Self-Training for Language Models

Reinforcement learning is commonly used to train language agents in interactive environments, but cannot be directly applied when rewards are unavailable. Recent methods use environmental feedback as privileged context for hindsight self-distillation, but our analysis suggests that simply conditioning the teacher on feedback is insufficient, motivating us to rethink how environmental feedback is used in agentic self-distillation. Given that environmental feedback contains rich supervision for modeling how the environment responds to agent actions, we introduce \textit{agentic SElf-distilLation with environmental Feedback modeling} (SELF), a framework that jointly optimizes environmental feedback modeling and hindsight self-distillation. SELF learns to predict environmental responses while distilling guidance from a feedback-conditioned self-teacher into the policy. Our analysis reveals a mutually reinforcing mechanism: environmental feedback modeling strengthens hindsight supervision and policy learning, while self-distillation enhances the model's ability to model environmental feedback. With Qwen3-8B, SELF outperforms SDPO and GRPO by 6.4 and 4.1 percentage points in $τ$-bench success rate, and by 10.71 and 3.57 percentage points in AppWorld task goal completion, respectively. These results show that SELF uses environmental feedback more effectively within agentic self-distillation, improving agent capabilities.

Test-time training (TTT) lets a model store information in its weights during inference. When the model learns from its own output, however, each update also changes the model that generates the next training example. Across 128K-token streams, retaining generated-text updates worsens prediction on independent human-written text with three TTT-E2E model configurations (labeled 125M, 760M, and 3B). The same failure occurs when Adam updates Qwen3-4B's existing weights. The same update mechanisms can improve on real text, so writing itself is not the failure. Three matched comparisons trace the causal pathway. Fixed Generation removes over 98% of the damage at 125M and 760M by using a frozen model to generate training chunks. Recorded Replay separates the loss caused by reading degraded text from the additional loss stored by updating on it. A paired one-update comparison then shows the local conflict: an update predicts its source better but new real text worse. This cost grows after Closed Loop adaptation, with a few trajectories accounting for most large failures. Finally, Settlement evaluates the candidate state on independent real text before commitment. It leaves mean endpoint gaps of 0.07 and -0.02 nats at 125M and 760M while retaining real-text adaptation. These results motivate checking prediction on independent evidence before retaining an update.

Self-evolving reasoning models learn from their own generated questions, yet repeated self-training can lead to performance collapse. In this paper, we investigate why performance deteriorates over successive rounds and how to sustain self-evolution. Our analysis identifies two recurring quality problems in self-generated questions: invalid questions and repeated variants of the same mathematical questions. First, invalid questions become more prevalent across rounds, and answer-consistency filtering further increases their proportion in training data. Second, existing question diversity controls based on lexical similarity can miss mathematically equivalent questions expressed in different ways, which leads to question diversity collapse in later training rounds. Building on these findings, we introduce R-Quest, which uses question validity and novelty feedback to guide self-evolution. We first train the solver to recognize and reject invalid questions, then use its judgments to guide questioner rewards and filter solver training data. To avoid question repetition, we use a frozen base model to compare sampled question pairs and provide novelty feedback. Empirically, our method consistently achieves the highest average performance on 12 benchmarks in mathematical reasoning, general-domain reasoning, and code generation across two model families. Additionally, R-Quest maintains stable performance gains over ten rounds of self-evolution, peaking in the final round and outperforming R-Zero by 17.32 points.

Audio deepfake detection (ADD) must remain effective when new spoofing attacks emerge after deployment. Emerging audio language model (ALM)-based ADD methods are built on predefined supervision from ground-truth labels or verified forensic rationales. However, this paradigm overlooks an ALM's own mistakes, which indicate where targeted supervision is most needed. To this end, we first introduce evolving spoofing environments for ALM-based ADD, where a new attack becomes dominant while previously observed attacks persist. Motivated by the above learning-from-mistakes perspective, we further propose SE-ADD, a self-evolving framework that iteratively adapts an ALM via low-rank adaptation (LoRA) using mistake-driven supervision built from its verdicts and self-generated forensic cues. All training samples receive direct authenticity supervision, while misclassified ones receive additional cue-augmented supervision. As verdicts and cues are regenerated by the updated ALM, the resulting supervision evolves accordingly. Experiments on two ALMs demonstrate the effectiveness of SE-ADD in generalizing to unseen attacks, reducing the equal error rate (EER) from $36.72\%$ to $7.52\%$ for Qwen2-Audio and from $19.93\%$ to $3.97\%$ for MOSS-Audio.

