added execises week 42

doc/LectureNotes/_build/html/exercisesweek41.html

@@ -28,7 +28,7 @@
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
 <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
 
-    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
+    <link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
     <link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
     <link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
     <link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -62,7 +62,7 @@
     <script>DOCUMENTATION_OPTIONS.pagename = 'exercisesweek41';</script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
-    <link rel="next" title="Project 1 on Machine Learning, deadline October 6 (midnight), 2025" href="project1.html" />
+    <link rel="next" title="Exercises week 42" href="exercisesweek42.html" />
     <link rel="prev" title="Week 41 Neural networks and constructing a neural network code" href="week41.html" />
   <meta name="viewport" content="width=device-width, initial-scale=1"/>
   <meta name="docsearch:language" content="en"/>
@@ -246,6 +246,16 @@
 
 
 
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek42.html">Exercises week 42</a></li>
+
+
+
+
+
+
+
+
+
 </ul>
 <p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
 <ul class="nav bd-sidenav">
@@ -435,29 +445,29 @@ doconce format html exercisesweek41.do.txt  -->
 <p>First, here are some functions you are going to need, don’t change this cell. If you are unable to import autograd, just swap in normal numpy until you want to do the final optional exercise.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">autograd.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>  <span class="c1"># We need to use this numpy wrapper to make automatic differentiation work later</span>
-<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">datasets</span>
-<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
-<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">accuracy_score</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>  <span class="c1"># We need to use this numpy wrapper to make automatic differentiation work later</span>
+<span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">accuracy_score</span>
 
 
 <span class="c1"># Defining some activation functions</span>
-<span class="k">def</span><span class="w"> </span><span class="nf">ReLU</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">ReLU</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
     <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">where</span><span class="p">(</span><span class="n">z</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">sigmoid</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">sigmoid</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
     <span class="k">return</span> <span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">z</span><span class="p">))</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">softmax</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">softmax</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Compute softmax values for each set of scores in the rows of the matrix z.</span>
 <span class="sd">    Used with batched input data.&quot;&quot;&quot;</span>
     <span class="n">e_z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span>
     <span class="k">return</span> <span class="n">e_z</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">e_z</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)[:,</span> <span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">]</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">softmax_vec</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">softmax_vec</span><span class="p">(</span><span class="n">z</span><span class="p">):</span>
 <span class="w">    </span><span class="sd">&quot;&quot;&quot;Compute softmax values for each set of scores in the vector z.</span>
 <span class="sd">    Use this function when you use the activation function on one vector at a time&quot;&quot;&quot;</span>
     <span class="n">e_z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">z</span><span class="p">))</span>
@@ -555,7 +565,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p><strong>a)</strong> Complete the function below so that it returns a list <code class="docutils literal notranslate"><span class="pre">layers</span></code> of weight and bias tuples <code class="docutils literal notranslate"><span class="pre">(W,</span> <span class="pre">b)</span></code> for each layer, in order, with the correct shapes that we can use later as our network parameters.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">create_layers</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
     <span class="n">layers</span> <span class="o">=</span> <span class="p">[]</span>
 
     <span class="n">i_size</span> <span class="o">=</span> <span class="n">network_input_size</span>
@@ -573,7 +583,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p><strong>b)</strong> Comple the function below so that it evaluates the intermediary <code class="docutils literal notranslate"><span class="pre">z</span></code> and activation <code class="docutils literal notranslate"><span class="pre">a</span></code> for each layer, with ReLU actication, and returns the final activation <code class="docutils literal notranslate"><span class="pre">a</span></code>. This is the complete feed-forward pass, a full neural network!</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">feed_forward_all_relu</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward_all_relu</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="nb">input</span><span class="p">):</span>
     <span class="n">a</span> <span class="o">=</span> <span class="nb">input</span>
     <span class="k">for</span> <span class="n">W</span><span class="p">,</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">layers</span><span class="p">:</span>
         <span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
@@ -605,7 +615,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p><strong>a)</strong> Complete the <code class="docutils literal notranslate"><span class="pre">feed_forward</span></code> function which accepts a list of activation functions as an argument, and which evaluates these activation functions at each layer.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">feed_forward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">feed_forward</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
     <span class="n">a</span> <span class="o">=</span> <span class="nb">input</span>
     <span class="k">for</span> <span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="n">activation_func</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
         <span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
@@ -639,7 +649,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p><strong>a)</strong> Complete the function <code class="docutils literal notranslate"><span class="pre">create_layers_batch</span></code> so that the weight matrix is the transpose of what it was when you only sent in one input at a time.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">create_layers_batch</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">create_layers_batch</span><span class="p">(</span><span class="n">network_input_size</span><span class="p">,</span> <span class="n">layer_output_sizes</span><span class="p">):</span>
     <span class="n">layers</span> <span class="o">=</span> <span class="p">[]</span>
 
