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Morten Hjorth-Jensen
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@@ -536,11 +536,6 @@ const thebe_selector_output = ".output, .cell_output"
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Mathematics of CNNs
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#id1">
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Mathematics of CNNs
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">
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Convolution Examples: Polynomial multiplication
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@@ -978,11 +973,6 @@ const thebe_selector_output = ".output, .cell_output"
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Mathematics of CNNs
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#id1">
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Mathematics of CNNs
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">
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Convolution Examples: Polynomial multiplication
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@@ -1319,7 +1309,7 @@ doconce format html week44.do.txt --no_mako -->
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<!-- dom:TITLE: Week 44, Convolutional Neural Networks (CNN) --><div class="tex2jax_ignore mathjax_ignore section" id="week-44-convolutional-neural-networks-cnn">
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<h1>Week 44, Convolutional Neural Networks (CNN)<a class="headerlink" href="#week-44-convolutional-neural-networks-cnn" title="Permalink to this headline">¶</a></h1>
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<p><strong>Morten Hjorth-Jensen</strong>, Department of Physics, University of Oslo, Norway</p>
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<p>Date: **October 28-November 1 **</p>
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<p>Date: <strong>October 28</strong></p>
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<div class="section" id="plan-for-week-44">
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<h2>Plan for week 44<a class="headerlink" href="#plan-for-week-44" title="Permalink to this headline">¶</a></h2>
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<p><strong>Material for the lecture Monday October 28, 2024.</strong></p>
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@@ -1330,10 +1320,12 @@ doconce format html week44.do.txt --no_mako -->
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<ul class="simple">
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<li><p>These lecture notes at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/pub/week44/ipynb/week44.ipynb">https://github.com/CompPhysics/MachineLearning/blob/master/doc/pub/week44/ipynb/week44.ipynb</a></p></li>
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<li><p>For a more in depth discussion on neural networks we recommend Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications</p></li>
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<li><p>Reading suggestions for implementation of CNNs see <Rashcka et al.’s chapter 14>:”<a class="reference external" href="https://github.com/rasbt/machine-learning-book/tree/main/ch14">https://github.com/rasbt/machine-learning-book/tree/main/ch14</a>”.</p></li>
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<li><p>Reading suggestions for implementation of CNNs see Rashcka et al.’s chapter 14 at <a class="reference external" href="https://github.com/rasbt/machine-learning-book/tree/main/ch14">https://github.com/rasbt/machine-learning-book/tree/main/ch14</a>.</p></li>
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<li><p>Video on Deep Learning at <a class="reference external" href="https://www.youtube.com/playlist?list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi">https://www.youtube.com/playlist?list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi</a></p></li>
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<li><p>Video on Convolutional Neural Networks from MIT at <a class="reference external" href="https://www.youtube.com/watch?v=iaSUYvmCekI&amp;ab_channel=AlexanderAmini">https://www.youtube.com/watch?v=iaSUYvmCekI&amp;ab_channel=AlexanderAmini</a></p></li>
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<li><p>Video on CNNs from Stanford at <a class="reference external" href="https://www.youtube.com/watch?v=bNb2fEVKeEo&amp;list=PLC1qU-LWwrF64f4QKQT-Vg5Wr4qEE1Zxk&amp;index=6&amp;ab_channel=StanfordUniversitySchoolofEngineering">https://www.youtube.com/watch?v=bNb2fEVKeEo&amp;list=PLC1qU-LWwrF64f4QKQT-Vg5Wr4qEE1Zxk&amp;index=6&amp;ab_channel=StanfordUniversitySchoolofEngineering</a></p></li>
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<li><p>Video of lecture October 28 at <a class="reference external" href="https://youtu.be/rfrSfikAz94">https://youtu.be/rfrSfikAz94</a></p></li>
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<li><p>Whiteboard notes at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOctober28">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOctober28</a></p></li>
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</ul>
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</div>
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<div class="section" id="lab-sessions-on-tuesday-and-wednesday">
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@@ -1342,8 +1334,7 @@ doconce format html week44.do.txt --no_mako -->
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<li><p>Main focus is discussion of and work on project 2</p></li>
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<li><p>If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday</p></li>
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</ul>
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<!-- * [Video of lab session from week 44](https://youtu.be/EajWMW__k0I) -->
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<!-- * [See also whiteboard notes from lab session week 44](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/Exercisesweek44.pdf) --></div>
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</div>
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<div class="section" id="material-for-lecture-monday-october-28">
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<h2>Material for Lecture Monday October 28<a class="headerlink" href="#material-for-lecture-monday-october-28" title="Permalink to this headline">¶</a></h2>
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</div>
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@@ -1723,37 +1714,6 @@ y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
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<p>Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.</p>
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<p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
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</div>
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<div class="section" id="id1">
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<h2>Mathematics of CNNs<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
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<p>The mathematics of CNNs is based on the mathematical operation of
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<strong>convolution</strong>. In mathematics (in particular in functional analysis),
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convolution is represented by mathematical operations (integration,
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summation etc) on two functions in order to produce a third function
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that expresses how the shape of one gets modified by the other.
