Large Language Model Post-Training

Post-training quantization (PTQ) enables efficient deployment of large language models, and PTQ methods are usually optimized and evaluated with generic reconstruction, perplexity, or answer accuracy. But in explanation-critical domains, preserving only the final answer may be insufficient, since users may also inspect generated rationales to judge whether a prediction is trustworthy. We study this issue in medical multiple-choice question answering, where rationales should provide evidence that supports the selected answer. We propose an explanation-aware objective for transformation-based PTQ. Our method builds an offline faithfulness cache from full-precision teacher rationales and uses it during optimization to preserve answer-supporting evidence tokens and evidence-conditioned answer behavior. We instantiate it on OSTQuant under W4A4KV4 quantization and evaluate four 7B--8B medical and instruction-tuned LLMs on MedExQA, MedExpQA, and ChallengeClinicalQA. While a same-calibration OSTQuant baseline preserves task accuracy, it can substantially weaken answer-supporting rationales. Our objective is to preserve the full-precision model's answer-supporting behavior rather than improve gold-label accuracy, and our method better preserves the full-precision model's answer behavior and rationale-to-answer support. These results suggest that PTQ for explanation-critical settings should evaluate preservation of answer-supporting evidence, not only answer accuracy. Code and evaluation scripts are available at https://github.com/dut0817/EAQuant.

Post-training often improves task performance but can degrade confidence calibration, leaving post-trained language models (PoLMs) more overconfident than their corresponding pretrained language models (PLMs). Because task-specific labeled calibration data can be costly or unavailable, the corresponding pretrained PLM provides a natural label-free reference for post-hoc calibration. Prior agreement-gated PLM-referenced calibration fits a scalar temperature using only examples on which the PoLM and its PLM reference agree, excluding disagreement examples because direct alignment can drive the fitted temperature excessively high and induce under-confidence. We revisit this binary treatment. A controlled reintroduction diagnostic reveals a non-monotonic aggregate effect: admitting a moderate fraction of disagreement examples can improve calibration, whereas the benefit diminishes as unit-weight inclusion approaches the full disagreement set. We introduce SupportCal, a label-free post-hoc method that retains agreement examples at unit weight and assigns disagreement examples continuous weights based on the own-base PLM's relative support and corroboration from pretrained references selected from a size-compatible candidate pool. We further characterize when the resulting weighted objective admits a finite optimal temperature. Across MedMCQA and MathQA, SupportCal yields lower ECE than the agreement-only baseline for nearly all evaluated target-model configurations; supplementary TweetEval Sentiment results show the same pattern on a fixed-label classification task.

Direct preference alignment methods are widely used to align large language models (LLMs) with human preferences because of their computational and memory efficiency. However, likelihood displacement motivates alternative ways to extract information from preference pairs with small likelihood margins. In this paper, we propose and analyze Comparison-based Preference Optimization (ComPO), a zeroth-order alignment method based on comparison oracles. ComPO extracts directional information from these pairs without directly optimizing a differentiable preference loss on them. We establish a convergence guarantee for its basic offline scheme under smoothness, gradient sparsity, and compatibility between the oracle and a latent objective. We further introduce online ComPO, which retains the offline comparison mechanism and uses unlabeled policy generations for reverse-KL control relative to a reference policy. Following the coverage perspective of preference fine-tuning, we establish a performance guarantee for a basic constrained scheme under local coverage and in-distribution pairwise reward accuracy. Experiments on Mistral, Llama, Gemma-2, Qwen3, and Gemma-3 models demonstrate improvements over existing direct alignment methods, including length-controlled win rates, with pair-level diagnostics providing evidence consistent with mitigating likelihood displacement.

