CS 420/594 Project 3 — Hopfield Net

Due  Nov. 27, 2007

General Description

For Undergraduate Credit

  1. Generate 50 random bipolar vectors (N = 100).
  2. For p = 1, ..., 50, imprint the first p patterns on a Hopfield net.  (The rule for imprinting p patterns is given on Slide 3 in Lecture 22.)
  3. Determine pstable, the number of stable imprinted patterns.  An imprinted pattern is considered unstable if any of its bits are unstable, that is, if bit i is of opposite sign to its local field hi.  Therefore, after imprinting the first p patterns, test each imprinted pattern k (k = 1, …, p) as follows: Initialize the cells to pattern k and compute the local fields hi of each bit. Compare each bit with local field to test for stability.  Repeat for each of the p patterns.  (The computation of the local field is described on slides 17–18 in Lecture 19.)
  4. Compute the probability of an imprinted pattern being stable, Pstable = pstable / p.  (Note that p, Pstable, and pstable are different; this is Bar-Yam’s notation, which I’ve retained for consistency with his book.)
  5. Repeat steps 2–4 for p = 1, ..., 50 and keep track of Pstable for each value of p.
  6. Repeat the forgoing for several sets of 50 random patterns and average over them.

For Graduate Credit

For all Students

If you have any other questions, please email me <maclennan@cs.utk.edu>.

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Last updated: 2007-11-16.