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Combating Corrupt Messages in Sparse Clustered Associative Memories

In this paper we analyze and extend the neural network based associative memory proposed by Gripon and Berrou. This associative memory resembles the celebrated Willshaw model with an added partite cluster structure. In the literature, two retrieving schemes have been proposed for the network dynamics, namely sum-of-sum and sum-of-max. They both offer considerably better performance than Willshaw and Hopfield networks, when comparable retrieval scenarios are considered. Former discussions and experiments concentrate on the erasure scenario, where a partial message is used as a probe to the network, in the hope of retrieving the full message. In this regard, sum-of-max outperforms sum-of-sum in terms of retrieval rate by a large margin. However, we observe that when noise and errors are present and the network is queried by a corrupt probe, sum-of-max faces a severe limitation as its stringent activation rule prevents a neuron from reviving back into play once deactivated. In this manuscript, we categorize and analyze different error scenarios so that both the erasure and the corrupt scenarios can be treated consistently. We make an amendment to the network structure to improve the retrieval rate, at the cost of an extra scalar per neuron. Afterwards, five different approaches are proposed to deal with corrupt probes. As a result, we extend the network capability, and also increase the robustness of the retrieving procedure. We then experimentally compare all these proposals and discuss pros and cons of each approach under different types of errors. Simulation results show that if carefully designed, the network is able to preserve both a high retrieval rate and a low running time simultaneously, even when queried by a corrupt probe.