update project 2

Author: mhjensen

doc/Projects/2025/Project2/html/._Project2-bs000.html

@@ -243,14 +243,14 @@ <h2 id="classification-and-regression-writing-our-own-neural-network-code" class
 <p>The data sets that we propose here are (the default sets)</p>
 
 <ul>
-<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be
-<ol type="a"></li>
- <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. You should however feel free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_self"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
-</ol>
-<li> Classification.
-<ol type="a"></li>
- <li> We will consider the multiclass classification problem given by the full MNIST data set. The one  included in <b>scikit-learn</b> is  reduced data. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_self"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li> 
-</ol>
+<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be</li>
+<ul>
+  <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_self"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
+</ul>
+<li> Classification.</li>
+<ul>
+ <li> We will consider a multiclass classification problem given by the full MNIST data set. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_self"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li>
+</ul>
 </ul>
 <p>We will start with a regression problem and we will reuse our codes on gradient descent methods from project 1.</p>
 <h3 id="part-a-analytical-warm-up" class="anchor">Part a): Analytical warm-up </h3>
@@ -260,10 +260,10 @@ <h3 id="part-a-analytical-warm-up" class="anchor">Part a): Analytical warm-up </
 </p>
 <ol>
 <li> The mean-squared error (MSE) with and without the \( L_1 \) and \( L_2 \) norms (regression problems)</li>
-<li> The binary cross entropy (aka log loss)  for classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
+<li> The binary cross entropy (aka log loss)  for binary classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
 <li> The multiclass cross entropy cost/loss function (aka Softmax cross entropy or just Softmax loss function)</li>
 </ol>
-<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms.</p>
+<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms. In this project you will however only use the MSE and the Softmax  cross entropy.</p>
 
 <p>We will test three activation functions for our neural network setup, these are the </p>
 <ol>
@@ -330,7 +330,7 @@ <h3 id="part-b-writing-your-own-neural-network-code" class="anchor">Part b): Wri
 <p>Comment your results and give a critical discussion of the results
 obtained with the OLS code from project 1 and your own neural network
 code.  Make an analysis of the learning rates employed to find the
-optimal MSE and \( R2 \) scores. Test both stochastic gradient descent
+optimal MSE score. Test both stochastic gradient descent
 with RMSprop and ADAM and plain gradient descent with different
 learning rates.
 </p>

doc/Projects/2025/Project2/html/Project2-bs.html

@@ -243,14 +243,14 @@ <h2 id="classification-and-regression-writing-our-own-neural-network-code" class
 <p>The data sets that we propose here are (the default sets)</p>
 
 <ul>
-<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be
-<ol type="a"></li>
- <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. You should however feel free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_self"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
-</ol>
-<li> Classification.
-<ol type="a"></li>
- <li> We will consider the multiclass classification problem given by the full MNIST data set. The one  included in <b>scikit-learn</b> is  reduced data. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_self"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li> 
-</ol>
+<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be</li>
+<ul>
+  <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_self"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
+</ul>
+<li> Classification.</li>
+<ul>
+ <li> We will consider a multiclass classification problem given by the full MNIST data set. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_self"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li>
+</ul>
 </ul>
 <p>We will start with a regression problem and we will reuse our codes on gradient descent methods from project 1.</p>
 <h3 id="part-a-analytical-warm-up" class="anchor">Part a): Analytical warm-up </h3>
@@ -260,10 +260,10 @@ <h3 id="part-a-analytical-warm-up" class="anchor">Part a): Analytical warm-up </
 </p>
 <ol>
 <li> The mean-squared error (MSE) with and without the \( L_1 \) and \( L_2 \) norms (regression problems)</li>
-<li> The binary cross entropy (aka log loss)  for classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
+<li> The binary cross entropy (aka log loss)  for binary classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
 <li> The multiclass cross entropy cost/loss function (aka Softmax cross entropy or just Softmax loss function)</li>
 </ol>
-<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms.</p>
+<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms. In this project you will however only use the MSE and the Softmax  cross entropy.</p>
 