     <span class="n">i_size</span> <span class="o">=</span> <span class="n">network_input_size</span>
@@ -660,7 +670,7 @@ doconce format html exercisesweek41.do.txt  -->
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">inputs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">feed_forward_batch</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">feed_forward_batch</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
     <span class="n">a</span> <span class="o">=</span> <span class="n">inputs</span>
     <span class="k">for</span> <span class="p">(</span><span class="n">W</span><span class="p">,</span> <span class="n">b</span><span class="p">),</span> <span class="n">activation_func</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">):</span>
         <span class="n">z</span> <span class="o">=</span> <span class="o">...</span>
@@ -715,7 +725,7 @@ doconce format html exercisesweek41.do.txt  -->
     <span class="n">targets</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">targets</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">accuracy</span><span class="p">(</span><span class="n">predictions</span><span class="p">,</span> <span class="n">targets</span><span class="p">):</span>
     <span class="n">one_hot_predictions</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">predictions</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
 
     <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">prediction</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">predictions</span><span class="p">):</span>
@@ -758,11 +768,11 @@ doconce format html exercisesweek41.do.txt  -->
 <p>Since we are doing a classification task with multiple output classes, we use the cross-entropy loss function, which can evaluate performance on classification tasks. It sees if your prediction is “most certain” on the correct target.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">cross_entropy</span><span class="p">(</span><span class="n">predict</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">cross_entropy</span><span class="p">(</span><span class="n">predict</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
     <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">-</span><span class="n">target</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">predict</span><span class="p">))</span>
 
 
-<span class="k">def</span><span class="w"> </span><span class="nf">cost</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">cost</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">,</span> <span class="n">target</span><span class="p">):</span>
     <span class="n">predict</span> <span class="o">=</span> <span class="n">feed_forward_batch</span><span class="p">(</span><span class="nb">input</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">)</span>
     <span class="k">return</span> <span class="n">cross_entropy</span><span class="p">(</span><span class="n">predict</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
 </pre></div>
@@ -777,7 +787,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p>Now we need to compute these gradients. This is pretty hard to do for a neural network, we will use most of next week to do this, but we can also use autograd to just do it for us, which is what we always do in practice. With the code cell below, we create a function which takes all of these gradients for us.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">autograd</span><span class="w"> </span><span class="kn">import</span> <span class="n">grad</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
 
 
 <span class="n">gradient_func</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span>
@@ -801,7 +811,7 @@ doconce format html exercisesweek41.do.txt  -->
 <p><strong>c)</strong> Finish the <code class="docutils literal notranslate"><span class="pre">train_network</span></code> function.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">train_network</span><span class="p">(</span>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">train_network</span><span class="p">(</span>
     <span class="n">inputs</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">activation_funcs</span><span class="p">,</span> <span class="n">targets</span><span class="p">,</span> <span class="n">learning_rate</span><span class="o">=</span><span class="mf">0.001</span><span class="p">,</span> <span class="n">epochs</span><span class="o">=</span><span class="mi">100</span>
 <span class="p">):</span>
     <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">epochs</span><span class="p">):</span>
@@ -865,11 +875,11 @@ doconce format html exercisesweek41.do.txt  -->
       </div>
     </a>
     <a class="right-next"
-       href="project1.html"
+       href="exercisesweek42.html"
        title="next page">
       <div class="prev-next-info">
         <p class="prev-next-subtitle">next</p>
-        <p class="prev-next-title">Project 1 on Machine Learning, deadline October 6 (midnight), 2025</p>
+        <p class="prev-next-title">Exercises week 42</p>
       </div>
       <i class="fa-solid fa-angle-right"></i>
     </a>