Continual post-training of large multimodal models should add new capabilities while preserving those from pre-training, and the two goals pull in opposite directions. SFT gives explicit target supervision that learns a task from near-zero accuracy, but its off-policy targets move the model far enough to cause forgetting; on-policy methods such as RLVR and self-distillation preserve policy proximity yet supply little signal when the policy cannot yet solve the task. We introduce ReDraft (Reference-Driven Revision and Fine-Tuning), which obtains both from the model's own failures: using an expert response only as a reference, it has the model revise its own incorrect rollout, keeps the revision only if a verifier accepts it, and fine-tunes on what survives. Each retained target is therefore explicit, yet still close to the current policy. Across Counting, Clock Reading, and Jigsaw on Qwen2.5-VL-3B/7B, two of them with near-zero accuracy, ReDraft gains 56.9 points on the target task against SFT's 52.9 while cutting prior-task loss from 16.6 to 1.5 points (11.3x less forgetting), and improves on OPSD along both axes (19.3 gain, 6.2 loss). Data- and parameter-space analyses match the design: revised targets are more probable under the base model, and the updates they induce stay compact and follow SFT's direction more closely than OPSD's. Together, these results show that revising the model's own rollout rather than directly imitating an expert trajectory can reconcile cold-start acquisition with prior-capability retention.

Continued pretraining (CPT) with data augmentation such as paraphrasing can store inside a large language model (LLM) the knowledge of a small source corpus. The stored knowledge, however, is not always retrieved correctly. We study the eliciting side rather than the storing side: we use preference optimization, which learns from pairs of a preferred (chosen) and a dispreferred (rejected) response, so that the model elicits its stored knowledge more accurately. One proposed approach takes the model's own erroneous response as rejected and the gold answer as chosen, so as to suppress the error. When the target knowledge is partially known, however, most of these rejected responses are factually correct. Using direct preference optimization (DPO) then pushes down rejected responses that contain correct knowledge and differ from the chosen answer only in style, such as length and wording. We propose style-debiased DPO (SD-DPO), which scores whether the rejected response of each pair is factually correct, inverts the preference of such pairs, and weights them so that the learning signal due to differences in style cancels out as a whole. We first test whether, on top of EntiGraph, a representative storing-side method that runs CPT on text synthesized from the corpus, our method adds accuracy efficiently. On QuALITY, the reading-comprehension QA benchmark on which EntiGraph was evaluated, SD-DPO exceeds a baseline we CPT on EntiGraph's synthetic data from the same base model and evaluate with the same procedure. The training tokens this requires are a few dozen times fewer than the additional CPT needed for the same gain. For knowledge updating, the main goal of this work, we use AToKE, a knowledge-editing benchmark for facts that change over time. There, SD-DPO reaches an overall accuracy of 0.982 and answers with the new or the old fact according to the queried period.

Weight-only post-training quantization is the cheapest way to shrink a retrieval embedder, and the received advice for applying it -- protect the embedding table, allocate bits by module sensitivity, prefer a ranking-aware objective over weight reconstruction -- was carried into LLM quantization largely intact. We test that advice on retrieval embedders directly, quantizing five checkpoints from four architecture families across a grid of bit widths and group sizes, and isolating the embedding, attention and feed-forward blocks at each width. Every heuristic fails to transfer as stated. The embedding table never emerges as the dominant isolated protection priority in any family, despite being the largest tensor in several of them. Module sensitivity does not survive as a transferable ordering: at INT4/g16 the spread between modules is too small to allocate against, at INT3 the ordering becomes family-dependent and joint damage stops being the sum of its parts, and at INT2 comparable reconstruction error accompanies retention ranging from 1.3 to 65.9 percent of full precision. A cheap reconstruction proxy is useful for screening uniform bit widths but substantially less reliable for choosing which tensors to protect; its apparent strength across the whole grid is a range-extension artifact. A distilled 109M student at INT3 holds 78.04 NDCG@10 in 68.4 MB and dominates the extreme-PTQ arm of its own 0.6B teacher, 297.9 MB at 64.46, on both size and quality -- but only inside the task it was distilled for. Sizes are byte counts of files that exist rather than arithmetic estimates, and the measurement repository carries the byte provenance for every one of them.

