Neural associative memory with optimal Bayesian learning.

Abstract:

:Neural associative memories are perceptron-like single-layer networks with fast synaptic learning typically storing discrete associations between pairs of neural activity patterns. Previous work optimized the memory capacity for various models of synaptic learning: linear Hopfield-type rules, the Willshaw model employing binary synapses, or the BCPNN rule of Lansner and Ekeberg, for example. Here I show that all of these previous models are limit cases of a general optimal model where synaptic learning is determined by probabilistic Bayesian considerations. Asymptotically, for large networks and very sparse neuron activity, the Bayesian model becomes identical to an inhibitory implementation of the Willshaw and BCPNN-type models. For less sparse patterns, the Bayesian model becomes identical to Hopfield-type networks employing the covariance rule. For intermediate sparseness or finite networks, the optimal Bayesian learning rule differs from the previous models and can significantly improve memory performance. I also provide a unified analytical framework to determine memory capacity at a given output noise level that links approaches based on mutual information, Hamming distance, and signal-to-noise ratio.

journal_name

Neural Comput

journal_title

Neural computation

authors

Knoblauch A

doi

10.1162/NECO_a_00127

subject

Has Abstract

pub_date

2011-06-01 00:00:00

pages

1393-451

issue

6

eissn

0899-7667

issn

1530-888X

journal_volume

23

pub_type

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