15-883 Homework #6
Computational Models of Neural Systems

Issued: March 16 , 2005. Due: March 23, 2005.

How to Run the Rescorla-Wagner Simulator

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

What the Simulator Does

The simulator offers three conditioned stimuli: cs1, cs2, and cs3. In addition, there is a background stimulus bkg that is always on. A "trial" is defined as a set of zero or more conditioned stimuli paired with either a US or no US. By setting the pushbuttons you can define trials as you wish. Clicking on the associated "train" button runs the trial and updates the weights according to the Rescorla-Wagner learning rule. The buttons are organized as two groups of five trials each, and each group has an "all" button that will train on all the trials in that group, and a "x10" button that will train all the trials 10 times.

Problems

For problems 1-5 below, create an appropriate set of trials, train the model, and then print out the window. You can print the screen to a file by typing print -deps -r300 myfile.ps. Make a separate printout for each problem; these are what you will hand in. Press the "Clear" button when you move on to the next problem. For problem 6, a one paragraph answer should suffice.

  1. Demonstrate blocking. Use one line in the first group of five trials to train on CS1 paired with the US. Note that if you just click on the "train" button for that line, both the CS1 and BKG weights grow. You will need to mix in some trials with no stimuli (but of course BKG will still be present) in order to train the model correctly. (If you use the "all" or "x10" button for this group you will include some of these empty trials.) Train the model for 30 epochs, i.e., 30 sets of trials. You should end up with a positive weight for CS1 but you should not reach asymptote, i.e., the CR value (shown in the gray box to the right of the trial) will not be 1.0.

    Then, use the second group of five trials to train on CS1 and CS2 paired with the US. Train to asymptote and see what the weights look like.

  2. Demonstrate overshadowing. You will need to modify an alpha variable to make one stimulus more salient than the other.

  3. Demonstrate extinction of a conditioned response.

  4. Demonstrate conditioned inhibition, and failure to extinguish a conditioned inhibitor.

  5. Demonstrate the effect of partial reinforcement, where the CS is paired with a US half of the time, and no US the other half of the time.

  6. Set up a trial where CS1 and CS2 are together paired with the US. Set up a second trial where CS1 and CS2 are not paired with the US. Train on all 5 trials (the extra three should be blank) to asymptote. Notice that the CR for the CS1-CS2 trials, shown in the gray box to the right of the trial, is 0.41 rather than 0.5

    Now reduce the Beta parameter from 0.1 to 0.02, click on "Start", and retrain. Notice that the new asymptote is 0.48. Why aren't we reaching the correct asymptotic value, and why does reducing Beta bring us closer to it? Explain what's going on here, paying attention to the form of the weight update rule and the actual values you're seeing in the simulation. (Hint: try running one trial at a time once the weights reach their steady-state value. And try calculating the value of delta-V by hand after a rewarded trial and after an unrewarded trial.)

Dave Touretzky
Last modified: Thu Apr 10 05:36:17 EDT 2003