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Convolution has a plethora of applications in a variety of
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disciplines, spanning from statistics to signal processing, computer
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vision, solutions of differential equations,linear algebra,
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engineering, and yes, machine learning.</p>
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<p>Mathematically, convolution is defined as follows (one-dimensional example):
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Let us define a continuous function <span class="math notranslate nohighlight">\(y(t)\)</span> given by</p>
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<div class="math notranslate nohighlight">
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\[
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y(t) = \int x(a) w(t-a) da,
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\]</div>
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<p>where <span class="math notranslate nohighlight">\(x(a)\)</span> represents a so-called input and <span class="math notranslate nohighlight">\(w(t-a)\)</span> is normally called the weight function or kernel.</p>
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<p>The above integral is written in a more compact form as</p>
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<div class="math notranslate nohighlight">
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\[
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y(t) = \left(x * w\right)(t).
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\]</div>
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<p>The discretized version reads</p>
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<div class="math notranslate nohighlight">
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\[
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y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
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\]</div>
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<p>Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.</p>
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<p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
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</div>
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<div class="section" id="convolution-examples-polynomial-multiplication">
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<h2>Convolution Examples: Polynomial multiplication<a class="headerlink" href="#convolution-examples-polynomial-multiplication" title="Permalink to this headline">¶</a></h2>
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<p>Our first example is that of a multiplication between two polynomials,
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@@ -2289,7 +2249,7 @@ classification.</p>
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labels = (n_inputs) = (1797,)
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</pre></div>
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</div>
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<img alt="_images/week44_125_1.png" src="_images/week44_125_1.png" />
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<img alt="_images/week44_118_1.png" src="_images/week44_118_1.png" />
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</div>
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</div>
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</div>
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@@ -8,7 +8,7 @@
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# # Week 44, Convolutional Neural Networks (CNN)
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# **Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway
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#
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# Date: **October 28-November 1 **
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# Date: **October 28**
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# ## Plan for week 44
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#
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@@ -22,21 +22,23 @@
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#
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# * For a more in depth discussion on neural networks we recommend Goodfellow et al chapter 9. See also chapter 11 and 12 on practicalities and applications
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#
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# * Reading suggestions for implementation of CNNs see <Rashcka et al.'s chapter 14>:"https://github.com/rasbt/machine-learning-book/tree/main/ch14".
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# * Reading suggestions for implementation of CNNs see Rashcka et al.'s chapter 14 at <https://github.com/rasbt/machine-learning-book/tree/main/ch14>.
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#
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# * Video on Deep Learning at <https://www.youtube.com/playlist?list=PLZHQObOWTQDNU6R1_67000Dx_ZCJB-3pi>
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#
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# * Video on Convolutional Neural Networks from MIT at <https://www.youtube.com/watch?v=iaSUYvmCekI&ab_channel=AlexanderAmini>
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#
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# * Video on CNNs from Stanford at <https://www.youtube.com/watch?v=bNb2fEVKeEo&list=PLC1qU-LWwrF64f4QKQT-Vg5Wr4qEE1Zxk&index=6&ab_channel=StanfordUniversitySchoolofEngineering>
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#
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# * Video of lecture October 28 at <https://youtu.be/rfrSfikAz94>
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#
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# * Whiteboard notes at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2024/NotesOctober28>
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# ## Lab sessions on Tuesday and Wednesday
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#
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# * Main focus is discussion of and work on project 2
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#
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# * If you did not get time to finish the exercises from week 43, you can also keep working on them and hand in this coming Friday
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# <!-- * [Video of lab session from week 44](https://youtu.be/EajWMW__k0I) -->
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# <!-- * [See also whiteboard notes from lab session week 44](https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/Exercisesweek44.pdf) -->
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# ## Material for Lecture Monday October 28
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@@ -337,43 +339,6 @@ for k in (5,10, 20, 100,200,400,500):
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print('Signa to noise ratio '+ str(round(srv)) +'dB')
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# ## Mathematics of CNNs
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#
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# The mathematics of CNNs is based on the mathematical operation of
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# **convolution**. In mathematics (in particular in functional analysis),
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# convolution is represented by mathematical operations (integration,
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# summation etc) on two functions in order to produce a third function
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# that expresses how the shape of one gets modified by the other.
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# Convolution has a plethora of applications in a variety of
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# disciplines, spanning from statistics to signal processing, computer
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# vision, solutions of differential equations,linear algebra,
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# engineering, and yes, machine learning.
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#
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# Mathematically, convolution is defined as follows (one-dimensional example):
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# Let us define a continuous function $y(t)$ given by
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# $$
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# y(t) = \int x(a) w(t-a) da,
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# $$
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# where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel.
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#
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# The above integral is written in a more compact form as
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# $$
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# y(t) = \left(x * w\right)(t).
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# $$
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# The discretized version reads
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# $$
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# y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
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# $$
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# Computing the inverse of the above convolution operations is known as deconvolution and the process is commutative.
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#
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# How can we use this? And what does it mean? Let us study some familiar examples first.
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# ## Mathematics of CNNs
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#
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# The mathematics of CNNs is based on the mathematical operation of
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