{ "cells": [ { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import random\n", "class Network(object):\n", " \n", " def _init_(self, sizes):\n", " self.num_layers=len(sizes)\n", " self.sizes=sizes\n", " self.biases=[np.random.randn(y,1) for y in sizes[1:]]\n", " self.weights=[np.random.randn(y,x) for x,y in zip(sizes[:-1], sizes[1:])]\n", "\n", "#sizes is the number of neurons in each layer\n", "#for example, say n_1st_layer=3, n_2nd_layer=3, n_3rd_layer=1, then net=Network([3,3,1])\n", "\n", "#The biases and weights are initialized randomly, using Gaussian distributions of mean=0, stdev=1\n", "#z is a vector (or a np.array)\n", "\n", " def feedforward(self,a):\n", " #returns output w/ 'a' as an input\n", " for b, w in zip(self.biases, self.weights):\n", " a=sigmoid(np.dot(w,b)+b)\n", " return a\n", " \n", "#Apply a Stochastic Gradient Descent (SGD) method:\n", " def SGD(self, training_data, epochs, mini_batch_size, eta, test_data=None):\n", " \"\"\"Trains network using batches incorporating SGD. The network will be evaluated against the\n", " test data after each epoch, with partial progress being printed out (this is useful for tracking,\n", " but slows the process.)\"\"\"\n", " if test_data: n_test=len(test_data)\n", " n=len(training_data)\n", " for j in xrange(epochs):\n", " random.shuffle(training_data)\n", " mini_batches=[training_data[k:k+mini_batch_size] for k in xrange(o,n,mini_batch_size)]\n", " for mini_batch in mini_batches:\n", " self.update_mini_batch(mini_batch, eta)\n", " if test_data:\n", " print (\"Epoch {0}: {1}/{2}\".format(j, self.evaluate(test_data), n_test))\n", " else:\n", " print (\"Epoch {0} complete\".format(j))\n", " \n", " \n", " def update_mini_batch(self, mini_batch, eta):\n", " #updates w and b using backpropagation to a single mini batch. eta is the learning rate.\"\n", " nabla_b=[np.zeros(b.shape) for b in self.biases]\n", " nabla_w=[np.zeros(w.shape) for w in self.weights]\n", " for x,y in mini_batch:\n", " delta_nabla_b, delta_nabla_w=self.backprop(x,y)\n", " nabla_b=[nb+dnb for nb, dnb in zip(nabla_b, delta_nabla_b)]\n", " nabla_w=[nw+dnw for nw, dnw in zip(nabla_w, delta_nabla_w)]\n", " self.weights=[w-(eta/len(mini_batch))*nw for w, nw in zip(self.weights, nabla_w)]\n", " self.biases=[b-(eta/len(mini_batch))*nb for b, nb in zip(self.biases, nabla_b)]\n", " \n", " def backprop(self, x, y):\n", " \"\"\"Return a tuple ``(nabla_b, nabla_w)`` representing the\n", " gradient for the cost function C_x. ``nabla_b`` and\n", " ``nabla_w`` are layer-by-layer lists of numpy arrays, similar\n", " to ``self.biases`` and ``self.weights``.\"\"\"\n", " nabla_b = [np.zeros(b.shape) for b in self.biases]\n", " nabla_w = [np.zeros(w.shape) for w in self.weights]\n", " # feedforward\n", " activation = x\n", " activations = [x] # list to store all the activations, layer by layer\n", " zs = [] # list to store all the z vectors, layer by layer\n", " for b, w in zip(self.biases, self.weights):\n", " z = np.dot(w, activation)+b\n", " zs.append(z)\n", " activation = sigmoid(z)\n", " activations.append(activation)\n", " # backward pass\n", " delta = self.cost_derivative(activations[-1], y) * \\\n", " sigmoid_prime(zs[-1])\n", " nabla_b[-1] = delta\n", " nabla_w[-1] = np.dot(delta, activations[-2].transpose())\n", " # Note that the variable l in the loop below is used a little\n", " # differently to the notation in Chapter 2 of the book. Here,\n", " # l = 1 means the last layer of neurons, l = 2 is the\n", " # second-last layer, and so on. It's a renumbering of the\n", " # scheme in the book, used here to take advantage of the fact\n", " # that Python can use negative indices in lists.\n", " for l in xrange(2, self.num_layers):\n", " z = zs[-l]\n", " sp = sigmoid_prime(z)\n", " delta = np.dot(self.weights[-l+1].transpose(), delta) * sp\n", " nabla_b[-l] = delta\n", " nabla_w[-l] = np.dot(delta, activations[-l-1].transpose())\n", " return (nabla_b, nabla_w)\n", "\n", " def evaluate(self, test_data):\n", " \"\"\"Return the number of test inputs for which the neural\n", " network outputs the correct result. Note that the neural\n", " network's output is assumed to be the index of whichever\n", " neuron in the final layer has the highest activation.\"\"\"\n", " test_results = [(np.argmax(self.feedforward(x)), y)\n", " for (x, y) in test_data]\n", " return sum(int(x == y) for (x, y) in test_results)\n", "\n", " def cost_derivative(self, output_activations, y):\n", " \"\"\"Return the vector of partial derivatives \\partial C_x /\n", " \\partial a for the output activations.