G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models
2026-07-02 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors study a type of neural network called SE-RRMs that can better handle larger problem sizes. They combine these neural models with traditional symbolic solvers to solve constraint satisfaction problems more efficiently. Their approach, G-RRM, uses neural networks to suggest solutions that guide classical solvers, speeding up some but not all solver types. They found that this works best when the problem is complex and the solver can change its decisions if the neural advice is wrong. This method notably speeds up Sudoku solving for certain solvers but not others.
Symbol-equivariant recurrent relational models (SE-RRMs)Neuro-symbolic methodsConstraint satisfaction problemsBacktracking solverSAT solversGlucose SAT solverCaDiCaL SAT solverCombinatorial searchBranching heuristicsRecurrent reasoning models (RRMs)
Authors
Timo Bertram, Sidhant Bhavnani, Richard Freinschlag, Erich Kobler, Andreas Mayr, Günter Klambauer
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.