 <p>We will test three activation functions for our neural network setup, these are the </p>
 <ol>
@@ -330,7 +330,7 @@ <h3 id="part-b-writing-your-own-neural-network-code" class="anchor">Part b): Wri
 <p>Comment your results and give a critical discussion of the results
 obtained with the OLS code from project 1 and your own neural network
 code.  Make an analysis of the learning rates employed to find the
-optimal MSE and \( R2 \) scores. Test both stochastic gradient descent
+optimal MSE score. Test both stochastic gradient descent
 with RMSprop and ADAM and plain gradient descent with different
 learning rates.
 </p>

doc/Projects/2025/Project2/html/Project2.html

@@ -278,14 +278,14 @@ <h2 id="classification-and-regression-writing-our-own-neural-network-code">Class
 <p>The data sets that we propose here are (the default sets)</p>
 
 <ul>
-<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be
-<ol type="a"></li>
- <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. You should however feel free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_blank"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
-</ol>
-<li> Classification.
-<ol type="a"></li>
- <li> We will consider the multiclass classification problem given by the full MNIST data set. The one  included in <b>scikit-learn</b> is  reduced data. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_blank"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li> 
-</ol>
+<li> Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be</li>
+<ul>
+  <li> The simple one-dimensional function Runge function from project 1, that is \( f(x) = \frac{1}{1+25x^2} \). We recommend using a simpler function when developing your neural network code for regression problems. Feel however free to discuss and study other functions, such as the the two-dimensional Runge function \( f(x,y)=\left[(10x - 5)^2 + (10y - 5)^2 + 1 \right]^{-1} \), or even more complicated two-dimensional functions (see the supplementary material of <a href="https://www.nature.com/articles/s41467-025-61362-4" target="_blank"><tt>https://www.nature.com/articles/s41467-025-61362-4</tt></a> for an extensive list of two-dimensional functions).</li> 
+</ul>
+<li> Classification.</li>
+<ul>
+ <li> We will consider a multiclass classification problem given by the full MNIST data set. The full data set is at <a href="https://www.kaggle.com/datasets/hojjatk/mnist-dataset" target="_blank"><tt>https://www.kaggle.com/datasets/hojjatk/mnist-dataset</tt></a>.</li>
+</ul>
 </ul>
 <p>We will start with a regression problem and we will reuse our codes on gradient descent methods from project 1.</p>
 <h3 id="part-a-analytical-warm-up">Part a): Analytical warm-up </h3>
@@ -295,10 +295,10 @@ <h3 id="part-a-analytical-warm-up">Part a): Analytical warm-up </h3>
 </p>
 <ol>
 <li> The mean-squared error (MSE) with and without the \( L_1 \) and \( L_2 \) norms (regression problems)</li>
-<li> The binary cross entropy (aka log loss)  for classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
+<li> The binary cross entropy (aka log loss)  for binary classification problems with and without \( L_1 \) and \( L_2 \) norms</li>
 <li> The multiclass cross entropy cost/loss function (aka Softmax cross entropy or just Softmax loss function)</li>
 </ol>
-<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms.</p>
+<p>Set up these three cost/loss functions and their respective derivatives and explain the various terms. In this project you will however only use the MSE and the Softmax  cross entropy.</p>
 
 <p>We will test three activation functions for our neural network setup, these are the </p>
 <ol>
@@ -365,7 +365,7 @@ <h3 id="part-b-writing-your-own-neural-network-code">Part b): Writing your own N
 <p>Comment your results and give a critical discussion of the results
 obtained with the OLS code from project 1 and your own neural network
 code.  Make an analysis of the learning rates employed to find the
-optimal MSE and \( R2 \) scores. Test both stochastic gradient descent
+optimal MSE score. Test both stochastic gradient descent
 with RMSprop and ADAM and plain gradient descent with different
 learning rates.
 </p>