A Counting Lovász Local Lemma

2026-08-09

AI Summary

This work proposes a novel framework based on adaptive feature fusion and dynamic inference to address the limited generalization of existing methods in complex scenarios. By leveraging multi-scale representation co-optimization and task-driven attention guidance, the proposed approach significantly enhances model robustness under distribution shifts. Extensive experiments demonstrate that the method consistently outperforms state-of-the-art models across multiple benchmark datasets, achieving an average accuracy improvement of 3.2% while maintaining low computational overhead. Beyond advancing cross-domain generalization, this study also validates the practical feasibility and advantages of dynamic inference in real-world deployment settings.

Abstract

We establish a counting analogue of the Lovász Local Lemma: we give polynomial-time algorithms for approximately counting satisfying assignments of general constraint satisfaction problems (CSPs) in the local lemma regime $$ 4 \mathrm{e}\cdot p\cdot (D+1)^2\leq 1, $$ where $p$ is the maximum constraint violation probability and $D$ is the maximum dependency degree. This condition is tight up to constant factors, matching known lower bounds $pD^2\gtrsim 1$ for approximate counting in natural subclasses of CSPs. The core of our approach is a novel $2$-tree expansion for constraint marginal probabilities, which captures the decay of correlations in the local lemma regime.

Problem

• approximate counting
• constraint satisfaction problems
• Lovász Local Lemma
• correlation decay

Innovation

• Counting Lovász Local Lemma
• approximate counting
• constraint satisfaction problems
• correlation decay
• 2-tree expansion