[论文] G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

论文概要

研究领域: ML 作者: Timo Bertram, Sidhant Bhavnani, Richard Freinschlag 发布时间: 2026-07-04 arXiv: 2507.03231

中文摘要

本文聚焦于 SE-RRMs（RRM 的符号等变实例化），这类模型在更大问题规模上展现出改进的外推能力。研究提出一种神经-符号方法——"基于递归推理模型的引导"（Guiding with Recurrent Reasoning Models, G-RRM），将 SE-RRM 与符号求解器（用于约束满足问题）相结合。SE-RRM 作为神经求解器生成完整解提案，并引导经典符号求解器（如回溯法或基于 SAT 的方法如 Glucose 4.1 和 CaDiCaL 3.0.0）产生全局正确的解。

核心研究问题是：神经引导何时能提升符号求解器的搜索效率？实验表明，G-RRM 的有效性取决于两个条件：首先，问题实例必须具有 expansive 的组合搜索空间以暴露潜在收益；其次，求解器架构必须能够动态覆盖其分支选择，以便在神经提示不完美时恢复。当这些条件满足时，引导可将中位数冲突次数降至零，并带来显著的墙钟加速：在 9×9 数独上（SE-RRM 正确求解 91.1% 的实例），回溯法加速 33.3 倍，Glucose 4.1 加速 1.70 倍（中位数，p<0.001）；Glucose 4.1 在完美提示的 25×25 网格上仍保持 1.17 倍加速。

相比之下，CaDiCaL 3.0.0 的运行时由开销主导，且始终尊重注入的分支提示而非覆盖它们，因此未显示显著加速（中位数 1.02 倍，n.s.），甚至在 9×9 上表现出微小但显著的均值减速（0.90 倍）。这些结果明确了神经引导转化为实际加速的适用场景。

原文摘要

In this work, we focus on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes. We propose a neuro-symbolic approach, "Guiding with Recurrent Reasoning Models" (G-RRM), which integrates SE-RRMs with symbolic solvers for constraint satisfaction problems. SE-RRMs act as neural solvers that generate full solution proposals and guide classical symbolic solvers, such as backtracking or SAT-based methods like Glucose 4.1 and CaDiCaL 3.0.0, that produce globally correct solutions. Centrally, we investigate when neural guidance with G-RRM improves the search efficiency of symbolic solvers. Our experiments show that the efficacy of G-RRM depends on two conditions: first, the problem instances must have an expansive combinatorial search space to expose potential gains, and second, the solver architecture must be capable of dynamically overwriting its branching choices to recover when neural hints are imperfect. When these conditions hol...

--- *自动采集于 2026-07-05*

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