Reinforcement learning with verifiable rewards (RLVR) has become an effective approach for improving mathematical reasoning in large language models. However, a fundamental question remains: when a model fails to solve a problem, does it truly lack the underlying capability? In this work, we reveal that direct failure does not necessarily imply inability. Some reasoning failures can be recovered by exploring the model's own trajectories, exposing a recoverable capability frontier: a policy-dependent region where solutions are not reliably generated through direct decoding but can be elicited through trajectory-level search. Based on this observation, we introduce ReSI-Math, a framework that explores recoverable capability frontiers and converts recovered capabilities into data-efficient RLVR supervision. ReSI-Math uses Self-Judge-guided evolutionary search to identify recoverable failures under a fixed policy and adaptively selects frontier problems for sequential RLVR as the policy evolves. On Qwen3-VL-8B, correct-incorrect trajectory crossover produces 272 verifier-confirmed correct offspring from 621 attempts (43.8%). After three sequential one-shot RLVR stages, the MATH500 and WE-MATH average improves from 78.71 to 80.16. Under matched single-problem RLVR, random selection reaches only 53.31 versus 54.16 for frontier-guided Q1.
Yuandong Wang Capital Normal University, Yao Cui, Yuxin Zhao, Zhen Yang, Yangfu Zhu, Zhenzhou Shao
Recent advances in Vision-Language Models (VLMs) have achieved impressive progress in multimodal mathematical reasoning. Yet, howmuch visual information truly contributes to reasoning remains unclear. Existing benchmarks report strong overall performance but seldom isolate the role of the image modality, leaving open whether VLMs genuinely leverage visual understanding or merely depend on linguistic priors. To address this, we present MathSight, a university-level multimodal mathematical reasoning benchmark designed to disentangle and quantify the effect of visual input. Each problem includes multiple visual variants—original, hand-drawn, photocaptured—and a text-only condition for controlled comparison. Experiments on state-of-the-art VLMs reveal a consistent trend: the contribution of visual information diminishes with increasing problem difficulty. Remarkably, Qwen3-VL without any image input surpasses both its multimodal variants and GPT-5, underscoring the need for benchmarks like MathSight to advance genuine vision-grounded reasoning in future models. The project page is available at https://cnu-bot-group.github.io/MathSight/.
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cs.CL · cs.CV
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表