Covariation Learning and Auto-Associative Memory Chapter 4, Tutorial on Neural Systems Modeling, Anastasio Learning Objectives: After mastering the material in this lesson, you should be able to: explain how the principle “neuron that fire together, wire together” can by used in neural circuits to store memories compute, by hand, the change in synaptic weights in a neuronal network due to different stimulus patterns use computer code to simulate memory formation and recall in a neuronal network

A simple model of habituation in Aplysia Input x contacts y with weight v Tutorial on Neural Systems Modeling, Anastasio, p. 7

Donald Hebb Neurons that fire together, wire together.

Auto-associator neural network Strengthened connections between activated neurons Pattern of activity from sensory input (e.g., hearing a song) --note that the connections that do NOT form are just as important as the connections that DO form --called an “auto-associative neural network” because it learns to associate different neurons with each other Entire pattern recovered Partial pattern presented (e.g., first few notes from a song)

4 different learning rules --for “post-synaptic,” you ‘punish’ the connection if the post-synaptic neuron is active when the pre-synaptic neuron is not “punish” when post-syn neuron is active when pre-syn is not Not biological— but useful

Summing over multiple patterns Pattern index Hebb Hopfield Pre-synaptic Post-synaptic i Pre-syn neuron index Post-syn neuron index Anastasio, p. 103

Implementing the Hopfield rule in a simple network Hopfield i p1 = [1 1 0] p2 = [0 0 1] How do the weights change when these two patterns are presented?

Set P = [1 1 0; 0 0 1; 1 0 1] What is the resulting matrix HP Set P = [1 1 0; 0 0 1; 1 0 1] What is the resulting matrix HP? Can you explain the change? HP measures the covariance between two neurons. The more they “do the same thing,” the more positive their connections become. The more they “do the opposite things,” the more negative their connections become. If they do the same thing half the time and the opposite thing half the time, their connection strength will be zero.

Run autoConnectivity.m for P = [1 1 1 1 0 0 0 0 0 0; 0 0 0 0 0 0 1 1 1 1] Compare the results for the four different learning rules.

Results for four different learning rules