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mhjensen 52c9b07580 updating week40
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<a class="navbar-brand" href="week40-bs.html">Week 40: From Stochastic Gradient Descent to Neural networks</a>
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<!-- navigation toc: --> <li><a href="._week40-bs001.html#___sec0" style="font-size: 80%;"><b>Plan for week 40</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs002.html#___sec1" style="font-size: 80%;"><b>Overview video for week 40</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs003.html#___sec2" style="font-size: 80%;"><b>Stochastic Gradient Descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs008.html#___sec7" style="font-size: 80%;"><b>When do we stop?</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs009.html#___sec8" style="font-size: 80%;"><b>Slightly different approach</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs010.html#___sec9" style="font-size: 80%;"><b>Program for stochastic gradient</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs011.html#___sec10" style="font-size: 80%;"><b>Momentum based GD</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs012.html#___sec11" style="font-size: 80%;"><b>More on momentum based approaches</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs015.html#___sec14" style="font-size: 80%;"><b>RMS prop</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs016.html#___sec15" style="font-size: 80%;"><b>ADAM optimizer</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs017.html#___sec16" style="font-size: 80%;"><b>Practical tips</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs021.html#___sec20" style="font-size: 80%;"><b>More complicated functions using the elements of their arguments directly</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs022.html#___sec21" style="font-size: 80%;"><b>Functions using mathematical functions from Numpy</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs023.html#___sec22" style="font-size: 80%;"><b>More autograd</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs024.html#___sec23" style="font-size: 80%;"><b>And with loops</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs025.html#___sec24" style="font-size: 80%;"><b>Using recursion</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs026.html#___sec25" style="font-size: 80%;"><b>Unsupported functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs027.html#___sec26" style="font-size: 80%;"><b>The syntax a.dot(b) when finding the dot product</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs028.html#___sec27" style="font-size: 80%;"><b>Recommended to avoid</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs029.html#___sec28" style="font-size: 80%;"><b>Neural networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs030.html#___sec29" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs031.html#___sec30" style="font-size: 80%;"><b>Neural network types</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs032.html#___sec31" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs033.html#___sec32" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs036.html#___sec35" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs037.html#___sec36" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs038.html#___sec37" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs040.html#___sec39" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs041.html#___sec40" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs042.html#___sec41" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs043.html#___sec42" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs044.html#___sec43" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation and activation</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs045.html#___sec44" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Activation functions</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs046.html#___sec45" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Activation functions, Logistic and Hyperbolic ones</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs047.html#___sec46" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Relevance</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs048.html#___sec47" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs049.html#___sec48" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs050.html#___sec49" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs051.html#___sec50" style="font-size: 80%;"><b>Definitions</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs055.html#___sec54" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs057.html#___sec56" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs058.html#___sec57" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
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<center><h1>Week 40: From Stochastic Gradient Descent to Neural networks</h1></center> <!-- document title -->
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<!-- author(s): Morten Hjorth-Jensen -->
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<center><h4>Oct 6, 2020</h4></center> <!-- date -->
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