AdaC-GRPO: Towards Mastering Long-Horizon Visual Sudoku Puzzles via Adaptive Curriculum Learning

Reinforcement learning (RL) with group relative policy optimization (GRPO) has become a widely adopted approach for enhancing the reasoning capabilities of multimodal large language models (MLLMs). While GRPO enables long-chain reasoning without a critic, it often suffers from sparse rewards on difficult problems and advantage vanishing when group-level rewards are too consistent for overly easy or hard problems. Existing solutions (sample expansion, selective utilization, and indirect reward design) often fail to maintain enough variance in within-group reward distributions to yield clear optimization signals. To address this, we propose DIVA-GRPO, a difficulty-adaptive variant advantage method that adjusts variant difficulty distributions from a global perspective. DIVA-GRPO dynamically assesses problem difficulty, samples variants with appropriate difficulty levels, and calculates advantages across local and global groups using difficulty-weighted and normalized scaling. This alleviates reward sparsity and advantage vanishing while improving training stability. Extensive experiments on six reasoning benchmarks demonstrate that DIVA-GRPO outperforms existing approaches in training efficiency and reasoning performance. Code: https://github.com/Siaaaaaa1/DIVA-GRPO

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.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a prevailing paradigm for enhancing reasoning in Multimodal Large Language Models (MLLMs). However, relying solely on outcome supervision risks reward hacking, where models learn spurious reasoning patterns to satisfy final answer checks. While recent rubric-based approaches offer fine-grained supervision signals, they suffer from high computational costs of instance-level generation and inefficient training dynamics caused by treating all rubrics as equally learnable. In this paper, we propose Stratified Rubric-based Curriculum Learning (RuCL), a novel framework that reformulates curriculum learning by shifting the focus from data selection to reward design. RuCL generates generalized rubrics for broad applicability and stratifies them based on the model's competence. By dynamically adjusting rubric weights during training, RuCL guides the model from mastering foundational perception to tackling advanced logical reasoning. Extensive experiments on various visual reasoning benchmarks show that RuCL yields a remarkable +7.83% average improvement over the Qwen2.5-VL-7B model, achieving a state-of-the-art accuracy of 60.06%.