Update ddasp_exercise_slides.tex

bugfix wording: perceptron -> neuron

Author: fs446

slides/ddasp_exercise_slides.tex

@@ -2977,9 +2977,9 @@ \subsection{Fundamentals}
 
 \begin{frame}[t]{Output Layer for Regression Model}
 
-$\cdot$ Output layer exhibits $i=1 \dots K$ perceptrons
+$\cdot$ Output layer exhibits $i=1 \dots K$ neurons
 
-$\cdot$ Activation function $\sigma(\cdot)$ for $i\text{-th}$ perceptron: \underline{linear}
+$\cdot$ Activation function $\sigma(\cdot)$ for $i\text{-th}$ neuron: \underline{linear}
 
 $$\sigma(z_i) = z_i$$
 
@@ -2993,9 +2993,9 @@ \subsection{Fundamentals}
 
 \begin{frame}[t]{Output Layer for Binary Classification Model}
 
-$\cdot$ Output layer exhibits two perceptrons with shared input weights, hence acting on same $z$
+$\cdot$ Output layer exhibits two neurons with shared input weights, hence acting on same $z$
 
-$\cdot$ Activation functions $\sigma(\cdot)_{1,2}$ for the two perceptrons: \underline{sigmoid} / complementary sigmoid
+$\cdot$ Activation functions $\sigma(\cdot)_{1,2}$ for the two neurons: \underline{sigmoid} / complementary sigmoid
 
 $$\sigma_1(z) = \frac{1}{1+\e^{-z}} = \frac{\e^{z}}{\e^{z}+1} \qquad\qquad \sigma_2(z) = 1-\sigma_1(z) = \frac{1}{1 + \e^{z}} = \frac{\e^{-z}}{\e^{-z}+1}$$
 
@@ -3029,9 +3029,9 @@ \subsection{Fundamentals}
 
 \begin{frame}[t]{Output Layer for Binary Classification Model}
 
-$\cdot$ Output layer exhibits a single perceptron
+$\cdot$ Output layer exhibits a single neuron
 
-$\cdot$ Activation function $\sigma(\cdot)$ for this single output perceptron: \underline{sigmoid}
+$\cdot$ Activation function $\sigma(\cdot)$ for this single output neuron: \underline{sigmoid}
 
 $$\sigma(z) = \frac{1}{1+\e^{-z}} = \frac{\e^{z}}{\e^{z}+1}$$
 
@@ -3064,15 +3064,15 @@ \subsection{Fundamentals}
 
 \begin{frame}[t]{Output Layer for Multi-Class Classification Model}
 
-$\cdot$ Output layer exhibits $i=1 \dots K$ perceptrons for $K$ mutually exclusive classes
+$\cdot$ Output layer exhibits $i=1 \dots K$ neurons for $K$ mutually exclusive classes
 
-$\cdot$ Activation function $\sigma(\cdot)$ for $i\text{-th}$ perceptron: \underline{softmax}
+$\cdot$ Activation function $\sigma(\cdot)$ for $i\text{-th}$ neuron: \underline{softmax}
 
 $$
 \sigma(z_i) = \frac{\e^{z_i}}{\sum\limits_{i'=1}^{K} \e^{z_{i'}}} \qquad \text{hence, }\sum\limits_{i=1}^{K} \sigma(z_i) = 1
-\text{, which couples the perceptrons}
+\text{, which couples the neurons}
 $$
-%which couples the perceptrons in the output layer
+%which couples the neurons in the output layer
 
 $\cdot$ Derivatives to set up the Jacobian matrix
 
@@ -3127,7 +3127,7 @@ \subsection{Exercise 11}
 \begin{itemize}
 \item XOR is a classification problem, which cannot be handled by linear algebra
 \item introduce two nonlinearities: add bias, non-linear activation function
-\item perceptron concept
+\item neuron / perceptron concept
 \item general architecture of non-linear models
 \end{itemize}
 \end{frame}
@@ -3357,7 +3357,7 @@ \subsection{Exercise 11}
 
 \begin{frame}[t]{A Non-Linear Model for XOR}
 
-$\cdot$ weight matrix and bias vector to represent perceptron \textcolor{C0}{1} and \textcolor{C3}{2}
+$\cdot$ weight matrix and bias vector to represent neurons \textcolor{C0}{1} and \textcolor{C3}{2}
 $$
 \bm{W}_\text{layer 1} =
 \begin{bmatrix}
@@ -3373,7 +3373,7 @@ \subsection{Exercise 11}
 \end{bmatrix}
 $$
 
-$\cdot$ weight vector and bias scalar to represent perceptron \textcolor{C1}{3}
+$\cdot$ weight vector and bias scalar to represent neuron \textcolor{C1}{3}
 $$
 \bm{W}_\text{layer 2} =
 \begin{bmatrix}
@@ -3416,7 +3416,7 @@ \subsection{Exercise 11}
 
 $\cdot$ solution known from book Goodfellow et al. (2016): Deep Learning. MIT Press, Ch. 6.1
 
-$\cdot$ weight matrix and bias vector to represent perceptron \textcolor{C0}{1} and \textcolor{C3}{2}
+$\cdot$ weight matrix and bias vector to represent neurons \textcolor{C0}{1} and \textcolor{C3}{2}
 $$
 \bm{W}_\text{layer 1} =
 \begin{bmatrix}
@@ -3432,7 +3432,7 @@ \subsection{Exercise 11}
 \end{bmatrix}
 $$
 
-$\cdot$ weight vector and bias scalar to represent perceptron \textcolor{C1}{3}
+$\cdot$ weight vector and bias scalar to represent neuron \textcolor{C1}{3}
 $$
 \bm{W}_\text{layer 2} =
 \begin{bmatrix}
@@ -3616,7 +3616,7 @@ \subsection{Exercise 12}
 \end{tikzpicture}
 \end{center}
 
-$\cdot$ Activation function $\sigma(\cdot)$ for this single output perceptron: \underline{sigmoid}
+$\cdot$ Activation function $\sigma(\cdot)$ for this single output neuron: \underline{sigmoid}
 
 $$\hat{y} = \sigma(z) = \frac{1}{1+\e^{-z}} = \frac{\e^{z}}{\e^{z}+1}\qquad\qquad
 \frac{\partial \sigma(z)}{\partial z} = \frac{\e^{z}}{(\e^{z}+1)^2} = \sigma(z) \cdot (1-\sigma(z))