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Bayesian retrieval in associative memories with storage errors.

F T Sommer¹, P Dayan

¹Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

IEEE Transactions on Neural Networks

|February 7, 2008

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Iterative retrieval in autoassociative neural networks is more effective than single-step methods. This study provides a probabilistic inference framework, justifying iterative strategies for enhanced information retrieval from noisy data.

Area of Science:

Computational neuroscience
Machine learning
Statistical physics

Background:

Single-step retrieval in autoassociative Willshaw networks is suboptimal for information extraction.
Iterative retrieval strategies offer improved performance but lack theoretical grounding.

Purpose of the Study:

To provide a principled, probabilistic inference framework for iterative retrieval in autoassociative networks.
To develop and analyze novel iterative retrieval algorithms based on probabilistic principles.

Main Methods:

Formulating retrieval as a probabilistic inference problem over exponentially many patterns.
Developing two approximate, tractable iterative retrieval methods: maximum likelihood inference and mean field approximation.
Analyzing the emergent properties of these methods, including Lyapunov functions and modified interaction terms.

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Main Results:

Iterative retrieval naturally emerges from probabilistic inference under noisy and corrupted conditions.
Maximum likelihood inference yields a Lyapunov function for retrieval, incorporating an antiferromagnetic interaction term and site-dependent thresholds when storage errors are present.
Mean field approximation leads to iterative equations interpretable as sigmoidal neural networks with similar interaction and threshold dynamics.

Conclusions:

Probabilistic inference provides a strong theoretical justification for iterative retrieval strategies in autoassociative networks.
The developed methods offer improved information retrieval from corrupted or noisy network states.
The findings bridge concepts from machine learning, statistical physics, and neuroscience, offering new insights into neural network dynamics.