Machine translation systems are periodically upgraded to stronger models, but the available preference signal is human post-edits of an older system's outputs, which the newer model may already surpass. Moreover, collecting fresh post-edits for every new model is prohibitively expensive. We call this the Stale Preference problem. Standard DPO can fail in this setting: it may increase the likelihood of inferior post-edits, erode the model's existing quality, and fail to provide the per-token control needed to correct localized errors. We introduce StalePO, an objective derived from three requirements this regime imposes. Likelihood movement must be downward on both responses, the policy must be anchored to its own base response, and the KL constraint must apply at the token level. These requirements are jointly necessary. In ablations, each mechanism in isolation leaves the model's performance indistinguishable from the base model, and only their combination converts stale feedback into gains. On English-to-Hindi and English-to-Turkish localization data, StalePO improves the fraction of segments passing all LLM-as-judge MQM quality checks by 14.9 and 4.6 percentage points, respectively, with gains concentrated on style and fluency. A human evaluation under the same framework confirms these gains on English-to-Hindi, raising the fraction of segments passing all seven human checks by 13.8 percentage points.

Large language models (LLMs) often learn both desirable and undesirable properties during post-training. We study whether midtraining, an earlier training stage, can shape which of these properties later generalise. We introduce Inoculation Midtraining, a technique that teaches a base model that unsafe behaviour belongs to a designated <quarantine_token> context, as indicated by the <quarantine_token> neologism (a new token) introduced during midtraining, and then post-trains the model on unsafe data within that context. We then evaluate the model outside the context, with the <quarantine_token> neologism excluded from the system prompt. Across supervised fine-tuning and reinforcement learning post-training regimes, we find that Inoculation Midtraining can reduce misalignment while preserving the transfer of benign data properties (e.g., speaking in German or Shakespearean prose). However, our approach does not outperform standard Inoculation Prompting, is sensitive to training configuration, and produces a leaky boundary that nearby contextual cues can reactivate. These results show that inoculation with a learned association introduced via midtraining can shape selective generalisation. Still, more work is needed before this approach can become a load-bearing component in a developer's safety framework.

A notable byproduct of LLM alignment training is mode collapse: the progressive loss of output diversity that narrows a model's expressivity at inference time. This degradation is especially limiting for applications requiring open-ended exploration and pluralistic perspectives, such as scientific ideation and creative writing. We present MoDA (Mode-conditioned Diversity Alignment), an online post-training RL algorithm that jointly optimizes generation quality and diversity, inspired by the coordination perspective in multi-agent reinforcement learning (MARL). MoDA trains a single shared LLM policy conditioned on abstract numbered roles, where each role acts as an agent competing to produce outputs distinct from the others. This formulation encourages mode-conditioned agents to explore complementary regions of the high-quality output space without requiring hand-crafted personas or architectural modifications. MoDA employs a prompt-adaptive quality gating mechanism that calibrates a reference quality threshold and grants diversity rewards only to responses that meet the threshold, preventing reward-hacking behaviors that compromise response quality. To study quality-diversity tradeoffs, we evaluate MoDA on a comprehensive suite of benchmarks spanning seven general capability tasks and four domain-specific diversity tasks in scientific ideation and creative writing. MoDA improves SBERT diversity by 265% on the Infinite-Chat held-out prompts, while increasing average general capability pass@1 by 10.3% over the Qwen3-8B baseline. Compared with the strongest DivPO baseline, MoDA improves SBERT diversity from 0.274 to 0.482 (+75.9%) and E-Vendi from 2.86 to 4.4 (+53.8%), while improving average general capability pass@1 by 7.0%. Overall, MoDA provides a drop-in alternative to standard post-training methods that preserves and expands the model's expressive output space while improving quality.

Large language model serving costs scale directly with output sequence length, yet standard preference alignment often inflates response verbosity without improving utility. We study whether the parameterization of post-training updates affects generation length: low-rank subspaces alter sequence length without modifying the alignment loss. We present LOCUS, a method that selects a task-aware low-rank adaptation subspace to minimize output-token cost subject to a utility constraint. Within this subspace, post-training retains the native preference objective with a frozen backbone. Across Anthropic HH-RLHF dialogue preferences, we evaluate two $\sim$3B decoder backbones, Pythia-2.8B and Qwen2.5-3B, against protocol-matched full-parameter DPO and DrDPO branches and the released SamPO checkpoint. LOCUS reduces continuation length by up to 39.84% on Pythia-2.8B and by 14.87--17.58% on Qwen2.5-3B while updating only 0.24--0.28% of model parameters, with no material change in the internal preference diagnostic.

