Stochastic Neural Networks with the Weighted Hebb Rule

TL;DR

This paper investigates stochastic neural networks using a weighted Hebb rule, showing how different weights affect pattern storage, stability, and convergence, especially with an extra pattern improving retrieval performance under noise.

Contribution

It introduces a weighted Hebb rule for stochastic neural networks, analyzing how pattern weights influence free energy landscape and retrieval robustness, with an emphasis on adding an extra pattern for improved performance.

Findings

Weighted Hebb rule alters free energy surface configuration.

Presence of an extra pattern lowers the temperature for eliminating spurious minima.

Adding an extra pattern improves convergence time and pattern overlap.

Abstract

Neural networks with synaptic weights constructed according to the weighted Hebb rule, a variant of the familiar Hebb rule, are studied in the presence of noise(finite temperature), when the number of stored patterns is finite and in the limit that the number of neurons $N\rightarrow \infty$. The fact that different patterns enter the synaptic rule with different weights changes the configuration of the free energy surface. For a general choice of weights not all of the patterns are stored as {\sl global} minima of the free energy function. However, as for the case of the usual Hebb rule, there exists a temperature range in which only the stored patterns are minima of the free energy. In particular, in the presence of a single extra pattern stored with an appropriate weight in the synaptic rule, the temperature at which the spurious minima of the free energy are eliminated is significantly lower than for a similar network without this extra pattern. The convergence time of the network, together with the overlaps of the equilibria of the network with the stored patterns, can thereby be improved considerably.