Solvable neural network model for input-output associations: Optimal recall at the onset of chaos

Abstract

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

Locations

• Physical Review Research - View - PDF
• arXiv (Cornell University) - View - PDF