Survey Propagation Revisited

TL;DR

Survey propagation is a powerful technique for solving large combinatorial problems, and this paper demonstrates its effectiveness and accuracy in computing marginals over covers in large formulas, challenging previous assumptions.

Contribution

The paper shows that covers exist in large formulas and SP accurately computes marginals over them, providing a new understanding of SP's success.

Findings

Covers exist in large hard random formulas.

SP accurately computes marginals over covers despite cycles.

This challenges previous beliefs that covers do not exist in large formulas.

Abstract

Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding the success of SP, it was recently shown that SP can be viewed as a form of belief propagation, computing marginal probabilities over certain objects called covers of a formula. This explanation was, however, shortly dismissed by experiments suggesting that non-trivial covers simply do not exist for large formulas. In this paper, we show that these experiments were misleading: not only do covers exist for large hard random formulas, SP is surprisingly accurate at computing marginals over these covers despite the existence of many cycles in the formulas. This re-opens a potentially simpler line of reasoning for understanding SP, in contrast to some alternative lines of explanation that have been proposed assuming covers do not exist.