MaxSAT-Based Feedback for Guiding Vision-Language Models in Sudoku

2026-07-14

AI Summary

This work addresses the tendency of vision-language models to produce invalid solutions in structured visual reasoning tasks such as Sudoku, due to insufficient enforcement of logical constraints. The authors propose a neuro-symbolic approach that integrates a MaxSAT solver into the vision-language reasoning pipeline for the first time. Specifically, candidate answers generated by the model are encoded as soft clauses and combined with the hard constraints inherent to Sudoku, forming a MaxSAT problem. Structured feedback from the solver is then used to iteratively refine the model’s outputs. Evaluated across multiple open- and closed-source vision-language models, this method substantially improves logical consistency and full-solution accuracy, with particularly strong performance under full-board optimization settings.

Abstract

Vision--Language Models (VLMs) have recently demonstrated promising performance on structured visual reasoning tasks, including grid-based puzzles. However, despite strong perceptual capabilities, these models lack explicit mechanisms for enforcing logical consistency and frequently generate assignments that violate underlying constraints. In this paper, we propose a neuro-symbolic approach that integrates formal constraint reasoning into the VLM solving process via a Maximum Satisfiability (MaxSAT) oracle. Rather than computing solutions directly, the symbolic component acts as a consistency validator and refinement engine. Candidate placements generated by the VLM are encoded as soft clauses in a partial MaxSAT formulation, while Sudoku constraints remain hard clauses. When inconsistencies arise, the MaxSAT solver identifies a largest mutually consistent subset of assignments, which is then translated into structured textual and visual feedback to guide subsequent refinements. We evaluate our approach on a Sudoku dataset across multiple open-source and closed-access VLMs. Results show that MaxSAT-based feedback improves logical consistency and increases the number of solved instances, particularly in full-board refinement mode. These findings demonstrate that symbolic optimisation can enhance the reliability of vision-language reasoning.

Problem

• Vision-Language Models
• Logical Consistency
• Sudoku
• Constraint Reasoning
• Structured Visual Reasoning

Innovation

• MaxSAT
• neuro-symbolic
• vision-language models
• constraint reasoning
• structured feedback