lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

update book

Browse Source
This commit is contained in:
Morten Hjorth-Jensen
2022-08-23 11:19:05 +02:00
parent 602b1c6ee0
commit 398fba5b97
233 changed files with 5964 additions and 6430 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/chapter12.html
+217 -209
View File
@@ -7,8 +7,8 @@
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>16. Convolutional Neural Networks &#8212; Applied Data Analysis and Machine Learning</title>
<link href="_static/css/theme.css" rel="stylesheet" />
<link href="_static/css/index.c5995385ac14fb8791e8eb36b4908be2.css" rel="stylesheet" />
<link href="_static/css/theme.css" rel="stylesheet">
<link href="_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
<link rel="stylesheet"
@@ -31,7 +31,7 @@
<link rel="stylesheet" type="text/css" href="_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css" />
<link rel="stylesheet" type="text/css" href="_static/panels-variables.06eb56fa6e07937060861dad626602ad.css" />
<link rel="preload" as="script" href="_static/js/index.1c5a1a01449ed65a7b51.js">
<link rel="preload" as="script" href="_static/js/index.be7d3bbb2ef33a8344ce.js">
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
@@ -41,22 +41,24 @@
<script src="_static/clipboard.min.js"></script>
<script src="_static/copybutton.js"></script>
<script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
<script src="_static/sphinx-book-theme.12a9622fbb08dcb3a2a40b2c02b83a57.js"></script>
<script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
<script async="async" src="https://unpkg.com/thebe@0.5.1/lib/index.js"></script>
<script>
const thebe_selector = ".thebe"
const thebe_selector_input = "pre"
const thebe_selector_output = ".output"
</script>
<script src="_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
<script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"
const thebe_selector = ".thebe,.cell"
const thebe_selector_input = "pre"
const thebe_selector_output = ".output, .cell_output"
</script>
<script async="async" src="_static/sphinx-thebe.js"></script>
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="17. Recurrent neural networks: Overarching view" href="chapter13.html" />
<link rel="prev" title="15. Solving Differential Equations with Deep Learning" href="chapter11.html" />
<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="docsearch:language" content="en" />
<meta name="docsearch:language" content="None">
<!-- Google Analytics -->
</head>
<body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
@@ -91,11 +93,11 @@
<ul class="nav bd-sidenav">
<li class="toctree-l1">
<a class="reference internal" href="intro.html">
Applied Data Analysis and Machine Learning, FYS-STK3155/4155 at the University of Oslo, Norway
Applied Data Analysis and Machine Learning
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
About the course
</span>
@@ -117,7 +119,7 @@
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Review of Statistics with Resampling Techniques and Linear Algebra
</span>
@@ -134,7 +136,7 @@
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
From Regression to Support Vector Machines
</span>
@@ -171,7 +173,7 @@
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Decision Trees, Ensemble Methods and Boosting
</span>
@@ -188,7 +190,7 @@
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Dimensionality Reduction
</span>
@@ -205,7 +207,7 @@
</a>
</li>
</ul>
<p class="caption" role="heading">
<p aria-level="2" class="caption" role="heading">
<span class="caption-text">
Deep Learning Methods
</span>
@@ -282,7 +284,7 @@
data-placement="left">.ipynb</button></a>
<!-- Download PDF via print -->
<button type="button" id="download-print" class="btn btn-secondary topbarbtn" title="Print to PDF"
onClick="window.print()" data-toggle="tooltip" data-placement="left">.pdf</button>
onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf</button>
</div>
</div>
@@ -300,7 +302,7 @@
</div>
<!-- Table of contents -->
<div class="d-none d-md-block col-md-2 bd-toc show">
<div class="d-none d-md-block col-md-2 bd-toc show noprint">
<div class="tocsection onthispage pt-5 pb-3">
<i class="fas fa-list"></i> Contents
@@ -384,7 +386,94 @@
</div>
<div id="main-content" class="row">
<div class="col-12 col-md-9 pl-md-3 pr-md-0">
<!-- Table of contents that is only displayed when printing the page -->
<div id="jb-print-docs-body" class="onlyprint">
<h1>Convolutional Neural Networks</h1>
<!-- Table of contents -->
<div id="print-main-content">
<div id="jb-print-toc">
<div>
<h2> Contents </h2>
</div>
<nav aria-label="Page">
<ul class="visible nav section-nav flex-column">
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#neural-networks-vs-cnns">
16.1. Neural Networks vs CNNs
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#layers-used-to-build-cnns">
16.2. Layers used to build CNNs
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#mathematics-of-cnns">
16.3. Mathematics of CNNs
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">
16.3.1. Convolution Examples: Polynomial multiplication
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">
16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#two-dimensional-objects">
16.4. Two-dimensional Objects
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#more-on-dimensionalities">
16.5. More on Dimensionalities
