# G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

arXiv: https://arxiv.org/abs/2607.02491 · HTML: https://mlsanity.com/paper/2607.02491/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 2 Jul 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 11 of 11)

- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Looped Transformers are Better at Learning Learning Algorithms](https://mlsanity.com/paper/2311.12424/) (2023)
- [Sudoku-Bench: Evaluating creative reasoning with Sudoku variants](https://mlsanity.com/paper/2505.16135/) (2025)
- [Semantic Strengthening of Neuro-Symbolic Learning](https://mlsanity.com/paper/2302.14207/) (2023)
- [A Survey on Verification and Validation, Testing and Evaluations of Neurosymbolic Artificial Intelligence](https://mlsanity.com/paper/2401.03188/) (2024)
- [Symbol-Equivariant Recurrent Reasoning Models](https://mlsanity.com/paper/2603.02193/) (2026)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [Neuro-Symbolic Sudoku Solver](https://mlsanity.com/paper/2307.00653/) (2023)

## Abstract (arXiv)

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 9×9 Sudoku, where the SE-RRM correctly solves 91.1% of instances, backtracking accelerates by 33.3× and Glucose 4.1 by 1.70× (median, p<0.001), with Glucose 4.1 retaining a 1.17× speedup on perfect-hint 25×25 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×, n.s.) and even a small significant mean slowdown (0.90×) on 9×9. These results delineate the regimes in which neural guidance translates into practical speedups.