Satisfiability transition in asymmetric neural networks

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.

24 pages + appendix, 7 figures

References in corpus (9)

• Non-reciprocal phase transitions
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Spectra of Sparse Random Matrices
• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Statistical learning theory of structured data
• Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks
• Counting equilibria in a random non-gradient dynamics with heterogeneous relaxation rates
• Beyond the storage capacity: data driven satisfiability transition
• On the number of limit cycles in diluted neural networks

Cited by in corpus (1)

• Supervised perceptron learning vs unsupervised Hebbian unlearning: Approaching optimal memory retrieval in Hopfield-like networks