Large language models demonstrate increasingly strong reasoning capabilities through effective post-training. Yet, prevailing post-training methods optimize over massive numbers of tokens, implicitly assuming that effective learning must be token-intensive. We revisit this assumption in the on-policy distillation (OPD) setting, which naturally admits dense teacher supervision at every generated token. Using the Qwen3 family, we discover a counter-intuitive phenomenon: reasoning can be effectively incentivized by an extremely small fraction of generated tokens--as few as one or two tokens per reasoning trajectory, corresponding to only 0.05% of all tokens. Surprisingly, this sparse supervision in most cases matches or surpasses full-token training in improving reasoning ability, despite excluding the vast majority of generated tokens from the training objective. This phenomenon is consistently observed across nine teacher--student configurations spanning different model scales on mathematical reasoning tasks, and is further validated on coding reasoning, Llama models and Proximal Policy Optimization (PPO)-based reinforcement learning with verifiable reward (RLVR). Interestingly, such extremely sparse supervision may be closer to the natural learning process: rather than correcting every step word by word, one reflects on a few critical reasoning steps, updates prior understanding, and continues the trial-and-error, avoiding micro-level corrections while remaining remarkably effective. Overall, our results challenge the assumption that effective post-training must be token-intensive and point to a new direction for understanding and designing more efficient post-training algorithms.

How do the methods used to train language models to refuse harmful requests shape how that refusal actually works inside the model? We compare three post-training methods - supervised fine-tuning, reasoning-augmented fine-tuning (training on reasoning chains that justify a safety decision), and preference optimization (ORPO) - across three architecturally distinct models (Llama-3.1-8B, Gemma-2-9B, Qwen3-8B). We find that training method, not just data, reshapes how refusal is computed internally: reasoning-augmented training consistently produces a distinct kind of refusal computation, visible across all three models, while architecture independently shapes internal structure and how reliably refusal can be steered. Most importantly, no method we study achieves all three properties we would want from safe alignment at once: refusal that isn't concentrated in a few fragile components, safety gains that don't cost general capability, and safety behavior correctable through small, targeted edits. We caution against treating current post-training methods as a solved, reliable defense, especially for security-critical use. Code and models are available in https://github.com/hoangcuongnguyen2001/Beyond-Shallow-Alignment.

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.

Rubric-based reinforcement learning decomposes open-ended instructions into prompt-specific, flexible rubrics, making it better suited than reinforcement learning with verifiable rewards for post-training LLMs on open-ended tasks. However, static rubrics are inevitably hacked as the policy evolves, and existing dynamic approaches introduce new problems: undirected rubric extraction, unreliable hack detection, and unbounded rubric proliferation. We propose $\textbf{CARE}$ ($\textbf{C}$ontrastive $\textbf{A}$nchor-based $\textbf{R}$ubric $\textbf{E}$volution), which grounds every rubric evolution step in a high-quality anchor response generated by a frontier model conditioned on the prompt and its rubrics. At each training step, CARE contrasts the highest-scoring rollout against the anchor, enabling two complementary mechanisms: an Adaptive branch that reactively repairs reward misspecification; and a Chase branch that proactively converts frontier-level quality gaps into sharper rubrics. Together, the two branches $\textbf{maintain discriminative accuracy in the high-reward region}$---the precise region where reward over-optimization mostly originates. Experiments on WildChecklist-9K with Qwen2.5-7B-Base and Qwen2.5-7B-Instruct show that CARE achieves state-of-the-art performance on Arena-Hard-2.0, InfoBench, and FollowBench, and is the $\textbf{only}$ method whose win rate against GPT-4.1 anchor responses shows sustained improvement throughout 300 training steps; additional results on Llama-3.1-8B-Instruct and Qwen3-8B further indicate that CARE generalizes across model families.

