MaxSAT Feedback Improves VLM Logical Consistency in Sudoku.

Vision-Language Models (VLMs) have shown promise in structured visual reasoning, such as solving grid-based puzzles like Sudoku. However, despite their strong visual understanding, these models often struggle with logical consistency, frequently producing solutions that violate underlying rules. To address this, researchers introduce a neuro-symbolic method that embeds formal constraint reasoning directly into the VLM's problem-solving process. This approach utilizes a Maximum Satisfiability (MaxSAT) oracle, which doesn't solve the puzzle directly but acts as a validator and refinement engine. Candidate placements generated by the VLM are treated as "soft" clauses, while the strict Sudoku rules are "hard" clauses within a partial MaxSAT formulation. When inconsistencies are detected, the MaxSAT solver identifies the largest consistent subset of assignments. This information is then translated into structured textual and visual feedback, which guides the VLM in making subsequent refinements. Experiments on a Sudoku dataset, using various VLMs, demonstrate that this MaxSAT-based feedback significantly enhances logical consistency and increases the number of successfully solved instances, particularly when refining full boards. This highlights the potential of symbolic optimization to boost the reliability of VLM reasoning.