# Exercise - Neural Network - Pen & Paper

TODO

TODO

## Exercises

Given are the following Informations for a neural network:

\begin{equation} W_{HIDDEN} = \begin{pmatrix} 10 & -20 & 20 & -40 \ 20 & -40 & 0 & 0 \end{pmatrix} \end{equation}

\begin{equation} W_{OUTPUT} = \begin{pmatrix} 20 & 40 & -40 \end{pmatrix} \end{equation}

Each row of $W_{HIDDEN}$ and $W_{OUTPUT}$ represents the weights of one neuron in layer HIDDEN, resp. the OUTPUT layer. The first column equals the bias(es).

Further, activation function $g(z)$, which applies to all neurons in the network:

\begin{equation} g(z)=\left{\begin{array}{cc} 0 & z\le-10\ 1 & z\ge10 \ 0.5 & else\end{array} \right. \end{equation}

### Draw the Network

Draw a graph of the network $N_{SIMPLE}$ including all neurons and their connections. Note all weight and bias values on the corresponding nodes and edges of the graph.

### Calculate the Forwardpass

Use the given vectors $x_1, x_2, x_3$ to create a mini-batch matrix as input for the network and calculate its output. Only use matrix operations for the calculation and note all intermediate results.

\begin{equation} \vec{x}{(1)} = [0,1,1] ,\; \vec{x}{(2)} =[1,1,0] ,\; \vec{x}_{(3)} = [1,0,1] \end{equation}

The following license applies to the complete notebook, including code cells. It does however not apply to any referenced external media (e.g., images).

Exercise - Neural Network - Pen & Paper
by Benjamin Voigt