Large language model post-training generates self-generated rollouts through reinforcement learning and on-policy distillation, yet this experience is often treated as stale once the policy advances. Historical rollouts can remain compatible with a later policy while preserving behaviors that the policy no longer expresses reliably. However, they may also contain mistakes, abandoned attempts, and redundant actions that should not be imitated, motivating finer-grained selective supervision. We introduce ROSS (Relearning from Self-Generated Rollouts through Selective Supervision), which preserves the full historical trajectory as context while applying loss only to selected model-generated continuations. Across domain-specific reinforcement learning, multi-teacher on-policy distillation, and agentic reinforcement learning, ROSS consistently improves upstream checkpoints and outperforms baselines across mathematics, code generation, instruction following, and software engineering. On Qwen3.6-35B-A3B, ROSS improves the six-benchmark MOPD average from 58.40% to 62.20% and SWE-bench Verified from 64.20% to 68.40%. These results show that self-rollout training leaves behind reusable behavioral experience that can yield further gains through offline supervised fine-tuning (SFT), without additional policy rollouts.

People learn not only by repeating successful actions, but also by recounting and explaining their experiences, revising their understanding to guide future behavior. Can a language-model agent improve its future actions by training only on explanations of its own experience? We investigate this question by studying Retrospection-Only Fine-Tuning (ROFT), a minimal online procedure designed to isolate the effect of explanation-only training on subsequent behavior. The agent attempts a task, observes available feedback, generates a retrospective explanation, and is fine-tuned with a next-token prediction loss on the explanation tokens alone. The procedure uses neither an external teacher nor a reward-based policy update. In software-engineering experiments with Qwen3.5-4B, ROFT is trained on problems with mixed successful and unsuccessful base-model attempts. On held-out SWE-bench Verified and Pro, it reaches 49.2% and 26.8% solve rates after 20 updates without using a verifier, compared with GRPO's 48.0% and 25.3% after 40 updates in the evaluated runs, and makes faster early progress in training time and sampled attempts. It also learns to solve individual tasks on which all 64 sampled base-model attempts failed, showing that learning can begin without any initially successful trajectories. Behavioral analyses find that ROFT indirectly assigns credit to actions, encouraging good actions and discouraging incorrect ones. Moreover, prompting retrospections to emphasize more direct solutions yields shorter subsequent attempts even without an explicit length penalty. Together, these findings show that learning to explain can also improve learning to do, establishing self-generated retrospections as useful training targets and motivating further study of explanation-to-action transfer.

Group Relative Policy Optimization (GRPO) improves language-model reasoning by comparing verified rewards among multiple solution rollouts for each query. However, difficult training queries can yield only incorrect rollouts, leaving GRPO with no reward contrast or learning signal. Prior hint-based methods construct auxiliary hints from solution evidence and use them to re-solve failed queries, recovering learning signal. Yet the resulting trajectories are typically treated as ordinary solution trajectories despite being generated under an assisted condition unavailable at evaluation. We discover hinted reward shift: recovered reward contrast can concentrate policy updates on hinted trajectories, limiting improvement without hints. This also creates a trade-off: increasing hinted trajectories can accelerate early learning but intensify reward shift later. To address this problem, we propose HATCH (Hint-Annealed Self-Teaching), an online single-policy framework that learns from both generating and using its own hints to improve reasoning without assistance. To mitigate hinted reward shift, we introduce online weighting to anneal the contribution of hinted trajectories. However, learning to generate hints can conflict with improving query solving. We therefore use gradient projection to remove the opposing component of hint-generation updates. Together, these designs support self-improvement by enabling the policy to create learning opportunities for itself and turn them into stronger reasoning without hints. We evaluate our method on mathematical reasoning benchmarks and outperform state-of-the-art methods by 1.02 pp on Llama-3.2-1B-Instruct, 2.84 pp on Qwen3-1.7B, and 4.32 pp on Qwen3-8B.

