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schedule/slides/21-nnets-intro.html

@@ -333,7 +333,7 @@
 <h2>21 Neural nets</h2>
 <p><span class="secondary">Stat 406</span></p>
 <p><span class="secondary">Geoff Pleiss, Trevor Campbell</span></p>
-<p>Last modified – 06 November 2024</p>
+<p>Last modified – 13 November 2024</p>
 <p><span class="math display">\[
 \DeclareMathOperator*{\argmin}{argmin}
 \DeclareMathOperator*{\argmax}{argmax}
@@ -478,8 +478,20 @@ <h2>Terminology</h2>
 <p><span class="math inline">\(w_k \in \R^p,\ k = 1,\ldots,K\)</span></p>
 <p><span class="math inline">\(\mathbf{W} \in \R^{K\times p}\)</span></p>
 </section>
-<section id="what-about-classification-10-classes-2-layers" class="slide level2">
-<h2>What about classification (10 classes, 2 layers)</h2>
+<section id="deep-nets" class="slide level2">
+<h2>Deep nets</h2>
+<p>Some comments on adding layers:</p>
+<ul>
+<li><p>It has been shown that one hidden layer is sufficient to approximate any bounded piecewise continuous function</p></li>
+<li><p>However, this may take a huge number of hidden units (i.e.&nbsp;<span class="math inline">\(K_1 \gg 1\)</span>).</p></li>
+<li><p>This is what people mean when they say that NNets are “universal approximators”</p></li>
+<li><p>By including multiple layers, we can have fewer hidden units per layer.</p></li>
+<li><p>Also, we can encode (in)dependencies that can speed computations</p></li>
+<li><p>We don’t have to connect everything the way we have been</p></li>
+</ul>
+</section>
+<section id="deep-nets-example-10-class-classification-2-layers" class="slide level2">
+<h2>Deep nets example (10 class classification, 2 layers)</h2>
 <div class="flex">
 <div class="w-40">
 <p><span class="math display">\[
@@ -501,8 +513,8 @@ <h2>What about classification (10 classes, 2 layers)</h2>
 </div>
 <p>Predict class with largest probability <span class="math inline">\(\longrightarrow\ \widehat{Y} = \argmax_{m} f_m(x)\)</span></p>
 </section>
-<section id="what-about-classification-10-classes-2-layers-1" class="slide level2">
-<h2>What about classification (10 classes, 2 layers)</h2>
+<section id="deep-nets-example-10-class-classification-2-layers-1" class="slide level2">
+<h2>Deep nets example (10 class classification, 2 layers)</h2>
 <div class="flex">
 <div class="w-40">
 <p>Notes:</p>
@@ -516,9 +528,9 @@ <h2>What about classification (10 classes, 2 layers)</h2>
 <p><img data-src="gfx/two-layer-net.svg" class="quarto-figure quarto-figure-center" width="500"></p>
 </figure>
 </div>
+<div class="git">
+
 </div>
-</div>
-</section>
 <section id="nonlinear-activation-functions" class="slide level2">
 <h2>(Nonlinear) activation functions</h2>
 
@@ -574,6 +586,10 @@ <h1>Next time…</h1>
 <div class="quarto-auto-generated-content">
 <div class="footer footer-default">
 <p>UBC Stat 406 - 2024</p>
+</div>
+</div>
+</section>
+
 </div>
 </div>
 </section>