# CS 5970 Homework 5 — Neuroevolutionary
Basics

## Due Monday, November 9, 2015

## 1. Motivation

One of the simplest forms of neuroevolution is to evolve the weights of
a standard feedforward artificial neural network (ANN). However, there has
been concern regarding what is known variously as "the
structural/functional mapping problem," "competing conventions," or the
"permutation problem." This refers to the possibility that the same
functional relationship between the input and output of the ANN could be
encoded in ways that are different and incompatible from the perspective of
crossover. To understand neuroevolution of weights, it makes sense to
understand the concept of competing conventions.

## 2. Goal

The goal of this assignment is to give you experience with a very simple
version of competing conventions. (Note that the real issue is far more
complex than shown here because the networks may be far larger and with
multiple layers of hidden nodes, the values of arbitrary GAs may be
continuous rather than discrete, and conventions may only need to be
similar rather than exact in order for them to compete.)

## 3. Assignment

Consider the following ANN setup:

- Two binary (0 or 1) input units.
- Three units in a single hidden layer.
- One output unit.
- Feedforward structure that is fully connected between the input layer
and the hidden layer and between the hidden layer and the output
layer.
- Weights are restricted to be integer values in the interval
[0,10].

Now, consider the following genome that represents the weights of the
network:

In the genome, the first three numbers represent the connections between
the first input unit and the three hidden units (in order), the second
three numbers represent the connections between the second input unit and
the three hidden units (in order), and the final three numbers represent
the connections between the hidden units (in order) and the output
unit.

**Draw** the ANN specified here, including its structure and
weights (as given in the genome above).
**List and explain** the possible output values of this ANN for
the possible input values.
**List and explain** at least ten alternative genomes that give
exact competing conventions for the genome given above.

## 4. What to Turn In

You will turn in via D2L a machine readable electronic copy of your
homework that completes the exercises given above.