One-to-one Mapping between Stimulus and Neural State: Memory and Classification

TL;DR

This paper proposes a theoretical framework where neural networks establish a one-to-one mapping between external stimuli and synaptic states, enabling memory storage and classification based on fixed points in neural dynamics.

Contribution

It introduces a novel theoretical model linking stimulus and synaptic strength through fixed points, suggesting a biological classifier leveraging this mapping.

Findings

Neural networks can memorize stimuli via fixed points.

The model demonstrates a one-to-one stimulus-synapse mapping.

A biological classifier based on this mapping is proposed.

Abstract

Synaptic strength can be seen as probability to propagate impulse, and according to synaptic plasticity, function could exist from propagation activity to synaptic strength. If the function satisfies constraints such as continuity and monotonicity, neural network under external stimulus will always go to fixed point, and there could be one-to-one mapping between external stimulus and synaptic strength at fixed point. In other words, neural network "memorizes" external stimulus in its synapses. A biological classifier is proposed to utilize this mapping.