Learning by random walks in the weight space of the Ising perceptron

TL;DR

This paper investigates stochastic local search methods, specifically random walks, for training Ising perceptrons, achieving high storage capacities and analyzing the structure of learned solutions in weight space.

Contribution

It introduces a random walk learning process for Ising perceptrons and demonstrates its effectiveness in reaching high storage capacities and analyzing solution space structure.

Findings

Achieves storage capacity of ~0.63 for N=101 and ~0.41 for N=1001.

Relearning improves capacity to ~0.80 for N=101.

Solutions are separated by Hamming distances that decrease with increased constraint density.

Abstract

Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the synaptic weight configuration is modified through a chain of single- or double-weight flips within the compatible weight configuration space of the earlier learned patterns. This process is able to reach a storage capacity of $\alpha \approx 0.63$ for pattern length N = 101 and $\alpha \approx 0.41$ for N = 1001. If in addition a relearning process is exploited, the learning performance is further improved to a storage capacity of $\alpha \approx 0.80$ for N = 101 and $\alpha \approx 0.42$ for N=1001. We found that, for a given learning task, the solutions constructed by the random walk learning process are separated by a typical Hamming distance, which decreases with the constraint density $\alpha$ of the learning task; at a fixed value of $\alpha$, the width of the Hamming distance distributions decreases with $N$.