Solvable Neural Network Model for Input-Output Associations: Optimal Recall at the Onset of Chaos

TL;DR

This paper introduces an exactly solvable neural network model that elucidates how neural dynamics and connectivity enable input-output associations, highlighting optimal recall performance at the onset of chaos.

Contribution

The paper presents a novel analytically solvable neural network model explicitly incorporating inputs and outputs, revealing dynamics including chaos and optimal recall conditions.

Findings

Response forms derived analytically

Chaotic dynamics emerge at bifurcation points

Optimal recall occurs at the onset of chaos

Abstract

In neural information processing, an input modulates neural dynamics to generate a desired output. To unravel the dynamics and underlying neural connectivity enabling such input-output association, we proposed an exactly soluble neural-network model with a connectivity matrix explicitly consisting of inputs and required outputs. An analytic form of the response upon the input is derived, whereas three distinctive types of responses including chaotic dynamics as bifurcation against input strength are obtained depending on the neural sensitivity and number of inputs. Optimal performance is achieved at the onset of chaos, and the relevance of the results to cognitive dynamics is discussed.