Aim: This homework is an exercise in computing auto-associative memories.

1. We seek to test if the auto-associative network is capable of recalling certain memories. Here you would test if patterns could be completed or recovered. You are given a single pattern s = (1, 1, 1, -1) which is stored in the weights W computed using Hebbian learning.

Find out if the following patterns could be recalled (Yes or No). Show your work and describe how you arrived at each conclusion.

• Training pattern (1 1 1 -1)

• Small noise pattern (-1 1 1 -1)

• Incomplete pattern (0 0 1 -1)

• Large noise pattern (-1 -1 1 -1)