Satisfiability transition in asymmetric neural networks

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