Constraint satisfaction problems and neural networks: a statistical physics perspective

TL;DR

This paper explores the intersection of statistical physics, neural networks, and constraint satisfaction problems, highlighting message passing algorithms' potential for solving complex inference tasks in neural data analysis.

Contribution

It introduces a new message passing algorithm for inferring variable interactions from correlation data, linking physics-inspired methods to neural network modeling.

Findings

Message passing algorithms effectively solve complex constraint satisfaction problems.

The new algorithm aids in analyzing multi-electrode neural recording data.

Insights into neural network functional complexity from physics-based approaches.

Abstract

A new field of research is rapidly expanding at the crossroad between statistical physics, information theory and combinatorial optimization. In particular, the use of cutting edge statistical physics concepts and methods allow one to solve very large constraint satisfaction problems like random satisfiability, coloring, or error correction. Several aspects of these developments should be relevant for the understanding of functional complexity in neural networks. On the one hand the message passing procedures which are used in these new algorithms are based on local exchange of information, and succeed in solving some of the hardest computational problems. On the other hand some crucial inference problems in neurobiology, like those generated in multi-electrode recordings, naturally translate into hard constraint satisfaction problems. This paper gives a non-technical introduction to this field, emphasizing the main ideas at work in message passing strategies and their possible relevance to neural networks modeling. It also introduces a new message passing algorithm for inferring interactions between variables from correlation data, which could be useful in the analysis of multi-electrode recording data.