Abstract
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.
Highlights
Associative memories (AM) are devices able to store and retrieve a set of information
In the so-called dense associative memories (DAMs) neurons are embedded on hyper-graphs in such a way that they are allowed to interact in p-tuples and α ∼ O(N p−1)
We considered dense AMs and we investigated the role of density in preventing retrieval break-down due to noise
Summary
Associative memories (AM) are devices able to store and retrieve a set of information (see, e.g., [1]). In the so-called dense associative memories (DAMs) neurons are embedded on hyper-graphs in such a way that they are allowed to interact in p-tuples and α ∼ O(N p−1) This model requires more resources as the number of connections encoding the learned information scales as N p instead of N 2 as in the standard pairwise model [6,7]. Here, possible effects due to fast noise ( referred to as temperature) are discarded and, since it typically makes neurons more prone to failure, our results provide an upper bound for the system performance This particular setting allows addressing the problem analytically via a signal-to-noise approach [2].
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