Exercise - Neural Network - Pen & Paper

Introduction

TODO

Requirements

Knowledge

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 WHIDDENW_{HIDDEN} and WOUTPUTW_{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)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

Task:

Draw a graph of the network NSIMPLEN_{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 x1,x2,x3x_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}

Licenses

Notebook License (CC-BY-SA 4.0)

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
is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://gitlab.com/deep.TEACHING.

Code License (MIT)

The following license only applies to code cells of the notebook.

Copyright 2018 Benjamin Voigt

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