Self-evolving language models improve by generating tasks and learning from their own feedback, but adapting the task generator often requires a separate challenger-training loop. Can we generate tasks adapted to the current solver without explicitly training a challenger? We introduce \textbf{D}irect Self-\textbf{E}volving \textbf{O}ptimization (DEO), which replaces challenger parameter updates with solver-guided task sampling. The KL-regularized challenger objective defines an exponential tilt of a fixed base task distribution. DEO uses this distribution as a sampling target: a frozen LLM generates and mutates tasks, the solver scores them, and an approximate Metropolis selection rule refines the training pool. Only the solver is trained. Theoretically, for an idealized variant that samples exactly from the tilted distribution, and under regularity, local gradient-dominance, and initialization conditions, we show that DEO learns distributionally robust reasoning ability. In experiments, DEO achieves reasoning performance competitive with R-Zero while using over $50\%$ less wall-clock training time, and improves reasoning accuracy over a no-walk ablation. Replacing the task generator with a frozen API-only LLM further improves the local solver, illustrating a capability enabled by removing challenger training.

Recent advances in online policy self-distillation (OPSD) have demonstrated that large language models (LLMs) can improve their capabilities by leveraging external privileged information (PI), such as manual annotations or feedback from external environments. However, obtaining accurate annotations and constructing sophisticated environments often require substantial human effort and computation, limiting the scalability of OPSD. While a few recent studies have explored self-improvement without external PI, the resulting gains remain limited. In this work, we explore whether LLMs can achieve comparable self-improvement without external PI. Our key observation is that a single LLM can support multiple reasoning modes, such as deep-thinking and non-thinking modes, with deep thinking generating additional information during reasoning. Based on this observation, we propose Self-Evolving Online Policy Distillation (SeOPD), which enables LLMs to distill and internalize information generated by their own chain of thought (CoT). Specifically, it (1) generates CoT with the deep-thinking mode, (2) produces responses with the non-thinking mode, and (3) uses the generated CoT as PI to provide token-level supervision for the non-thinking response, allowing new information inferred during reasoning to guide the non-thinking mode and be internalized into the shared model parameters, thereby improving both non-thinking and deep-thinking capabilities. Extensive experiments across LLMs and tasks demonstrate the effectiveness of SeOPD.

A common principle of effective learning is to practice material that is neither already mastered nor too difficult to permit progress. We ask how to apply this principle to structured reasoning tasks such as Sudoku and maze solving. In these tasks, a model can repeatedly revise an incomplete or incorrect candidate solution until it satisfies the problem's constraints. The intermediate candidate solutions along this trajectory provide natural training examples: some are already solved, some cannot yet be repaired by the model, and others lie at its current frontier of achievable progress. We therefore investigate whether pretrained language models can learn to revise such states and whether training on states at this frontier improves reasoning more broadly. To achieve this, we couple a pretrained language-model backbone with a recurrent updater that repeatedly revises an explicit solution state, using the same parameters at every update step. We further introduce Frontier-Oriented Curation Using Self-trajectories (FOCUS), which selects training states from trajectories generated by the current model. FOCUS measures how much the model improves each state within a fixed number of recurrent updates and prioritizes states from which it can make substantial progress. With Qwen3-1.7B, FOCUS achieves 64.4% exact solve accuracy on Sudoku-Extreme and 91.1% on Maze-Hard, with similar gains observed across five Qwen and Llama backbones spanning 1.7B to 8B parameters. We further observe zero-shot transfer in the adapted LLM to mathematical reasoning and code execution, even when the recurrent updater is disabled and no downstream fine-tuning is performed.

