Morten Hjorth-Jensen
314 lines
18 KiB
HTML
314 lines
18 KiB
HTML
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<a class="navbar-brand" href="week40-bs.html">Week 40: Gradient descent methods (continued) and start Neural networks</a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week40-bs001.html#lecture-monday-september-30-2024" style="font-size: 80%;"><b>Lecture Monday September 30, 2024</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs002.html#suggested-readings-and-videos" style="font-size: 80%;"><b>Suggested readings and videos</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs003.html#lab-sessions-tuesday-and-wednesday" style="font-size: 80%;"><b>Lab sessions Tuesday and Wednesday</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs004.html#automatic-differentiation" style="font-size: 80%;"><b>Automatic differentiation</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs005.html#using-autograd" style="font-size: 80%;"><b>Using autograd</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs006.html#autograd-with-more-complicated-functions" style="font-size: 80%;"><b>Autograd with more complicated functions</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs007.html#more-complicated-functions-using-the-elements-of-their-arguments-directly" style="font-size: 80%;"><b>More complicated functions using the elements of their arguments directly</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs008.html#functions-using-mathematical-functions-from-numpy" style="font-size: 80%;"><b>Functions using mathematical functions from Numpy</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs009.html#more-autograd" style="font-size: 80%;"><b>More autograd</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs010.html#and-with-loops" style="font-size: 80%;"><b>And with loops</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs011.html#using-recursion" style="font-size: 80%;"><b>Using recursion</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs012.html#using-autograd-with-ols" style="font-size: 80%;"><b>Using Autograd with OLS</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs015.html#same-code-but-now-with-momentum-gradient-descent" style="font-size: 80%;"><b>Same code but now with momentum gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs014.html#including-stochastic-gradient-descent-with-autograd" style="font-size: 80%;"><b>Including Stochastic Gradient Descent with Autograd</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs015.html#same-code-but-now-with-momentum-gradient-descent" style="font-size: 80%;"><b>Same code but now with momentum gradient descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs016.html#similar-second-order-function-now-problem-but-now-with-adagrad" style="font-size: 80%;"><b>Similar (second order function now) problem but now with AdaGrad</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs017.html#rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent" style="font-size: 80%;"><b>RMSprop for adaptive learning rate with Stochastic Gradient Descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs018.html#and-finally-adam-https-arxiv-org-pdf-1412-6980-pdf" style="font-size: 80%;"><b>And finally "ADAM":"https://arxiv.org/pdf/1412.6980.pdf"</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs019.html#and-logistic-regression" style="font-size: 80%;"><b>And Logistic Regression</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs019.html#introducing-jax-https-jax-readthedocs-io-en-latest" style="font-size: 80%;"><b>Introducing "JAX":"https://jax.readthedocs.io/en/latest/"</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs019.html#getting-started-with-jax-note-the-way-we-import-numpy" style="font-size: 80%;"> Getting started with Jax, note the way we import numpy</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs019.html#a-warm-up-example" style="font-size: 80%;"> A warm-up example</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs019.html#a-more-advanced-example" style="font-size: 80%;"> A more advanced example</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs020.html#introduction-to-neural-networks" style="font-size: 80%;"><b>Introduction to Neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs021.html#artificial-neurons" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs022.html#neural-network-types" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs023.html#feed-forward-neural-networks" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs024.html#convolutional-neural-network" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs025.html#recurrent-neural-networks" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs026.html#other-types-of-networks" style="font-size: 80%;"><b>Other types of networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs027.html#multilayer-perceptrons" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs028.html#why-multilayer-perceptrons" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs029.html#illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model" style="font-size: 80%;"><b>Illustration of a single perceptron model and a multi-perceptron model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs030.html#examples-of-xor-or-and-and-gates" style="font-size: 80%;"><b>Examples of XOR, OR and AND gates</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs031.html#does-logistic-regression-do-a-better-job" style="font-size: 80%;"><b>Does Logistic Regression do a better Job?</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs032.html#adding-neural-networks" style="font-size: 80%;"><b>Adding Neural Networks</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs037.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs037.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs037.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs037.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs037.html#mathematical-model" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs038.html#matrix-vector-notation" style="font-size: 80%;"> Matrix-vector notation</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs039.html#matrix-vector-notation-and-activation" style="font-size: 80%;"> Matrix-vector notation and activation</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs040.html#activation-functions" style="font-size: 80%;"> Activation functions</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs041.html#activation-functions-logistic-and-hyperbolic-ones" style="font-size: 80%;"> Activation functions, Logistic and Hyperbolic ones</a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs042.html#relevance" style="font-size: 80%;"> Relevance</a></li>
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</ul>
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<a name="part0000"></a>
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<!-- ------------------- main content ---------------------- -->
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<center>
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<h1>Week 40: Gradient descent methods (continued) and start Neural networks</h1>
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</center> <!-- document title -->
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b>
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</center>
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<!-- institution -->
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<center>
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<b>Department of Physics, University of Oslo, Norway</b>
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</center>
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<br>
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<center>
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<h4>September 29-October 3, 2025</h4>
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</center> <!-- date -->
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<br>
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<p><a href="._week40-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
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<li class="active"><a href="._week40-bs000.html">1</a></li>
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<li><a href="._week40-bs001.html">2</a></li>
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<li><a href="._week40-bs002.html">3</a></li>
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<li><a href="._week40-bs003.html">4</a></li>
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<li><a href="._week40-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week40-bs042.html">43</a></li>
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