Continuous or discrete attractors in neural circuits? A self-organized switch at maximal entropy

TL;DR

This paper presents a neural network model with Hebbian plasticity capable of learning both continuous and discrete attractors, depending on stimulus presentation frequency and sensory coding structure, revealing a switch at maximal entropy.

Contribution

The authors introduce a solvable model demonstrating how neural circuits can switch between continuous and discrete attractors based on experience and sensory coding.

Findings

Continuous attractors are learned when experience matches sensory coding.

Maximal entropy occurs when neural activity displays no processing of sensory information.

Exceeding sensory coding experience destabilizes continuous attractors into discrete ones.

Abstract

A recent experiment suggests that neural circuits may alternatively implement continuous or discrete attractors, depending on the training set up. In recurrent neural network models, continuous and discrete attractors are separately modeled by distinct forms of synaptic prescriptions (learning rules). Here, we report a solvable network model, endowed with Hebbian synaptic plasticity, which is able to learn either discrete or continuous attractors, depending on the frequency of presentation of stimuli and on the structure of sensory coding. A continuous attractor is learned when experience matches sensory coding, i.e. when the distribution of experienced stimuli matches the distribution of preferred stimuli of neurons. In that case, there is no processing of sensory information and neural activity displays maximal entropy. If experience goes beyond sensory coding, processing is initiated and the continuous attractor is destabilized into a set of discrete attractors.