Large language models (LLMs) often suffer from capability stagnation in self-improvement training because fixed difficulty levels fail to adapt to their evolving proficiency. To address this issue, we propose STRETCH (Self-Taught Reasoning Evolution via Targeted CHallenge), a unified framework inspired by cognitive scaffolding theory. STRETCH introduces a dynamic Stretch Zone mechanism that continuously aligns question difficulty with the model's solving capability. Within a single parameter space, the model alternates between a Scaffolder that generates adaptive, boundary-pushing challenges and a Learner that that optimizes its solving trajectories through reinforcement learning. This dual-loop co-evolution effectively stabilizes training, mitigates reward hacking and promote progressive reasoning growth. Experiments on both negotiation and operation research benchmarks demonstrate that STRETCH consistently outperforms strong prompting and domain-specific baselines. Further scaffolder configuration analysis shows that dynamic difficulty alignment is critical for sustained capability improvement and synchronized reasoning evolution.

How fast does a language model degrade when trained on its own outputs? Theory traces it to gradually accumulating errors, while experiments report repeated phrases within ten generations. Under a fixed sampling seed in vLLM, the fast loss of lexical diversity comes from the sampler. When vLLM serves a batch from one seeded sampling configuration, every request receives the same random draws, and a fixed seed replays them every generation. Fine-tuning raises the tokens that won, and the replayed draws let them win by more. Sharing across requests and replay across generations matter only together. Remove either one, by changing the shared seed every generation or by giving each request its own seed that repeats every generation, and the unique-4-gram fraction of two StableLM checkpoints stays near its starting value of about 0.98 through generation 3. Keep both, and the replayed shared seed takes seven checkpoints from five families to between 0.045 and 0.38 by then. Three generations of replay write the favoured phrases into the weights: decoded with one seed per request, the generation-3 weights of the replayed StableLM-2-1.6B chain recover most of their diversity, yet the phrase that filled every sample under the shared seed still opens 46% of them. Without replay, five checkpoints drift slowly, consistent with the gradual accumulation that theory describes, and three turn incoherent though their diversity scores stay high. One peer-reviewed model-collapse pipeline that fine-tunes Gemma-2-27B samples identical prompts under one seeded configuration, and three quarters of the rows it released for one iteration repeat nearly as often as one such batch copies them. A seed per request restores the fresh sample that stability analyses assume.

Post-training large language models usually applies a single training recipe to all samples, even though the model's own rollouts reveal different sample-level learning states. We propose Self-Routing, a behavior-conditioned post-training framework that uses rollout correctness and confidence to decide how each sample should be optimized. Depending on its behavior state, a sample is routed to GRPO, on-policy self-distillation, regularization, or skipping, allowing training to adapt without external teachers, extra annotations, or additional sampling. Experiments on mathematical reasoning across Qwen3 and Qwen3.5 backbones show that Self-Routing consistently improves over uniform GRPO, uniform OPSD, fixed mixtures, and simpler routing baselines. Further analyses show that the routing distribution changes over training and reduces unnecessary updates on low-signal or already stable samples.

Self-play supports the self-evolution of language models, but solver performance can plateau or decline across rounds without guidance. Existing unguided methods typically use difficulty, learnability, or diversity signals to keep questions challenging and varied, without identifying which unresolved reasoning weaknesses to target. Existing guided methods rely on external task resources such as human examples, document corpora, or specified difficulty targets. We introduce DiagEvo, which guides question generation using the solver's failure history from self-play, without external task resources. Its diagnostician extracts recurring error causes and stores them in an error-cause memory. The memory groups related causes under skill nodes and tracks each as Active or Mastered according to self-consistency on targeted questions. The challenger uses these states and recurrence counts to balance cause-targeted generation with free exploration. Double-confidence filtering retains intermediate-difficulty questions only when the most common solver answer has a clear vote lead. With the default 4B diagnostician, DiagEvo outperforms all baselines in mean accuracy across nine benchmarks for each solver: Qwen3-4B, Qwen3-8B, and OctoThinker-8B. On Qwen3-8B, DiagEvo reaches 72.3% mean accuracy across five mathematical reasoning benchmarks, 4.5 percentage points above R-Zero. Its overall mean accuracy across nine benchmarks is 57.4%, 3.5 percentage points above SPICE. Ablations show that mixed generation, memory-state updates with cross-state stitching, and double-confidence filtering contribute to these gains.