\"\"\"\n", " return (output_activations-y)\n", " \n", " \n", " \n", "#Functions\n", "def sigmoid(z):\n", " return 1.0/(1.0+np.exp(-z))\n", "\n", "def sigmoid_prime(z):\n", " return sigmoid(z)*(1-sigmoid(z))\n", "\n", "network=Network()" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "ename": "AttributeError", "evalue": "'Network' object has no attribute 'Network'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m \u001b[0mnet\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnetwork\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mNetwork\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m784\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 89\u001b[0m \u001b[0mnet\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mSGD\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraining_data\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m30\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtest_data\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtest_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mAttributeError\u001b[0m: 'Network' object has no attribute 'Network'" ] } ], "source": [ "# %load neural-networks-and-deep-learning/src/mnist_loader.py\n", "\"\"\"\n", "mnist_loader\n", "~~~~~~~~~~~~\n", "\n", "A library to load the MNIST image data. For details of the data\n", "structures that are returned, see the doc strings for ``load_data``\n", "and ``load_data_wrapper``. In practice, ``load_data_wrapper`` is the\n", "function usually called by our neural network code.\n", "\"\"\"\n", "\n", "#### Libraries\n", "# Standard library\n", "import pickle\n", "import gzip\n", "\n", "# Third-party libraries\n", "import numpy as np\n", "\n", "def load_data():\n", " \"\"\"Return the MNIST data as a tuple containing the training data,\n", " the validation data, and the test data.\n", "\n", " The ``training_data`` is returned as a tuple with two entries.\n", " The first entry contains the actual training images. This is a\n", " numpy ndarray with 50,000 entries. Each entry is, in turn, a\n", " numpy ndarray with 784 values, representing the 28 * 28 = 784\n", " pixels in a single MNIST image.\n", "\n", " The second entry in the ``training_data`` tuple is a numpy ndarray\n", " containing 50,000 entries. Those entries are just the digit\n", " values (0...9) for the corresponding images contained in the first\n", " entry of the tuple.\n", "\n", " The ``validation_data`` and ``test_data`` are similar, except\n", " each contains only 10,000 images.\n", "\n", " This is a nice data format, but for use in neural networks it's\n", " helpful to modify the format of the ``training_data`` a little.\n", " That's done in the wrapper function ``load_data_wrapper()``, see\n", " below.\n", " \"\"\"\n", " f = gzip.open('../data/mnist.pkl.gz', 'rb')\n", " training_data, validation_data, test_data = cPickle.load(f)\n", " f.close()\n", " return (training_data, validation_data, test_data)\n", "\n", "def load_data_wrapper():\n", " \"\"\"Return a tuple containing ``(training_data, validation_data,\n", " test_data)``. Based on ``load_data``, but the format is more\n", " convenient for use in our implementation of neural networks.\n", "\n", " In particular, ``training_data`` is a list containing 50,000\n", " 2-tuples ``(x, y)``. ``x`` is a 784-dimensional numpy.ndarray\n", " containing the input image. ``y`` is a 10-dimensional\n", " numpy.ndarray representing the unit vector corresponding to the\n", " correct digit for ``x``.\n", "\n", " ``validation_data`` and ``test_data`` are lists containing 10,000\n", " 2-tuples ``(x, y)``. In each case, ``x`` is a 784-dimensional\n", " numpy.ndarry containing the input image, and ``y`` is the\n", " corresponding classification, i.e., the digit values (integers)\n", " corresponding to ``x``.\n", "\n", " Obviously, this means we're using slightly different formats for\n", " the training data and the validation / test data. These formats\n", " turn out to be the most convenient for use in our neural network\n", " code.\"\"\"\n", " tr_d, va_d, te_d = load_data()\n", " training_inputs = [np.reshape(x, (784, 1)) for x in tr_d[0]]\n", " training_results = [vectorized_result(y) for y in tr_d[1]]\n", " training_data = zip(training_inputs, training_results)\n", " validation_inputs = [np.reshape(x, (784, 1)) for x in va_d[0]]\n", " validation_data = zip(validation_inputs, va_d[1])\n", " test_inputs = [np.reshape(x, (784, 1)) for x in te_d[0]]\n", " test_data = zip(test_inputs, te_d[1])\n", " return (training_data, validation_data, test_data)\n", "\n", "def vectorized_result(j):\n", " \"\"\"Return a 10-dimensional unit vector with a 1.0 in the jth\n", " position and zeroes elsewhere. This is used to convert a digit\n", " (0...9) into a corresponding desired output from the neural\n", " network.\"\"\"\n", " e = np.zeros((10, 1))\n", " e[j] = 1.0\n", " return e\n", "\n", "net=network.Network([784,30,30])\n", "net.SGD(training_data,30,10,3,test_data=test_data)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }