ReSI-Math：利用可恢复能力前沿提升数学推理效率
ReSI-Math: Exploring Recoverable Capability Frontiers for Efficient Reasoning Improvement
研究团队发现模型答错的数学题里有一小半其实能靠搜索轨迹救回来，他们就拿这部分数据去训练，Qwen3-VL-8B 用更少数据提了分，做法挺巧的。
论文 ReSI-Math 提出一个观察：模型直接解码失败不代表缺乏底层能力，部分失败可通过轨迹级搜索恢复，称为可恢复能力前沿。该框架用 Self-Judge 引导的进化搜索在固定策略下识别可恢复失败，并随策略演进自适应选取前沿问题做顺序 RLVR。在 Qwen3-VL-8B 上，正确-错误轨迹交叉从 621 次尝试中产出 272 个验证器确认的正确后代，占比 43.8%。经过三个顺序 one-shot RLVR 阶段后，MATH500 与 WE-MATH 平均分从 78.71 提升到 80.16；在单题 RLVR 对比中，前沿引导选择得 54.16，随机选择仅 53.31。
ReSI-Math: Exploring Recoverable Capability Frontiers for Efficient Reasoning Improvement
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.