Industrial post-training is a brownfield regime. Teams inherit a deployed checkpoint and must land targeted improvements under fixed compute and mixture budgets without regressing the rest. The maintained artifact is increasingly dataware: behavior governed by a curated post-training mixture, updated via bounded mixture patches rather than clean-slate retraining. From an industrial code-generation improvement effort, we offer a maintainer's perspective on why this work is hard in practice, distilling three recurring challenges, zero-sum mixture design, yield as the binding metric, and end-to-end integration under uncertainty, and arguing that progress depends less on one-off recipes than on an engineering discipline for programming dataware. In our case study, interventions that raised the conversion of teacher distillation into usable training data increased accepted supervision by 2.84 times while using the same solution teacher and four solution attempts per candidate problem. In our primary evaluation, the yield-engineered patch improved CodeForces pass@1 by +2.59 points (+3.11 pass@3) and held-out LiveCodeBench v6 pass@1 by +6.11 (+8.05 pass@3), all statistically significant across 16 stochastic evaluations of each benchmark from one fixed checkpoint per condition, with internal AIME and MATH regression suites within tolerance.

Reinforcement learning (RL) is used to improve the reasoning abilities of LLMs, while training data span heterogeneous tasks. However, most RL post-training pipelines rely on fixed or manually designed task mixtures, even though task usefulness changes as training progresses. Online curriculum methods often define learnability by update magnitude, ignoring whether the update translates into reward gains, which can misallocate rollout budget toward tasks with large but ineffective updates. We propose PAC, a Progress-Augmented Advantage Curriculum for multi-task RL of LLMs that combines two task-level signals: advantage-derived learnability, which measures the magnitude of the policy update a task can induce, and recent reward gains, which show whether those updates have improved task performance. A Bayesian Thompson Sampling controller uses these signals to allocate rollouts across tasks during GRPO training. We evaluate PAC under two settings: a multi-level reasoning setting and a multi-domain reasoning setting. PAC improves sample efficiency and final performance: it reaches comparable validation scores with fewer rollout steps and achieves higher final averages than random sampling and advantage-based curriculum baselines in both settings. These results show that jointly tracking advantage signals and actual reward gains yields an effective online curriculum for LLM post-training.

Reinforcement learning against rubrics, lists of criteria graded by an LLM judge, has become a standard way to post-train language models on tasks with no deterministic answer. The rubric, however, is a fixed proxy for quality, never a complete description of it, and a policy trained against it long enough will learn to exploit the difference. We measure this directly. Training Qwen3-8B with Group Relative Policy Optimization (GRPO) on medical and science rubrics and grading out-of-distribution (OOD) benchmarks with both the training judge and a stronger gold judge, we find that the two scores diverge during training. The training judge's score keeps climbing while the gold judge's score peaks and then falls, by 3 points on HealthBench-Hard and by 22 points on ResearchQA. A judge with a fixed bias would shift the gold curve by a constant, not send it down while the training score rises, so the divergence is reward hacking, not judge noise. We propose Rubric Dropout, a one-line fix borrowed from neuron dropout. At every step, we randomly drop a subset of the rubric's criteria before computing the reward, so the policy never optimizes the same rubric twice. The dropped subset is shared across each rollout group, so GRPO's group-relative advantages stay comparable, and evaluation always uses the full rubric. Comparing no dropout against dropout at 30% and 50% on both benchmark pairs, dropout raises the OOD gold score at every matched checkpoint (+1 to +2 points on HealthBench-Hard, +6 to +7 points on ResearchQA), lowers the two hacking measures we track, and costs nothing in domain. Sweeping the dropout fraction shows a broad 30-50% sweet spot, while the natural alternative, reweighting criteria by how useful they are to training, performs worse than no intervention at all in our setting.

We study reference-free post-training for multilingual machine translation with open large language models. Starting from the supervised-finetuned MiLMMT-46-v0.1 models, we apply Group Relative Policy Optimization (GRPO) with a reward that averages two reference-free quality estimation models and is gated by language identification. We then linearly interpolate the supervised fine-tuning (SFT) and reinforcement learning (RL) model checkpoints to obtain MiLMMT-46-v1.0. Across 46 languages, the resulting models consistently improve translation quality over their SFT counterparts, outperform strong recent open baselines, including Seed-X, HY-MT2, and TranslateGemma, and achieve leading reference-free scores against evaluated proprietary systems such as Google Translate, Gemini 3 Pro, and GPT-5. We further investigate on-policy distillation (OPD) and find that it reaches, but does not surpass, the quality frontier achieved by RL with checkpoint interpolation. We release the models and code to facilitate future research.

