Robust exponential binary pattern storage in Little-Hopfield networks

Christopher Hillar; Ngoc Tran; Kilian Koepsell

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arXiv · 1206.2081

Robust exponential binary pattern storage in Little-Hopfield networks

Christopher Hillar·Ngoc Tran·Kilian Koepsell

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Abstract

The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-states of the network dynamics. However, the number of binary memories so storable scales linearly in the number of neurons, and it has been a long-standing open problem whether robust exponential storage of binary patterns was possible in such a network memory model. In this note, we design simple families of Little-Hopfield networks that provably solve this problem affirmatively. As a byproduct, we produce a set of novel (nonlinear) binary codes with an efficient, highly parallelizable denoising mechanism.

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Christopher Hillar, Ngoc Tran, Kilian Koepsell. 2015-04-29. Robust exponential binary pattern storage in Little-Hopfield networks. https://arxiv.org/abs/1206.2081

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