/ Paper arXiv 2611.04787
In short
In shortReport a mistake
Key numbers
From the paperCopied from the abstract, not written by AI.
Abstract
From the paperThe authors' own words.
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.
From the full paper
From the paperCopied from the paper itself by our code.
Reading the paper on arXiv…
Ask this paper
/ Ask a questionAnswers come from the full paper and name the section
/ Your notes
Select text in the abstract to highlight it or add a note. They stay in this browser.