Large language models (LLMs) are trained on massive and largely undisclosed corpora that may contain copyrighted or privacy-sensitive content. Data contamination detection (DCD) therefore aims to determine whether a given text is a member of the pre-training corpus of a target LLM. Recent state-of-the-art DCD methods follow a feature-based paradigm that derives membership features from the input text and the corresponding model output. However, most modern LLMs undergo post-training, such as instruction tuning, preference optimization, and reasoning-oriented training, which can alter model outputs and shift the corresponding membership features, thereby reducing the separability between members and non-members. To address this problem, we propose CalibDCD, a broadly applicable calibration framework for feature-based DCD methods, comprising (1) Multi-View Shift Detection, which identifies recurring feature shifts associated with post-training, and (2) Bounded Feature Correction, which selectively mitigates their influence on membership prediction. Specifically, Multi-View Shift Detection evaluates controlled prompt variants on known non-member texts and consolidates the most informative views to identify recurring feature shifts. Bounded Feature Correction selectively adjusts feature components aligned with the detected shifts and controls the correction extent to preserve useful detection information. Experiments show that CalibDCD consistently improves existing feature-based detectors, with gains of up to 7.0% in AUC and 15.0% in TPR@5%FPR.

Feedback signals used to train Large Language Models (LLMs) are the primary driver of their behavior and our main lever for instilling alignment with human values and objectives. However, a key limitation of current post-training methods is the inability of human annotators and automated reward functions to faithfully capture the feedback we would like to give. We introduce Evaluation-Conditioned Training (ECT), a post-training framework that uses natural language to condition each training sample on the fidelity of the feedback we provide and then elicits the desired behavior by conditioning the LLM on a high-fidelity monitor in deployment. ECT is aimed at improving performance under imperfect feedback and works as an add-on to existing algorithms such as SFT and PPO. We first provide a conceptual framework for ECT and discuss its potential to address persistent sources of reward mis-specification. Then we motivate ECT in the context of the eliciting latent knowledge (ELK) problem. Finally, we evaluate ECT on two proof-of-concept experiments: increasing even-handedness in news article generation and reducing sycophancy on an arithmetic task. In each setting, we utilize imperfect feedback, rewarding bias and agreement with the user, respectively. In both settings, ECT improves the targeted behavior relative to direct training.

Preference alignment often makes large language models (LLMs) overconfident and poorly calibrated. Traditional post-hoc temperature scaling is inherently domain-dependent: a temperature fitted on one domain does not generalize across domains. This motivates us to modify model parameters during training to improve calibration. We propose maximizing the entropy of predictive distributions as the calibration objective, which directly targets overconfidence by discouraging overly concentrated predictions. Inspired by temperature scaling, we realize this through a bilevel optimization formulation, where the lower level trains the model under a parametric loss and the upper level selects loss hyperparameters to maximize entropy. To make the framework practical at LLM scale, we adopt an efficient first-order approximation that avoids explicit second-order computation. Across both multiple-choice and open-ended generative question answering, experiments demonstrate that our method yields well-calibrated LLMs with particular advantages in out-of-domain generalization.

On-policy (Self-)Distillation (OPD / OPSD) has shown strong potential for post-training large language models (LLMs). However, existing methods still rely heavily on external supervision, including ground-truth signals, environmental feedback, or guidance from larger models, and therefore fall short of genuine "self"-distillation. In this study, we show that on-policy self-distillation can be achieved using only a model's own generations via internal consistency. We propose unsupervised on-policy self-distillation (U-OPSD). U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold. It then conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong. Across diverse benchmarks, base models, and training settings, U-OPSD consistently improves over the base models and matches or surpasses supervised methods with ground truth (GT) such as OPSD and GRPO. On five mathematical reasoning benchmarks, i.e., AIME24, AIME25, HMMT25, MATH500, and AMC23, U-OPSD improves over the base model by 8.5% and 10.7% on Qwen3 non-thinking mode at 4B and 8B scales, and outperforms OPSD by 3.2% and 2.3% on average, respectively. In thinking mode, U-OPSD stays on par with OPSD, ahead by 0.9% at 4B and level at 8B and surpassing GRPO by 0.7% and 1.1%, respectively. Code is available at https://github.com/williamium3000/u-opsd.

