  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.
