Attractors in fully asymmetric neural networks

TL;DR

This paper analyzes the cycle lengths and attraction basin weights in fully asymmetric neural networks, revealing they behave like a symmetric random map, with results supported by numerical comparisons.

Contribution

It introduces an annealed approximation for fully asymmetric neural networks, showing they behave like a symmetric random map, and suggests this approximation may be exact at infinite size.

Findings

Networks behave like symmetric random maps

Approximation aligns with numerical results

Potential exactness in infinite size limit

Abstract

The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation which we previously introduced for the study of Kauffman networks. Our results show that this model behaves essentially as a Random Map possessing a reversal symmetry. Comparison with numerical results suggests that the approximation could become exact in the infinite size limit.