# 15-883 Homework #5

Computational Models of Neural Systems

Issued: November 9, 2015. Due: November 16, 2015.
This homework is based on the Baxter & Byrne reading from section 4.1.

### How to Run the Synaptic Learning Rules Demo

You should cd to the directory matlab/ltp, or
download the file ltp.zip and
unzip it. When you're ready to begin, type "matlab" to start up
Matlab. Then type "run" to start the demo.

### Questions

- Create a pure Hebbian learning rule. Describe the performance on
in-phase, antiphase, and random stimulus patterns. (Note: the inputs
vary between 0 and 1, not -1 and 1. Also, the time scale for the
random pattern is different than for the sine wave patterns.)

- Add an exponential weight decay term to your learning rule; set
the delta parameter to 0.01. Describe the performance on the above
three patterns.

- For random inputs (uniformly distributed between 0 and 1), the
learning rule you constructed is moving the weight towards an
asymptotic value. At asymptote, dw/dt = 0. Use this fact, the
learning rule, and the alpha and delta parameter values of your
simulation, to solve for the asymptotic value of the weight. Show
your work.

- Verify the asymptote by changing w
_{AB}(0) from 0.5 to
4.0. Notice that the weight trends downward over time. Now set the
initial weight to the value you calculated for the asymptote. What do
you see?

- Reset all parameters by clicking on the green Reset button. Once
again, compare the response of Hebbian learning with exponential
weight decay in the in-phase vs. anti-phase cases. Can we approximate
this behavior using only the non-associative terms? Set the gamma
parameter to 0.0125. Turn off the the Hebbian learning and weight
decay terms (first and fourth buttons). Using only the second and
third buttons, find a nonassociative learning rule that behaves
similarly to the Hebbian-with-decay rule in both the in-phase and
anti-phase cases. It need only be qualitatively similar, not an exact
numerical match. Write down your learning rule.

- How does your non-associative learning rule compare to the
Hebbian-with-decay rule (using a value of 0.01 for delta) on random
inputs?

Last modified: Sun Nov 29 18:42:52 EST 2015