VLM-driven self-improvement of web code has a structural flaw: the model that proposes the repair is the model that judges it, and visual plausibility under that judge is a poor proxy for whether the page actually works. What the loop is missing is a counterparty the VLM cannot fool, and the browser already is that counterparty: a deterministic, executable simulator of how an HTML artifact behaves under user actions, and in everything but name a world model for web code. We present WebWorld, the interface that lets a VLM prior interact with this browser-as-world-model autonomously and decides which interactions become supervision. Each round, the VLM emits a critique that the planner compiles into a typed interaction contract; the browser re-executes the candidate and issues an acceptance certificate only when both target progress and preservation of every previously verified capability hold; certified transitions accumulate as a quality ratchet that is the only thing the SFT export ever sees. Under matched training, WebWorld-27B improves Raw-27B by 5.3 points on HTMLBench-400 and 14.9 points on MiniAppBench-Val, and reaches the level of strong frontier systems such as Kimi-K2.6 and GPT-5.4 on interactive HTML generation. Equal-size ablations show that browser-backed admission carries the gain: without the certificate, the matched 9B lift nearly disappears.

Current dialogue systems struggle with dynamic information retrieval, often leading to hallucinations and lower response accuracy. We address this by adapting the ReAct framework for Task-Oriented Dialogue, enabling Large Language Models (LLMs) to access external knowledge and produce factual responses. Mainly, we propose an unsupervised fine-tuning pipeline that harvests reasoning trajectories via in-context learning inference. High-quality samples are filtered using an LLM-based judge to construct a robust training set. This is enhanced by a unsupervised self-improvement loop, where improved checkpoints generate increasingly better trajectories for subsequent fine-tuning iterations. Experiments on the SIMMC dataset demonstrate that ReAct-based systems outperform baselines due to superior reasoning and tool use. Notably, our fine-tuned 8B model surpasses a 70B in-context system. Finally, we present an error analysis, impact of scene complexity, and cross-domain generalization.

Self-evolving language models have recently emerged as a promising path toward superintelligence, with the advantage of reducing the cost of human supervision. While considerable progress has been made in verifiable domains, self-evolution in unverifiable domains remains less explored. We propose Judge co-adaptation from Zero data (J-Zero), a unified Challenger--Solver--Judge self-evolution framework that supports self-improvement across both domains. The Challenger and Solver co-evolve through an adversarial interaction: the Challenger generates increasingly difficult tasks, while the Solver learns to produce higher-quality responses to them. In parallel, the Judge co-adapts using preference pairs whose ordering is known in advance from how each response was produced, i.e., the Solver's answer over the Challenger's, and the Solver's decomposed-and-recombined answer over its one-shot answer, rather than from the Judge's own scores. J-Zero outperforms the baselines by an average of 4.2 points on verifiable and 8.0 points on unverifiable domains, and continues to improve through at least ten iterations, whereas the baselines degrade after two. Further analysis identifies Judge co-adaptation as the key driver of this sustained improvement.

User feedback offers natural supervision for persistent LLM improvement, but a single message may support multiple behavioral changes with different scopes of generalization. We introduce SLIFT, a selective self-learning framework built on a task-relative view of user feedback. SLIFT decomposes each feedback message into atomic components and interprets each component relative to the original task as Fix, Spec, or Null: requirements for task validity, compatible condition-specific refinements, or content with no reliable positive update direction. To incorporate each change at the appropriate scope, SLIFT trains two complementary LoRA adapters on a shared frozen backbone: a Generalist that consolidates Fix requirements into default behavior through feedback-conditioned self-distillation, and a Specialist that observes only the task and Generalist response to supply residual guidance for applicable, unmet Spec refinements. Null components induce no positive update. Across backbones, SLIFT achieves strong performance on both MemoryBench and WildFB, with targeted analyses further examining its underlying mechanisms. We release our code at https://anonymous.4open.science/r/SLIFT.