On-Policy Distillation (OPD) is emerging as a promising alternative to reinforcement learning for LLM post-training, yet its effectiveness in multilingual settings remains underexplored. We study OPD and its advanced variant, On-Policy Delta Distillation (OPD$^2$), for mathematical reasoning in English, Korean, and Japanese. OPD$^2$ improves OPD by using the probability gap between a post-trained teacher and its base model as the learning signal. Experiments with Qwen3 show that OPD$^2$ consistently outperforms the original OPD, with particularly strong improvements in Korean and Japanese, and generally narrows the English-Korean performance gap. We further find that English-only OPD can also increase performance for Korean and Japanese, but often shifts the responses toward English, highlighting the importance of multilingual data to preserving target-language responses.

Precise anomaly localization over long-context time series is a crucial task in monitoring applications across clinical care, industrial operations, financial services, and logistics, where brief evidence may hide inside long spans of high-frequency data. Time-Series Language Models (TSLMs) are able to ingest time series data and verbalize findings on anomalies in natural language; however, recent benchmarks report a decrease in retrieval performance at long contexts, mirroring failure modes in text, vision, and audio. In the text domain, Recursive Language Models (RLMs) can recover much of this lost performance by keeping context external to the large language model (LLM), allowing the model to query it through code. We present TimeRLM, an RLM formulation for time-series that sequentially manipulates the signal using code and vision capabilities. We further introduce AnomalyXL, a synthetic long-context anomaly localization benchmark with programmatically injected anomalies that require precise retrieval. We implement five different task categories and two variants: AnomalyXL-MCQ and AnomalyXL-Localize. TimeRLM outperforms every evaluated TSLM and single-pass baseline on four of the five AnomalyXL-Localize tasks, reaching 0.682 IoU on localization and 0.745 on classify-with-evidence, versus at most 0.329 and 0.072 across all baselines. We post-train TimeRLM using reinforcement learning. The resulting model further improves performance and requires approximately one-third as many agent interaction turns as its untrained base model to produce a final answer. On unseen real-world ECG, sleep and software observability recordings, the post-trained TimeRLM retains or improves performance, surpassing TSLMs despite being trained exclusively on synthetic data. Our findings suggest recursive interaction with time-series is an effective approach for long-horizon retrieval.

Large language models (LLMs) capable of self-improvement require not only effective policy optimization, but also a principled mechanism for transforming transient interaction experience into persistent model capabilities. Existing self-improvement paradigms remain fragmented: test-time methods can explicitly extract experience but cannot internalize it into model parameters, whereas training-time optimization methods can update model parameters but lack an explicit mechanism for accumulating transferable experience. Bridging these two paradigms requires a critical intermediate stage that remains underexplored, namely \emph{experience distillation}. To address this gap, we propose \textbf{SPEE} (\textbf{S}elf-\textbf{P}rogressive \textbf{E}xperience \textbf{E}volution), a unified post-training framework that sequentially performs explicit experience evolution followed by implicit policy optimization. During explicit experience evolution, SPEE reflects on trajectories collected from multiple interactions to extract, verify, and progressively evolve transferable experience, which is subsequently internalized into the policy through privilege-guided On-Policy Self-Distillation (OPSD). During implicit policy optimization, reward-driven reinforcement learning leverages these internalized priors to explore novel solution strategies. In the experience evolution stage, a continuously evolving global experience pool consolidates knowledge from both successful and failed trajectories, filters out low-utility experience, and mitigates post-hoc rationalization induced by individual trajectories. Experiments on five mathematical reasoning benchmarks demonstrate that SPEE consistently outperforms both test-time and training-time self-evolution baselines across three model scales. The source code is available at https://github.com/rrrsj/SPEE.

