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A large number of neural network models of associative memory have beenproposed in the literature. These include the classical Hopfield networks(HNs), sparse distributed memories (SDMs), and more recently the moderncontinuous Hopfield networks (MCHNs), which possesses close links withself-attention in machine learning. In this paper, we propose a generalframework for understanding the operation of such memory networks as a sequenceof three operations: similarity, separation, and projection. We derive allthese memory models as instances of our general framework with differingsimilarity and separation functions. We extend the mathematical framework ofKrotov et al (2020) to express general associative memory models using neuralnetwork dynamics with only second-order interactions between neurons, andderive a general energy function that is a Lyapunov function of the dynamics.Finally, using our framework, we empirically investigate the capacity of usingdifferent similarity functions for these associative memory models, beyond thedot product similarity measure, and demonstrate empirically that Euclidean orManhattan distance similarity metrics perform substantially better in practiceon many tasks, enabling a more robust retrieval and higher memory capacity thanexisting models.

Universal Hopfield Networks: A General Framework for Single-Shot Associative Memory Models