在这项工作, 中，我们重点关注 SE-RRM,，这是 RRM 的符号等变实例，它对更大的问题规模表现出改进的外推能力。我们提出了一种神经符号方法, ``指导循环推理模型 (G-RRM),，它将SE-RRM与符号求解器集成以解决约束满足问题。 SE-RRM 充当神经求解器，生成完整的解决方案建议并指导经典符号求解器,，例如回溯或基于 SAT 的方法（如 Glucose 4.1 和 CaDiCaL 3.0.0,），生成全局正确的解决方案。我们主要研究, G-RRM 的神经引导何时可以提高符号求解器的搜索效率。 % 我们的实验表明，G-RRM 的功效取决于两个条件: 首先, 问题实例必须具有广阔的组合搜索空间以暴露潜在收益, 第二, 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善时进行恢复。当这些条件满足, 指导时，中值冲突计数为零，并在 $9\times9$ 数独, 上产生显着的挂钟加速:，其中 SE-RRM 正确解决了 $91.1\%$ 的实例, 回溯加速了 $33.3\times$，葡萄糖 4.1 加速了$1.70\times$ (median, $p<0.001$),，Glucose 4.1 在完美提示 $25\times25$ 网格上保留 $1.17\times$ 加速。相比之下，, CaDiCaL 3.0.0, 的运行时间是开销主导的，并且始终尊重注入的分支提示而不是覆盖它们, 显示没有显着的加速 (median $1.02\times$, n.s.) 甚至有一个小的显着平均减速 ($0.90\times$) $9\×9$。这些结果描绘了神经引导转化为实际加速的机制。

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 hold, guidance drives median conflict counts to zero and yields significant wall-clock speedups: on $9\times9$ Sudoku, where the SE-RRM correctly solves $91.1\%$ of instances, backtracking accelerates by $33.3\times$ and Glucose 4.1 by $1.70\times$ (median, $p<0.001$), with Glucose 4.1 retaining a $1.17\times$ speedup on perfect-hint $25\times25$ grids. In contrast, CaDiCaL 3.0.0, whose runtime is overhead-dominated and which always respects the injected branching hints rather than overwriting them, shows no significant speedup (median $1.02\times$, n.s.) and even a small significant mean slowdown ($0.90\times$) on $9\times9$. These results delineate the regimes in which neural guidance translates into practical speedups.

科目:人工智能(cs.AI)

Subjects: Artificial Intelligence (cs.AI)