Satisfiability transition in asymmetric neural networks

TL;DR

This paper investigates how asymmetry in neural network connections affects the ability to store memories, revealing transitions in solvability and frustration that influence memory capacity and retrieval.

Contribution

It introduces an analysis of satisfiability and clustering transitions in asymmetric neural networks, highlighting a new frustration-induced transition even with a single memory.

Findings

Identifies a SAT/UNSAT transition at a critical number of memories

Discovers an additional transition caused by asymmetry-induced frustration

Shows that even single-memory networks can experience frustration without disorder

Abstract

Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a network of neurons connected by a synaptic matrix with a definite degree of asymmetry. We study the corresponding satisfiability and clustering transitions in the space of solutions of the constraint satisfaction problem associated with finding synaptic matrices given the memories. We find, besides the usual SAT/UNSAT transition at a critical number of memories to store in the network, an additional transition for very asymmetric matrices, where the competing constraints (definite asymmetry vs. memories storage) induce enough frustration in the problem to make it impossible to solve. This finding is particularly striking in the case of a single memory to store, where no quenched disorder is present in the system.