University of Washington, Bothell

CSS 485: Introduction to Artificial Neural Networks
Fall 2002
Homework Assignment 5: Backpropagation

Assigned: Wednesday, November 27, 2002
Due: Wednesday, December 11, 2002 (start of class)

1. In this problem, you are asked to solve the same pattern recognition problem as in homework 4. To review, the input patterns are:
   $$\begin{array}{\vert c\vert c\vert c\vert c\vert c\vert}\hlin... ...-0.5mm]{3mm}{3mm}& \rule[-0.5mm]{3mm}{3mm}\\ \hline \end{array}$$

   Your network should have a single hidden layer and three outputs, with each corresponding to one of the three characters. In other words, the outputs for the three patterns should be:

   $$\mathbf{t}_0 = [\begin{array}{rrr}1 & 0 & 0\end{array}]\ensuremat... ...athbf{t}_2 = [\begin{array}{rrr}0 & 0 & 1\end{array}]\ensuremath{^{\mathsf{T}}}$$

   Write code to implement the forward computation of such a network and the error backpropagation and weight update of backpropagation learning. I leave it up to you to test your code for smaller networks and simpler problems. Verify the operation of the network for ``clean'' input. Next, investigate the network's ability to retrieve ``damaged'' patterns. Do this by producing ``noisy'' patterns, in which $n$ elements of a pattern are ``flipped'' (1 changed to 0; 0 to 1). Select the elements to flip randomly, and run multiple trials for each value of $n$ and each pattern. For each value of $n$, you should get a single value which is the fraction of noisy patterns which were correctly recalled. Plot that fraction versus $n$.

2. For extra credit, build a backpropagation network that outputs the ASCII code for each of the characters above (it will have 7 outputs).