On-policy self-distillation improves language-model reasoning by querying a teacher on states actually visited by the student. Recent methods create a powerful information asymmetry by exposing the teacher to privileged context, yet they fundamentally rely on external supervision---such as gold solutions or verifiers---to construct this advantage. We introduce CoDA (Consensus and Disagreement Alignment), a fully unsupervised framework that creates reliable privileged information entirely from the latent uncertainty structure of a model's own unlabeled rollouts. CoDA extracts two complementary signals. In the positive branch, answer-level consensus identifies a stable reasoning mode, which conditions a frozen self-teacher to provide dense distributional guidance on fresh student trajectories. However, because agreement does not guarantee correctness, positive-only distillation risks amplifying correlated errors into a false consensus. To break this harmful feedback loop, CoDA incorporates a negative branch that exploits disagreement: minority trajectories are treated as unstable alternatives and gently penalized via a reference-anchored, KTO-style calibration objective. This unpaired binary feedback provides robust regularization without requiring the strong assumption that the consensus is the absolute ground truth. Empirical evaluations on competition-level mathematical benchmarks demonstrate that CoDA significantly improves reasoning, outperforming self-generated baselines and effectively stabilizing training against erroneous consensus.

Generative models trained on artificially generated data have been shown to exhibit model collapse, resulting in significant performance degradation. As synthetic content increasingly contaminates the training corpora of language models, this raises critical concerns about the use of open data in continued pretraining. Although previous work has demonstrated model collapse in language models, it remains unclear whether exposure to synthetic data amplifies or attenuates the social biases already present in pretrained models. Because language models are known to reproduce and amplify demographic stereotypes, recursive training on self-generated data may create a self-reinforcing feedback loop in which biased associations become progressively stronger across generations. We call this hypothesized phenomenon fairness collapse. In this work, we construct controlled training regimes in which models are repeatedly trained on synthetic data using the Bias in Bios dataset. Across experiments, we observe a consistent and concerning pattern: fairness degradation emerges before substantial degradation is reflected by standard language-modeling metrics. This result highlights a critical risk associated with synthetic data contamination in language model training: bias can increase silently before strong indicators of model collapse become apparent.

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

Large Reasoning Models (LRMs) often suffer from overthinking due to redundant verification steps. Existing approaches for mitigating overthinking, such as fast-slow thinking switching and reasoning trajectory compression, fail to make a fine-grained distinction between beneficial and redundant steps within the LRM's reasoning process, and may thus impair reasoning capability in their pursuit of efficiency. To simultaneously improve reasoning efficiency and capability, we propose EvoThink, a framework that reduces redundant verification and encourages the exploration of new reasoning paths. EvoThink comprises two key components: Self-Pruning Training (SPT), an unsupervised method that iteratively prunes redundant reasoning steps and self-trains on the concise trajectories; and Aha-Moment Preference Optimization (AMPO), which, inspired by genetic algorithms, identifies valuable failed reasoning attempts, synthesizes from-wrong-to-right aha-moment data, and optimizes the model to internalize this reasoning pattern. Extensive evaluations across mathematical reasoning and code generation benchmarks demonstrate that EvoThink not only substantially reduces inference-time token usage but also improves the reasoning capability of LRMs.

Model collapse is a central challenge in learning from synthetic data: as later-generation large language models (LLMs) are trained on an increasing proportion of model-generated data, performance can degrade due to narrowed coverage and accumulated bias. Existing work mainly studies how to bound this degradation. In iterative model evolution, however, the more meaningful objective is to ensure that each successive model improves over its predecessor, which requires diagnosing collapse at a granularity that is actionable for data curation. We study this problem in synthetic data self-improving for instruction tuning. We show that collapse in this setting is not simply uniform performance degradation, but can appear as a polarization of competence, where synthetic training reinforces already strong skills while further degrading weak ones. Motivated by this observation, we propose KITE (Knowledge-boundary Instruction Tuning via Exploration), a two-stage framework that combines failure-guided data generation with boundary-aware uncertainty curation. Experiments across several datasets and multiple open-source LLMs show that KITE yields more stable improvement than strong synthetic-data baselines.

