32m 438\u001b[0m _plugin_dir \u001b[38;5;241m=\u001b[39m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mjoin(_s, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtensorflow-plugins\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 439\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m _os\u001b[38;5;241m.\u001b[39mpath\u001b[38;5;241m.\u001b[39mexists(_plugin_dir):\n\u001b[0;32m--> 440\u001b[0m \u001b[43m_ll\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mload_library\u001b[49m\u001b[43m(\u001b[49m\u001b[43m_plugin_dir\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 441\u001b[0m \u001b[38;5;66;03m# Load Pluggable Device Library\u001b[39;00m\n\u001b[1;32m 442\u001b[0m _ll\u001b[38;5;241m.\u001b[39mload_pluggable_device_library(_plugin_dir)\n",
|
||||
"File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/framework/load_library.py:151\u001b[0m, in \u001b[0;36mload_library\u001b[0;34m(library_location)\u001b[0m\n\u001b[1;32m 148\u001b[0m kernel_libraries \u001b[38;5;241m=\u001b[39m [library_location]\n\u001b[1;32m 150\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m lib \u001b[38;5;129;01min\u001b[39;00m kernel_libraries:\n\u001b[0;32m--> 151\u001b[0m \u001b[43mpy_tf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mTF_LoadLibrary\u001b[49m\u001b[43m(\u001b[49m\u001b[43mlib\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 153\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m 154\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mOSError\u001b[39;00m(\n\u001b[1;32m 155\u001b[0m errno\u001b[38;5;241m.\u001b[39mENOENT,\n\u001b[1;32m 156\u001b[0m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mThe file or folder to load kernel libraries from does not exist.\u001b[39m\u001b[38;5;124m'\u001b[39m,\n\u001b[1;32m 157\u001b[0m library_location)\n",
|
||||
"\u001b[0;31mNotFoundError\u001b[0m: dlopen(/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow-plugins/libmetal_plugin.dylib, 0x0006): symbol not found in flat namespace '_TF_GetInputPropertiesList'"
|
||||
]
|
||||
@@ -1892,7 +1892,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
|
||||
"version": "3.9.15"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
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@@ -1798,10 +1798,10 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"-0.009134699065945493\n",
|
||||
"4.0244965108017645\n",
|
||||
"[[0.85613835 2.50655379]\n",
|
||||
" [2.50655379 8.3404509 ]]\n"
|
||||
"0.04718566894028431\n",
|
||||
"4.11080997912276\n",
|
||||
"[[ 1.10517643 3.48455788]\n",
|
||||
" [ 3.48455788 12.00216162]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -1845,10 +1845,10 @@
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||||
"name": "stdout",
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||||
"output_type": "stream",
|
||||
"text": [
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
@@ -1905,30 +1905,30 @@
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||||
"name": "stdout",
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||||
"output_type": "stream",
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||||
"text": [
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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@@ -1974,37 +1974,37 @@
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||||
"text": [
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" 0 1 2 3 4 5 6 7 \\\n",
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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||||
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|
||||
"\n",
|
||||
" 8 9 10 11 12 13 14 \n",
|
||||
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||||
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||||
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|
||||
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||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"10 0.075864 0.073260 0.077608 0.074866 0.072223 0.069676 0.067224 \n",
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
"1 0.072148 0.072902 0.063646 0.064071 0.064514 0.064980 0.065472 \n",
|
||||
"2 0.076101 0.077180 0.065859 0.066452 0.067074 0.067731 0.068429 \n",
|
||||
"3 0.082240 0.082670 0.075320 0.075576 0.075838 0.076108 0.076389 \n",
|
||||
"4 0.083128 0.083714 0.075498 0.075838 0.076189 0.076555 0.076938 \n",
|
||||
"5 0.083801 0.084548 0.075472 0.075897 0.076340 0.076803 0.077292 \n",
|
||||
"6 0.080150 0.080237 0.075478 0.075542 0.075602 0.075658 0.075711 \n",
|
||||
"7 0.080474 0.080651 0.075409 0.075525 0.075639 0.075753 0.075868 \n",
|
||||
"8 0.080766 0.081038 0.075293 0.075463 0.075634 0.075809 0.075988 \n",
|
||||
"9 0.081038 0.081411 0.075136 0.075363 0.075595 0.075834 0.076082 \n",
|
||||
"10 0.075293 0.075136 0.072406 0.072329 0.072240 0.072140 0.072028 \n",
|
||||
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|
||||
"12 0.075634 0.075595 0.072240 0.072234 0.072220 0.072199 0.072171 \n",
|
||||
"13 0.075809 0.075834 0.072140 0.072173 0.072199 0.072221 0.072238 \n",
|
||||
"14 0.075988 0.076082 0.072028 0.072101 0.072171 0.072238 0.072303 \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
@@ -3557,7 +3557,14 @@
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[2. 2.]\n",
|
||||
"[2. 2.]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"Training MSE for OLS\n",
|
||||
"3.0\n"
|
||||
]
|
||||
@@ -3571,7 +3578,7 @@
|
||||
},
|
||||
"metadata": {
|
||||
"filenames": {
|
||||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_252_1.png"
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||||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_252_2.png"
|
||||
}
|
||||
},
|
||||
"output_type": "display_data"
|
||||
@@ -5828,7 +5835,7 @@
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
|
||||
"version": "3.9.15"
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},
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||||
"nbformat": 4,
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|
||||
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|
||||
"name": "python",
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||||
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|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.9.18"
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||||
"version": "3.9.15"
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}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user