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#further-dimensionality-remarks">
16.6. Further Dimensionality Remarks
</a>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">
16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
</a>
<ul class="nav section-nav flex-column">
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#the-mnist-dataset-again">
16.7.1. The MNIST dataset again
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#systematic-reduction">
16.7.2. Systematic reduction
</a>
</li>
<li class="toc-h3 nav-item toc-entry">
<a class="reference internal nav-link" href="#prerequisites-collect-and-pre-process-data">
16.7.3. Prerequisites: Collect and pre-process data
</a>
</li>
</ul>
</li>
<li class="toc-h2 nav-item toc-entry">
<a class="reference internal nav-link" href="#the-cifar01-data-set">
16.8. The CIFAR01 data set
</a>
</li>
</ul>
</nav>
</div>
</div>
</div>
<div>
<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
@@ -1036,6 +1125,12 @@ labels = (n_inputs) = (1797,)
</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/jax/_src/lib/__init__.py:33: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.
warnings.warn(&quot;JAX on Mac ARM machines is experimental and minimally tested. &quot;
</pre></div>
</div>
</div>
</div>
<div class="cell docutils container">
<div class="cell_input docutils container">
@@ -1091,192 +1186,117 @@ labels = (n_inputs) = (1797,)
</div>
</div>
<div class="cell_output docutils container">
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2021-12-08 06:58:03.630224: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: SSE4.1 SSE4.2 AVX AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
/Users/MortenImac/anaconda3/lib/python3.8/site-packages/keras/optimizer_v2/optimizer_v2.py:355: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
warnings.warn(
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/keras/optimizer_v2/gradient_descent.py:102: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
super(SGD, self).__init__(name, **kwargs)
</pre></div>
</div>
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2021-12-08 06:58:04.114437: I tensorflow/compiler/mlir/mlir_graph_optimization_pass.cc:185] None of the MLIR Optimization Passes are enabled (registered 2)
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 3.2703 - accuracy: 0.0000e+00
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 2.4411 - accuracy: 0.2500
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
10/12 [========================&gt;.....] - ETA: 0s - loss: 3.2526 - accuracy: 0.1125
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 853us/step - loss: 2.4410 - accuracy: 0.1944
12/12 [==============================] - ETA: 0s - loss: 3.2225 - accuracy: 0.1139
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 12ms/step - loss: 3.2225 - accuracy: 0.1139
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 1e-05
Test accuracy: 0.194
Test accuracy: 0.114
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 4.2597 - accuracy: 0.0938
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 3.2772 - accuracy: 0.0000e+00
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
11/12 [==========================&gt;...] - ETA: 0s - loss: 3.2195 - accuracy: 0.1136
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 842us/step - loss: 3.4744 - accuracy: 0.1361
12/12 [==============================] - 0s 6ms/step - loss: 3.2299 - accuracy: 0.1139
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 0.0001
Test accuracy: 0.136
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 3.0466 - accuracy: 0.1562
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 743us/step - loss: 2.9400 - accuracy: 0.1028
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 0.001
Test accuracy: 0.103
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 3.8064 - accuracy: 0.1250
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 912us/step - loss: 3.8175 - accuracy: 0.1056
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 0.01
Test accuracy: 0.106
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 12.1612 - accuracy: 0.0938
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 763us/step - loss: 12.3063 - accuracy: 0.1361
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 0.1
Test accuracy: 0.136
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 91.8768 - accuracy: 0.2812
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 922us/step - loss: 92.0923 - accuracy: 0.2972
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 1.0
Test accuracy: 0.297
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 529.5700 - accuracy: 0.2188
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 935us/step - loss: 529.7050 - accuracy: 0.1861
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 1e-05
Lambda = 10.0
Test accuracy: 0.186
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 1s - loss: 1.2495 - accuracy: 0.5312
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 750us/step - loss: 1.5138 - accuracy: 0.4694
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
Lambda = 1e-05
Test accuracy: 0.469
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 1.4077 - accuracy: 0.6562
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 954us/step - loss: 1.4837 - accuracy: 0.5611
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
Lambda = 0.0001
