Exercise 5.1.2

Task: Demonstrate and understand the use of a matrix memory network to store and recall pairs of items.

Load the simulator, BrainWave.

Load the network:

Question 5.1.2.1 What rank tensor does this network implement? The input set contains the items FROG, KOALA and SNAIL, paired with items in the output set FLIES, LEAVES and LETTUCE, respectively. Another input item, TOAD [0.5, 0.4, 0.6, 0.45], can be used to test the network on unfamiliar input. Calculate the similarity value of the items FROG, KOALA, SNAIL and TOAD with themselves, and each other, and record the values in the correlation table below:


















Train the network for one epoch. Test each of the items FROG, KOALA, SNAIL and TOAD.

Question 5.1.2.2 What output is produced in each case? (Give the output pattern and also describe the output patterns in terms of their similarity to FLIES, LEAVES and LETTUCE)

Question 5.1.2.3 Give the algebraic equation that describes the matrix memory formed from the three pairs of associates:
Question 5.1.2.4 Give the equations that describe each of the cued recall tests from question 5.1.2.2. Use the similarity measures from the table above to simplify each equation to a weighted sum of the target patterns.