Exercise 5.1.3

Task: Demonstrate and understand use of a rank three tensor network to store and recall triples of items. Compare and contrast the performance of a rank two versus a rank three network given equivalent input.

Load the simulator, BrainWave.

Load the network:

Question 5.1.3.1 What rank tensor does this network implement?

The items in this exercise comprise

Cues:

Relations: Targets: The cue+relation input set contains the items FROG-EATS, KOALA-EATS, SNAIL-EATS, FROG-LIVES_IN, KOALA-LIVES_IN and SNAIL-LIVES_IN, paired with items in the output set FLIES, LEAVES, LETTUCE, POND, TREE, and SHELL, respectively. Two other input items, TOAD-EATS and TOAD-LIVES_IN, can be used to test the network's response to unfamiliar input.

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

Question 5.1.3.2 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, LETTUCE, POND, TREE and SHELL)

Question 5.1.3.3 How does the performance of this network compare with the performance of the network in Exercise 5.1.2? Why is it not as good?

Question 5.1.3.4 Give the algebraic equation that describes the matrix memory formed from the three pairs of associates:

Question 5.1.3.5 Give the equations that describe each of the cued recall tests from question 5.1.3.2. Use the similarity measures from the table above to simplify each equation to a weighted sum of the target patterns. Load a new network: Question 5.1.3.6 What rank tensor does this network implement?

The inputs and outputs for this network are the same as for the previous one, but the connections and hidden SigmaPi units perform different calculations on the inputs to try and achieve the correct outputs.

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

Question 5.1.3.7 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, LETTUCE, POND, TREE and SHELL)

Question 5.1.3.8 Which of the two networks performs the memory task better? Why?




Question 5.1.3.9 Give the algebraic equation that describes the matrix memory formed from the three pairs of associates:

Question 5.1.3.10 Give the equations that describe each of the cued recall tests from question 5.1.3.7. Use the similarity measures from the table above to simplify each equation to a weighted sum of the target patterns.