The paper proposes a self‑improvement loop for reasoning models that leverages hindsight: when a problem is too hard, a supplied solution can help the model learn useful solution ideas. The method trains a single model to (1) predict solution ideas from problems alone, (2) reverse‑engineer ideas from problems and known solutions, and (3) solve problems using provided ideas. The loop alternates between reverse‑engineering ideas from problems with supplied solutions and using these ideas as additional supervision for joint training of all three capabilities, with a formal specification and an instantiation for interactive theorem proving in Lean.
arXiv:2506. 17104v2 Announce Type: replace Abstract: Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas.
arXiv:2509. 14274v3 Announce Type: replace Abstract: Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving.
arXiv:2602.22583v2 Announce Type: replace Abstract: Example-based guidance is widely used to improve mathematical reasoning at inference time, yet its effectiveness is highly unstable across problems...
arXiv:2609.24760v1 Announce Type: new Abstract: When facing complex problems, humans tend to try various ideas for different issues. Human thinking patterns exhibit remarkable flexibility in adapting...
arXiv:2604. 06628v2 Announce Type: replace Abstract: A prevailing narrative in LLM post-training holds that supervised finetuning (SFT) memorizes while reinforcement learning (RL) generalizes.
BoundaryEvo introduces a two‑stage data‑model co‑evolution framework for distilling long‑chain reasoning from large teacher models into small language models. First, Capability Priming distills a small set of teacher trajectories to give the student an initial reasoning baseline. Then, Capability‑Boundary Co‑Evolution iteratively selects questions the student has not mastered but the teacher can solve, updating the training data as the student’s capability grows. With only 1,000 examples, BoundaryEvo improves Qwen3.5‑4B accuracy from 62.9 % to 75.3 % on IMO‑AnswerBench and from 26.8 % to 46.0 % on AMO‑Bench, outperforming static and dynamic baselines across 11 benchmarks.
arXiv:2509. 25004v2 Announce Type: replace Abstract: Online reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving the reasoning abilities of large language models, but most methods still optimize reasoning trajectories over the static problem set, wasting rollout budget on solved or overly difficult problems.
arXiv:2610.09665v1 Announce Type: new Abstract: On-policy post-training can improve large language models by learning from their own trajectories, but requires costly rollout generation. We ask wheth...
arXiv:2606. 09052v1 Announce Type: cross Abstract: Self-evolution offers a scalable path to stronger reasoning: a pretrained language model improves itself with only minimal external supervision.
arXiv:2507. 16518v3 Announce Type: replace-cross Abstract: Recent advances in multimodal large language models (MLLMs) have shown impressive reasoning capabilities.
arXiv:2605. 03862v4 Announce Type: replace Abstract: Reinforcement learning with verifiable rewards has become a common way to improve explicit reasoning in large language models, but final-answer correctness alone does not reveal whether the reasoning trace is faithful, reliable, or useful to the model that consumes it.
arXiv:2509. 16456v3 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used in various domains, showing impressive potential on different tasks.