Test accuracy: 0.561
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 1/12 [=&gt;............................] - ETA: 0s - loss: 1.5539 - accuracy: 0.5625
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
12/12 [==============================] - 0s 932us/step - loss: 1.5615 - accuracy: 0.5639
</pre></div>
</div>
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate = 0.0001
Lambda = 0.001
Test accuracy: 0.564
Test accuracy: 0.114
</pre></div>
</div>
<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="o">/</span><span class="n">var</span><span class="o">/</span><span class="n">folders</span><span class="o">/</span><span class="n">jy</span><span class="o">/</span><span class="n">g42mrgv128v34gnnhxwk9nrc0000gp</span><span class="o">/</span><span class="n">T</span><span class="o">/</span><span class="n">ipykernel_47647</span><span class="o">/</span><span class="mf">2018906331.</span><span class="n">py</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
<span class="o">&lt;</span><span class="n">ipython</span><span class="o">-</span><span class="nb">input</span><span class="o">-</span><span class="mi">6</span><span class="o">-</span><span class="n">c95af3df0cdd</span><span class="o">&gt;</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
<span class="g g-Whitespace"> </span><span class="mi">6</span> <span class="n">n_filters</span><span class="p">,</span> <span class="n">n_neurons_connected</span><span class="p">,</span> <span class="n">n_categories</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">7</span> <span class="n">eta</span><span class="p">,</span> <span class="n">lmbd</span><span class="p">)</span>
<span class="ne">----&gt; </span><span class="mi">8</span> <span class="n">CNN</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">Y_train</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="n">verbose</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">9</span> <span class="n">scores</span> <span class="o">=</span> <span class="n">CNN</span><span class="o">.</span><span class="n">evaluate</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span> <span class="n">Y_test</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">10</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/keras/engine/training.py</span> in <span class="ni">fit</span><span class="nt">(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_batch_size, validation_freq, max_queue_size, workers, use_multiprocessing)</span>
<span class="g g-Whitespace"> </span><span class="mi">1182</span> <span class="n">_r</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">1183</span> <span class="n">callbacks</span><span class="o">.</span><span class="n">on_train_batch_begin</span><span class="p">(</span><span class="n">step</span><span class="p">)</span>
<span class="ne">-&gt; </span><span class="mi">1184</span> <span class="n">tmp_logs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">train_function</span><span class="p">(</span><span class="n">iterator</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">1185</span> <span class="k">if</span> <span class="n">data_handler</span><span class="o">.</span><span class="n">should_sync</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">1186</span> <span class="n">context</span><span class="o">.</span><span class="n">async_wait</span><span class="p">()</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/keras/utils/traceback_utils.py</span> in <span class="ni">error_handler</span><span class="nt">(*args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">62</span> <span class="n">filtered_tb</span> <span class="o">=</span> <span class="kc">None</span>
<span class="g g-Whitespace"> </span><span class="mi">63</span> <span class="k">try</span><span class="p">:</span>
<span class="ne">---&gt; </span><span class="mi">64</span> <span class="k">return</span> <span class="n">fn</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">65</span> <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span> <span class="c1"># pylint: disable=broad-except</span>
<span class="g g-Whitespace"> </span><span class="mi">66</span> <span class="n">filtered_tb</span> <span class="o">=</span> <span class="n">_process_traceback_frames</span><span class="p">(</span><span class="n">e</span><span class="o">.</span><span class="n">__traceback__</span><span class="p">)</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py</span> in <span class="ni">__call__</span><span class="nt">(self, *args, **kwds)</span>
<span class="g g-Whitespace"> </span><span class="mi">883</span>
<span class="g g-Whitespace"> </span><span class="mi">884</span> <span class="k">with</span> <span class="n">OptionalXlaContext</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_jit_compile</span><span class="p">):</span>
<span class="ne">--&gt; </span><span class="mi">885</span> <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_call</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">kwds</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">886</span>
<span class="g g-Whitespace"> </span><span class="mi">887</span> <span class="n">new_tracing_count</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">experimental_get_tracing_count</span><span class="p">()</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/keras/engine/training.py</span> in <span class="ni">fit</span><span class="nt">(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_batch_size, validation_freq, max_queue_size, workers, use_multiprocessing)</span>
