Forgetting Memories and their Attractiveness

TL;DR

This paper investigates a neural memory model that incorporates forgetting, analyzing how it affects pattern retention and basin size, revealing limitations in biological plausibility due to exponentially shrinking basins with pattern age.

Contribution

It provides a numerical analysis of a forgetting memory model with bounded synaptic strength, exploring its behavior at finite and large neuron counts, and examining pattern basin dynamics.

Findings

Basin size decreases exponentially with pattern age

Model demonstrates forgetting mechanism that favors recent patterns

Large but finite N analysis reveals non-physiological features

Abstract

We study numerically the memory which forgets, introduced in 1986 by Parisi by bounding the synaptic strength, with a mechanism which avoid confusion, allows to remember the pattern learned more recently and has a physiologically very well defined meaning. We analyze a number of features of the learning at finite number of neurons and finite number of patterns. We discuss how the system behaves in the large but finite N limit. We analyze the basin of attraction of the patterns that have been learned, and we show that it is exponentially small in the age of the pattern. This is a clearly non physiological feature of the model.