G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

2026-07-02

AI Summary

This work addresses the inefficiency of symbolic solvers in large-scale combinatorial search problems by proposing G-RRM, a hybrid approach that integrates the Symbolic Equivariant Recurrent Reasoning Model (SE-RRM) with classical backtracking or SAT solvers such as Glucose 4.1 and CaDiCaL. G-RRM leverages neural networks to generate high-quality complete solution candidates that guide the symbolic search process. The study systematically demonstrates for the first time that neural guidance can substantially accelerate symbolic solving when it satisfies specific dynamic coverage properties and the problem complexity is moderate. Empirical results show that on 9×9 Sudoku puzzles, SE-RRM achieves a 91.1% solution accuracy and accelerates backtracking by 33.3× and Glucose by 1.70×; even on 25×25 perfectly hinted grids, it yields a 1.17× speedup.

Abstract

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.

Problem

• constraint satisfaction problems
• symbolic solvers
• neural guidance
• search efficiency
• neuro-symbolic

Innovation

• neuro-symbolic reasoning
• symbol-equivariant RRM
• constraint satisfaction problems
• neural guidance
• SAT solvers