<span class="g g-Whitespace"> </span><span class="mi">1382</span> <span class="n">_r</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">1383</span> <span class="n">callbacks</span><span class="o">.</span><span class="n">on_train_batch_begin</span><span class="p">(</span><span class="n">step</span><span class="p">)</span>
<span class="ne">-&gt; </span><span class="mi">1384</span> <span class="n">tmp_logs</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">train_function</span><span class="p">(</span><span class="n">iterator</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">1385</span> <span class="k">if</span> <span class="n">data_handler</span><span class="o">.</span><span class="n">should_sync</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">1386</span> <span class="n">context</span><span class="o">.</span><span class="n">async_wait</span><span class="p">()</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py</span> in <span class="ni">_call</span><span class="nt">(self, *args, **kwds)</span>
<span class="g g-Whitespace"> </span><span class="mi">915</span> <span class="c1"># In this case we have created variables on the first call, so we run the</span>
<span class="g g-Whitespace"> </span><span class="mi">916</span> <span class="c1"># defunned version which is guaranteed to never create variables.</span>
<span class="ne">--&gt; </span><span class="mi">917</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stateless_fn</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">kwds</span><span class="p">)</span> <span class="c1"># pylint: disable=not-callable</span>
<span class="g g-Whitespace"> </span><span class="mi">918</span> <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stateful_fn</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">919</span> <span class="c1"># Release the lock early so that multiple threads can perform the call</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/util/traceback_utils.py</span> in <span class="ni">error_handler</span><span class="nt">(*args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">148</span> <span class="n">filtered_tb</span> <span class="o">=</span> <span class="kc">None</span>
<span class="g g-Whitespace"> </span><span class="mi">149</span> <span class="k">try</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">150</span> <span class="k">return</span> <span class="n">fn</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">151</span> <span class="k">except</span> <span class="ne">Exception</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">152</span> <span class="n">filtered_tb</span> <span class="o">=</span> <span class="n">_process_traceback_frames</span><span class="p">(</span><span class="n">e</span><span class="o">.</span><span class="n">__traceback__</span><span class="p">)</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">__call__</span><span class="nt">(self, *args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">3037</span> <span class="p">(</span><span class="n">graph_function</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">3038</span> <span class="n">filtered_flat_args</span><span class="p">)</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_maybe_define_function</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="ne">-&gt; </span><span class="mi">3039</span> <span class="k">return</span> <span class="n">graph_function</span><span class="o">.</span><span class="n">_call_flat</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">3040</span> <span class="n">filtered_flat_args</span><span class="p">,</span> <span class="n">captured_inputs</span><span class="o">=</span><span class="n">graph_function</span><span class="o">.</span><span class="n">captured_inputs</span><span class="p">)</span> <span class="c1"># pylint: disable=protected-access</span>
<span class="g g-Whitespace"> </span><span class="mi">3041</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/def_function.py</span> in <span class="ni">__call__</span><span class="nt">(self, *args, **kwds)</span>
<span class="g g-Whitespace"> </span><span class="mi">913</span>
<span class="g g-Whitespace"> </span><span class="mi">914</span> <span class="k">with</span> <span class="n">OptionalXlaContext</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_jit_compile</span><span class="p">):</span>
<span class="ne">--&gt; </span><span class="mi">915</span> <span class="n">result</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_call</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">kwds</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">916</span>
<span class="g g-Whitespace"> </span><span class="mi">917</span> <span class="n">new_tracing_count</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">experimental_get_tracing_count</span><span class="p">()</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">_call_flat</span><span class="nt">(self, args, captured_inputs, cancellation_manager)</span>
<span class="g g-Whitespace"> </span><span class="mi">1961</span> <span class="ow">and</span> <span class="n">executing_eagerly</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">1962</span> <span class="c1"># No tape is watching; skip to running the function.</span>