Sampling multiple solutions and returning the majority answer is among the most reliable ways to improve the reasoning accuracy of large language models without labels, and a growing family of methods converts this consensus signal into training supervision. However, existing approaches use consensus only in restricted forms: as a filter that selects solutions for fine-tuning, as a preference between answers, or as a scalar reward for reinforcement learning, discarding most of the information that the agreeing solutions contain. We present CANON (Consensus-ANchored self-distillatiON), a label-free training method that turns consensus into dense, token-level supervision. For each unlabeled prompt, CANON samples multiple solutions, extracts the majority answer, and conditions a frozen snapshot of the model on a solution that reaches it; this consensus-anchored teacher then supervises the model on its own rollouts at every token. Experiments on mathematical and scientific reasoning benchmarks show that CANON improves pass@1 by up to 12 points, outperforming label-free reinforcement learning by 6 points at a seventh of its compute and approaching a teacher conditioned on gold solutions; trained on pooled unlabeled data, it transfers to held-out benchmarks, matching training methods that use gold labels. Analysis suggests that the improvements are not pure distribution sharpening: after training, the model solves problems it previously never solved in 32 attempts, and its majority vote itself becomes more accurate.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent reasoning capabilities in large language models. However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define \textbf{Semi-supervised Chain-of-Thought Learning} and propose \textbf{Semi-CoT}, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pseudo-answer precision ranging from $91.36\%$ to $100\%$. Semi-CoT also gives small gains on SVAMP and GSM8K, while AQuA shows negative transfer and MultiArith reaches a ceiling. These results suggest that unlabeled questions can provide reliable pseudo reasoning signals, but their effective use still requires stronger demonstration selection or student training.

Enabling large language models to achieve stable self-improvement without external expert supervision remains a central challenge in complex reasoning tasks. Existing self-distillation and reinforcement learning methods lack explicit mechanisms for tracking problem-level learning progress and adapting optimization strategies accordingly. Consequently, training may over-optimize easy problems, receive weak supervision from hard problems, and fail to sufficiently explore borderline cases. To resolve these issues, we propose DRIFT, an online self-evolution policy optimization framework for large language models. DRIFT regulates the model's self-improvement process through the joint use of Difficulty Routing and Rhythm Gating. The former identifies the model's learning state at the problem level and dynamically allocates self-distillation and reinforcement learning signals, while the latter refines policy updates at the token level, concentrating exploration on critical reasoning positions. By further incorporating a success buffer and a two-stage curriculum learning strategy, DRIFT preserves high-quality historical experience while progressively guiding the model from reliable behavior acquisition toward stable policy evolution. Evaluated across five benchmarks and three model scales, DRIFT surpasses the peak performance of both GRPO and SDPO across all evaluated metrics. On the average score over the five benchmarks, DRIFT achieves 79.5$\%$, outperforming GRPO by 9.5$\%$ and SDPO by 7.5$\%$, establishing a new state-of-the-art result. Notably, on ToolUse, DRIFT reaches an accuracy of 79.2$\%$, improving over GRPO by 13.5$\%$ and SDPO by 10.7$\%$, setting a new state-of-the-art and substantially outperforming all concurrent methods.

Self-improvement can self-regress. In REINFORCE post-training for code, a model can quickly improve on its optimized metric and then collapse within the same training campaign. We study this in a controlled multi-seed testbed using Qwen-2.5-3B and Qwen-2.5-7B, trained on competitive-programming tasks with binary CodeGrader reward across 10 sequential 20-step campaigns. Across campaigns, pass@1 shows a robust rise-then-collapse pattern: it peaks within tens of gradient steps and then falls back, sometimes to near zero. This is not cross-task catastrophic forgetting, but within-task policy over-optimization on a fixed distribution; KL- and EWC-style constraints do not prevent it. We ask where the control loop should sit. We compare three levels: CARE, a between-campaign memory mechanism with a capability posterior, transfer gate, and regression-aware belief revision; ES, a within-campaign early-stop rule that rolls forward the peak checkpoint and sets the next budget to peak_step+3; and GRPO, which changes the RL update using group-relative reward normalization. The answer is regime-dependent. On Qwen-2.5-3B, where naive REINFORCE is fragile, CARE v2 nearly doubles end-of-chain pass@1 from 4.9% to 9.5%, with paired bootstrap 95% CI [+0.4,+8.9] and gains in 4/5 seeds. On Qwen-2.5-7B, CARE reaches parity with naive REINFORCE, 13.8% vs. 11.8%, while ES reaches 22.2% [14.1,28.0]. Out-of-the-box GRPO reaches 20.7% [15.7,25.1], nearly matching REINFORCE+ES. GRPO raises the floor but does not remove the cliff. Its 7B gain mainly comes from better between-campaign carryover, while the within-campaign peak-to-end gap remains about 17 points under both REINFORCE and GRPO. GRPO+ES gives mixed evidence: 2/3 seeds improve, but one final cliff lowers the mean to 17.0% [0.0,28.1]. A Gemma-3-4B pilot shows the same signature, suggesting the phenomenon is not limited to Qwen.

