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研究提出「Weight-Space Programming」：让 GPT-6 Astra 直接编辑 Qwen3.5-0.8B 的权重，在不使用梯度或训练的情况下仅修改 0.016% 权重，修复推理循环并将数学能力提升至 6 倍、指令遵循提升 3 倍。
The paper proposes Stepwise-Querying, a method that elicits step-specific explanations from black-box teachers without accessing their internal chain-of-thought traces, assembling them into training data for supervised fine-tuning of smaller student models. It achieves the top score in 14 of 16 comparisons across two teachers, two students, and four math/code benchmarks, and introduces the SEIG diagnostic for measuring stepwise explanation information gain.
论文提出 REWIND，一种基于 token 熵动态的训练-free 控制器，用于在测试时对 LLM 推理轨迹进行定点后缀重新生成修复，在三个模型系列和五个基准上超越所有基线。
CoTranslator 提出将逆向思维链推理轨迹翻译为经验证的正向推理分布，实现高效且可迁移的推理蒸馏；在六个数学基准上较语义抑制最高提升5.82个百分点，并以约35.9%的计算量保留拒采样95.0%的平均准确率。
提出 CriticOPD，通过让教师模型利用参考答案对错误的学生 rollout 进行批判、学生据此重写后续内容，从而恢复可靠的 on-policy 蒸馏监督信号，在六个数学推理基准上相比 OPD 平均提升 4 个百分点以上。
本文提出 MagicBeanStalk，一种自顶向下分解与自底向上递归结合的 RLVR 数据合成算法，用以逃逸约88%数学语料落入的“零优势陷阱”，在多个数学与金融基准上显著提升 gpt-oss-120b、DeepSeek v4 Flash 和 Qwen3 的推理性能。
该论文提出 Tracking-Value PPO（TPPO），通过在对数几率空间对前缀值进行贝叶斯分解，构建累积值参数化以更好地跟踪语言模型推理中的值演化。TPPO 在 Qwen3-4B-Base 和 Qwen3-8B-Base 上分别比 PPO 提升 7.0 和 8.4 个数学推理分数点，并改善了分布外泛化能力。
OpenAI's unreleased model solved most math benchmark problems from a single prompt, with each problem requiring about 3 hours of thinking time, despite the model not existing before the end of August.
论文提出 BranchOPD（Branching On-Policy Distillation），通过在学生不确定或与教师分歧的决策点进行分支采样，并共享前缀以降低成本，同时提出协议边界修复（PBR）来缓解重复生成。在数学推理与 ALFWorld/WebShop 代理任务上，BranchOPD 显著优于 Vanilla OPD 和 Multi-Rollout OPD。
VeriLoop E2 是由清华 SIGS 机器人实验室发布的 27B 开源后训练模型，基于 Qwen3.8-27B，专注代码、数学与物理推理，采用 VeriLoop-Governed Recurrence（VGR）验证机制，在 SWE-bench Pro、AIME 2026 等多项基准上取得强劲成绩。
该论文提出 Language-Aware Skeleton Exploration Framework (LASEF)，系统研究多层数学推理中骨架提示语言的选择问题，发现英语骨架平均略有优势但并非普遍最优，骨架语言是一个依赖上下文的设计变量。
COMPASS提出一种无需预定义推理特征的推理时激活转向方法：利用模型自身答案的正确性作为信号，定位少数关键注意力头并沿正确性方向干预其激活，在数学基准上以显著更少的token逼近CoT精度。
论文提出Universal Textual Teaching (UTT)，一种免参数更新的知识蒸馏框架，将师生模型的能力差距提炼为可解释、可复用的自然语言工件Primer，在KernelBench和Omni-MATH-2上显著提升学生模型准确率（如9.4%提升至48.6%），且Primer可跨不同师生组合泛化。
The paper proposes HEST, a method that embeds LLM hidden states into the Poincaré ball with an entropy-trained probe and steers only high-entropy (hesitant) tokens along hyperbolic geodesics, improving math reasoning accuracy on Qwen2.5-Math and Llama-3.1 models where fixed-vector Euclidean steering fails.
This paper introduces SymCE, a corpus of 4,707 false math conjectures with executable Python verifiers, and shows that counterexample-only SFT collapses true-theorem recognition while GRPO-style reinforcement learning repairs it and improves performance beyond the base model.
该论文提出 Seg-OPD（分段在线策略蒸馏），通过选择学生模型的不确定推理片段并用教师重写稿作为显式修订监督，训练学生学习如何修订推理步骤。实验显示在数学推理与竞赛编程任务上，相比基线平均相对提升 5.22% 的推理准确率。
This paper introduces on-policy power distillation (OPPD), which trains a language model to produce the sharpened samples that sequence-level power distributions would normally require search to obtain. OPPD improves reasoning accuracy by up to 23.0 points on MATH500 and outperforms GRPO with verified rewards while using no reference answers, with code released on GitHub.
The paper identifies why self-evolving reasoning models suffer performance collapse — invalid questions and mathematically-equivalent question repetition — and proposes R-Quest, which uses validity and novelty feedback to sustain self-evolution, outperforming R-Zero by 17.32 points across 12 benchmarks over ten rounds.
GPT-6.1 Sol has saturated the FrontierMath Tier 4 benchmark, which was still considered exceptionally difficult for research-level math less than a year ago, and Astra reportedly solved 5 Erdős problems, 2 of them under budget.
The paper introduces Activation-Conditioned Self-Distillation (ACSD), which extracts a steering vector from activation contrasts between a model's correct and incorrect self-generated trajectories to build a frozen self-teacher, achieving state-of-the-art mean accuracy across five models on mathematical benchmarks, including 71.9% on DeepSeek-R1-0528-Qwen3-8B.