G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

Paper Overview

Field: Machine Learning Authors: Timo Bertram, Sidhant Bhavnani, Richard Freinschlag Published: 2026-07-04 arXiv: 2507.03231

Summary

This paper focuses on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes. The authors 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.

The central research question: when does neural guidance with G-RRM improve the search efficiency of symbolic solvers?

Experiments show the efficacy of G-RRM depends on two conditions:

1. The problem instances must have an expansive combinatorial search space to expose potential gains. 2. The solver architecture must be capable of dynamically overwriting its branching choices to recover when neural hints are imperfect.

When these conditions hold, guidance can reduce median conflict counts to zero and brings substantial wall-clock speedups:

• On 9×9 Sudoku (where SE-RRM correctly solves 91.1% of instances), backtracking accelerates 33.3× and Glucose 4.1 accelerates 1.70× (median, p<0.001).
• Glucose 4.1 retains a 1.17× speedup on perfectly hinted 25×25 grids.

In contrast, CaDiCaL 3.0.0's runtime is overhead-dominated and it always respects injected branching hints rather than overwriting them, showing no significant speedup (median 1.02×, n.s.) and even a small but significant mean slowdown on 9×9 (0.90×).

These results clarify the scenarios in which neural guidance translates into practical acceleration for symbolic solvers.

Original Abstract (excerpt)

> 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... 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.

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*Auto-collected on 2026-07-05.*