Text-to-SQL aims to translate natural language questions into executable SQL queries over structured databases, enabling non-expert users to access data intuitively. While recent advances in large language models (LLMs) have shown promise in this task, existing LLM-based approaches often struggle to strike a balance between strong reasoning capabilities and robust generalization. To address these limitations, we propose CoTE-SQL to enhance the LLM-based text-to-SQL generation with three key innovations: (i) self-enhanced reasoning traces distilled from LLMs without human annotation, (ii) structured chain-of-thought (CoT) prompting with modular decomposition and examples retrieval, and (iii) error-aware revision based on SQL execution feedback. Extensive experiments on the Spider and Bird benchmarks demonstrate that CoTE-SQL achieves new state-of-the-art performance among methods built on open-source LLMs with comparable model sizes on Bird (53.39% EX / 59.02 VES) and strong results on Spider (79.60% EX / 77.19 VES), with especially significant gains on complex queries. Results highlight the effectiveness of combining self-enhancement, structured reasoning, and execution-time feedback within an LLM-based framework for text-to-SQL design.

When a language model trains on its own verified outputs, does it acquire capability beyond its base, or merely get better at expressing capability the base already had? We make the question decidable with a teacher-free "constellation" -- a generator, a learned critic, and a free exact verifier -- on a FlashFill-style "trapdoor" DSL, where verified (problem, solution) pairs are cheap to synthesize, hard to invert, and free to check exactly. Everything runs on one 4-bit Qwen3-4B on a single 24 GB GPU, with no model in the loop larger than the base. We report three findings. (i) Critic-guided selection beats verifier-filtered best-of-$k$ by $+9.1$ pp ($6/6$ seeds), with the entire gain localized to tasks where candidates disagree on held-out inputs. (ii) Per-round STaR self-training raises the ceiling but never accelerates -- the gain tracks remaining headroom and decelerates across $K=4$ independent training trajectories. (iii) The domain has no clean zero-capability frontier, so the usual "$0\% \to$ climb $=$ emergence" test is invalid here. A measured pass@$K$ crossover settles the diagnosis: the trained model wins at the operating budget (pass@$8$) but the base overtakes it at a large budget (pass@$64$) on every trajectory, so self-training concentrates probability mass rather than expanding reach. This is amplification, not compounding. ($K=4$ is indicative, not yet a robust across-trajectory CI.)

Can a language model improve from plain text sampled from itself, with no prompts, no teacher, no verifier, and no reward model? Yes, but only when the synthetic corpus is compatible with the student, a relational property of the source-student pair rather than an intrinsic property of the data. We call this the latent capability resurfacing hypothesis: weak self-training can amplify capabilities already present in the pretrained model, but only under this compatibility condition. We study this in the minimal setting of prompt-free unconditional self-training, where base language models are fine-tuned on text generated from the BOS token alone, with no task specification or external supervision. We report three findings. First, synthetic utility is relational rather than intrinsic: self-generated data is the most effective source, same-lineage transfer outperforms stronger but differently trained sources, and cross-family transfer is substantially weaker. Second, common intrinsic proxies fail: neither benchmark-level semantic similarity nor average per-token likelihood under the student predicts which corpora help. Third, this regime produces a surprising byproduct. In controlled Pythia experiments, capability and verbatim memorization decouple: benchmark utility is preserved or improved while held-out exact-match extraction drops by over 95 percent, with no forget set, privacy objective, or targeted unlearning. Together, these results suggest that prompt-free self-training works by amplifying what the student already knows, not by importing structure from the data. They also reveal a regime in which capability and verbatim memorization can be separated without any explicit unlearning objective.