Tolerance versus synaptic noise in dense associative memories

The retrieval capabilities of associative neural networks are known to be impaired by fast noise, which endows neuron behavior with some degree of stochasticity, and by slow noise, due to interference among stored memories; here, we allow for another source of noise, referred to as “synaptic noise,” which may stem from i. corrupted information provided during learning, ii. shortcomings occurring in the learning stage, or iii. flaws occurring in the storing stage, and which accordingly affects the couplings among neurons. Indeed, we prove that this kind of noise can also yield to a break-down of retrieval and, just like the slow noise, its effect can be softened by relying on density, namely by allowing p-body interactions among neurons.