<span class="ne">-&gt; </span><span class="mi">1963</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_build_call_outputs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_inference_function</span><span class="o">.</span><span class="n">call</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">1964</span> <span class="n">ctx</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">cancellation_manager</span><span class="o">=</span><span class="n">cancellation_manager</span><span class="p">))</span>
<span class="g g-Whitespace"> </span><span class="mi">1965</span> <span class="n">forward_backward</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_select_forward_and_backward_functions</span><span class="p">(</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/def_function.py</span> in <span class="ni">_call</span><span class="nt">(self, *args, **kwds)</span>
<span class="g g-Whitespace"> </span><span class="mi">945</span> <span class="c1"># In this case we have created variables on the first call, so we run the</span>
<span class="g g-Whitespace"> </span><span class="mi">946</span> <span class="c1"># defunned version which is guaranteed to never create variables.</span>
<span class="ne">--&gt; </span><span class="mi">947</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stateless_fn</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">kwds</span><span class="p">)</span> <span class="c1"># pylint: disable=not-callable</span>
<span class="g g-Whitespace"> </span><span class="mi">948</span> <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stateful_fn</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">949</span> <span class="c1"># Release the lock early so that multiple threads can perform the call</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">call</span><span class="nt">(self, ctx, args, cancellation_manager)</span>
<span class="g g-Whitespace"> </span><span class="mi">589</span> <span class="k">with</span> <span class="n">_InterpolateFunctionError</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">590</span> <span class="k">if</span> <span class="n">cancellation_manager</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">591</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">execute</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">592</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">signature</span><span class="o">.</span><span class="n">name</span><span class="p">),</span>
<span class="g g-Whitespace"> </span><span class="mi">593</span> <span class="n">num_outputs</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_num_outputs</span><span class="p">,</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">__call__</span><span class="nt">(self, *args, **kwargs)</span>
<span class="g g-Whitespace"> </span><span class="mi">2954</span> <span class="p">(</span><span class="n">graph_function</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">2955</span> <span class="n">filtered_flat_args</span><span class="p">)</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_maybe_define_function</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="ne">-&gt; </span><span class="mi">2956</span> <span class="k">return</span> <span class="n">graph_function</span><span class="o">.</span><span class="n">_call_flat</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">2957</span> <span class="n">filtered_flat_args</span><span class="p">,</span> <span class="n">captured_inputs</span><span class="o">=</span><span class="n">graph_function</span><span class="o">.</span><span class="n">captured_inputs</span><span class="p">)</span> <span class="c1"># pylint: disable=protected-access</span>
<span class="g g-Whitespace"> </span><span class="mi">2958</span>
<span class="nn">~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/execute.py</span> in <span class="ni">quick_execute</span><span class="nt">(op_name, num_outputs, inputs, attrs, ctx, name)</span>
<span class="g g-Whitespace"> </span><span class="mi">57</span> <span class="k">try</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">58</span> <span class="n">ctx</span><span class="o">.</span><span class="n">ensure_initialized</span><span class="p">()</span>
<span class="ne">---&gt; </span><span class="mi">59</span> <span class="n">tensors</span> <span class="o">=</span> <span class="n">pywrap_tfe</span><span class="o">.</span><span class="n">TFE_Py_Execute</span><span class="p">(</span><span class="n">ctx</span><span class="o">.</span><span class="n">_handle</span><span class="p">,</span> <span class="n">device_name</span><span class="p">,</span> <span class="n">op_name</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">60</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">attrs</span><span class="p">,</span> <span class="n">num_outputs</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">61</span> <span class="k">except</span> <span class="n">core</span><span class="o">.</span><span class="n">_NotOkStatusException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">_call_flat</span><span class="nt">(self, args, captured_inputs, cancellation_manager)</span>
