Binary Willshaw learning yields high synaptic capacity for long-term familiarity memory

TL;DR

This paper analyzes the Willshaw learning rule's efficiency in familiarity memory tasks, showing it achieves high synaptic capacity with low activity rates, relevant for understanding biological synaptic pruning and neural memory storage.

Contribution

It provides a detailed computational analysis of the Willshaw learning rule's synaptic and network capacities, highlighting its effectiveness under biologically plausible activity levels.

Findings

Synaptic capacity diverges and is comparable to pattern association case.

Network capacity is sensitive to pattern coding rates, which must be low.

Willshaw learning achieves high synaptic efficiency at moderate activity levels.

Abstract

We investigate from a computational perspective the efficiency of the Willshaw synaptic update rule in the context of familiarity discrimination, a binary-answer, memory-related task that has been linked through psychophysical experiments with modified neural activity patterns in the prefrontal and perirhinal cortex regions. Our motivation for recovering this well-known learning prescription is two-fold: first, the switch-like nature of the induced synaptic bonds, as there is evidence that biological synaptic transitions might occur in a discrete stepwise fashion. Second, the possibility that in the mammalian brain, unused, silent synapses might be pruned in the long-term. Besides the usual pattern and network capacities, we calculate the synaptic capacity of the model, a recently proposed measure where only the functional subset of synapses is taken into account. We find that in terms of network capacity, Willshaw learning is strongly affected by the pattern coding rates, which have to be kept fixed and very low at any time to achieve a non-zero capacity in the large network limit. The information carried per functional synapse, however, diverges and is comparable to that of the pattern association case, even for more realistic moderately low activity levels that are a function of network size.