<span class="g g-Whitespace"> </span><span class="mi">1851</span> <span class="ow">and</span> <span class="n">executing_eagerly</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">1852</span> <span class="c1"># No tape is watching; skip to running the function.</span>
<span class="ne">-&gt; </span><span class="mi">1853</span> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_build_call_outputs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_inference_function</span><span class="o">.</span><span class="n">call</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">1854</span> <span class="n">ctx</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">cancellation_manager</span><span class="o">=</span><span class="n">cancellation_manager</span><span class="p">))</span>
<span class="g g-Whitespace"> </span><span class="mi">1855</span> <span class="n">forward_backward</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_select_forward_and_backward_functions</span><span class="p">(</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/function.py</span> in <span class="ni">call</span><span class="nt">(self, ctx, args, cancellation_manager)</span>
<span class="g g-Whitespace"> </span><span class="mi">497</span> <span class="k">with</span> <span class="n">_InterpolateFunctionError</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="g g-Whitespace"> </span><span class="mi">498</span> <span class="k">if</span> <span class="n">cancellation_manager</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="ne">--&gt; </span><span class="mi">499</span> <span class="n">outputs</span> <span class="o">=</span> <span class="n">execute</span><span class="o">.</span><span class="n">execute</span><span class="p">(</span>
<span class="g g-Whitespace"> </span><span class="mi">500</span> <span class="nb">str</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">signature</span><span class="o">.</span><span class="n">name</span><span class="p">),</span>
<span class="g g-Whitespace"> </span><span class="mi">501</span> <span class="n">num_outputs</span><span class="o">=</span><span class="bp">self</span><span class="o">.</span><span class="n">_num_outputs</span><span class="p">,</span>
<span class="nn">~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/python/eager/execute.py</span> in <span class="ni">quick_execute</span><span class="nt">(op_name, num_outputs, inputs, attrs, ctx, name)</span>
<span class="g g-Whitespace"> </span><span class="mi">52</span> <span class="k">try</span><span class="p">:</span>
<span class="g g-Whitespace"> </span><span class="mi">53</span> <span class="n">ctx</span><span class="o">.</span><span class="n">ensure_initialized</span><span class="p">()</span>
<span class="ne">---&gt; </span><span class="mi">54</span> <span class="n">tensors</span> <span class="o">=</span> <span class="n">pywrap_tfe</span><span class="o">.</span><span class="n">TFE_Py_Execute</span><span class="p">(</span><span class="n">ctx</span><span class="o">.</span><span class="n">_handle</span><span class="p">,</span> <span class="n">device_name</span><span class="p">,</span> <span class="n">op_name</span><span class="p">,</span>
<span class="g g-Whitespace"> </span><span class="mi">55</span> <span class="n">inputs</span><span class="p">,</span> <span class="n">attrs</span><span class="p">,</span> <span class="n">num_outputs</span><span class="p">)</span>
<span class="g g-Whitespace"> </span><span class="mi">56</span> <span class="k">except</span> <span class="n">core</span><span class="o">.</span><span class="n">_NotOkStatusException</span> <span class="k">as</span> <span class="n">e</span><span class="p">:</span>
<span class="ne">KeyboardInterrupt</span>:
</pre></div>
@@ -1456,54 +1476,42 @@ history = model.fit(train_images, train_labels, epochs=10,
</div>
<div class='prev-next-bottom'>
<div id="prev">
<a class="left-prev" href="chapter11.html" title="previous page">
<i class="prevnext-label fas fa-angle-left"></i>
<div class="prevnext-info">
<p class="prevnext-label">previous</p>
<p class="prevnext-title"><span class="section-number">15. </span>Solving Differential Equations with Deep Learning</p>
</div>
</a>
<!-- Previous / next buttons -->
<div class='prev-next-area'>
<a class='left-prev' id="prev-link" href="chapter11.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"><span class="section-number">15. </span>Solving Differential Equations with Deep Learning</p>
</div>
</a>
<a class='right-next' id="next-link" href="chapter13.html" title="next page">
<div class="prev-next-info">
<p class="prev-next-subtitle">next</p>
<p class="prev-next-title"><span class="section-number">17. </span>Recurrent neural networks: Overarching view</p>
</div>
<div id="next">
<a class="right-next" href="chapter13.html" title="next page">
<div class="prevnext-info">
<p class="prevnext-label">next</p>
<p class="prevnext-title"><span class="section-number">17. </span>Recurrent neural networks: Overarching view</p>
</div>
<i class="prevnext-label fas fa-angle-right"></i>
</a>
</div>
<i class="fas fa-angle-right"></i>
</a>
</div>
</div>
</div>
<footer class="footer">
<div class="container">
<p>
By Morten Hjorth-Jensen<br/>
&copy; Copyright 2021.<br/>
</p>
</div>
</footer>
<p>
By Morten Hjorth-Jensen<br/>
&copy; Copyright 2021.<br/>
</p>
</footer>
</main>
</div>
</div>
<script src="_static/js/index.1c5a1a01449ed65a7b51.js"></script>
<script src="_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
</body>
</html>