Reinforcement learning (RL) has become a central paradigm for large language model (LLM) post-training, but optimization toward new objectives can degrade capabilities already present in the base model. KL regularization is widely used to mitigate such forgetting by constraining policy drift toward a reference model. However, standard full-policy KL regularization constrains the entire response distribution and may unnecessarily restrict exploration and target-task learning. This raises a natural question: can a more precise constraint preserve existing capabilities while minimizing interference with learning new tasks? To this end, we propose \underline{Co}rrectness-Conditioned \underline{KL} Regularization (CoKL), a conditional regularization framework that narrows the preservation constraint from the full output distribution to correctness-conditioned response distributions. We instantiate CoKL with forward KL divergence and derive a practical finite-group training objective for RL-based LLM post-training. At the population level, CoKL decouples the total probability assigned to correct responses from their correctness-conditioned distribution, thereby regularizing the relative probability allocation among reference-supported correct responses without directly anchoring incorrect outputs or total correctness mass. We further show that full-policy forward and reverse KL regularization induce a strict optimal correctness gap when the reference policy is imperfect, whereas CoKL avoids this limitation. Experiments in controlled multi-solution environments and continual post-training settings across multiple model scales demonstrate that CoKL achieves a more favorable balance between target-task improvement and prior-capability retention than existing regularization methods. Our code is available at https://github.com/Lumina04/CoKL.

While on-policy distillation (OPD) effectively addresses sparse rewards and exposure bias in large language model post-training, its extension to flow models remains underexplored. To this end, we propose Flow Continuous Trajectory Supervision (FlowCTS), which matches subsequent student and reference trajectories initialized from the same student-visited state. Using the integral relation between trajectories and velocity fields, we derive a temporally weighted velocity-matching upper bound and discretize it into practical objectives parameterized by the number of supervision steps. Under a multi-reference setup, single-state FlowCTS-OPD outperforms vanilla KL-based OPD with faster convergence. FlowCTS-OPD improves GenEval from 0.90 to 0.93, OCR from 0.90 to 0.92, and PickScore from 22.75 to 23.06, while outperforming a mixed-reward RL baseline across all target metrics. Further analysis reveals a clear temporal supervision mismatch in vanilla KL-based OPD arising from its auxiliary SDE transition kernels. Beyond on-policy setting,FlowCTS also consistently outperforms vanilla SFT , particularly on OCR, while increasing supervision steps exhibit a trade-off between richer trajectory information and greater optimization difficulty.

Large language model (LLM) performance increasingly depends not only on the base model, but also on the inference-time controller used to organize reasoning. Existing post-training methods, however, typically optimize for a single fixed interaction pattern, despite real deployments relying on diverse controllers such as Chain-of-Thought, self-consistency, debate, planning, and verification pipelines. This creates a training--deployment mismatch and limits transfer to new workflows. We introduce CALM (Controller-Aware Language Models), a post-training framework that explicitly places controllers in the training loop. We formulate controller-aware post-training as multi-task reinforcement learning over controller-induced interaction protocols, where controllers are compositions of reusable local reasoning modules. This structure also induces a module-level decomposition of mixed-controller training under a turn-level GRPO objective, enabling a systematic study of controller and module-aware training strategies. We evaluate CALM on held-out controller compositions and broader controller shifts, showing that controller-aware post-training improves generalization across inference-time workflows beyond single-controller optimization.

Recent work has shown that large language models (LLMs) can iteratively improve their outputs by incorporating generated samples and their corresponding evaluation scores as in-context examples. Despite these empirical findings, the theoretical foundations underlying this phenomenon remain poorly understood. In this paper, we show that score-conditioned In-Context Learning (ICL) admits a structural correspondence to policy gradient optimization. We first provide a constructive proof that self-attention mechanisms can implement reward-weighted aggregation analogous to the REINFORCE algorithm under specific weight matrix configurations, and discuss the relationship between this construction and the behavior of pretrained transformers. The correspondence is directional in hidden-state space and holds exactly only under the stated simplifying conditions; we quantify its strength empirically. Within our simplified hidden-state model, we furthermore derive an exact upper bound on the distribution shift induced by a bounded attention update, yielding a trust-region-like analogy to KL-constrained policy optimization. We validate our theory through extensive experiments across multiple LLMs, demonstrating that LLMs effectively utilize score information to shift output distributions toward high-scoring exemplars, and that attention weights exhibit a strong correlation with example scores.

Multimodal large language models (MLLMs) require huge memory and computational costs, which limits their practical deployment. Post-training quantization (PTQ) techniques offer an efficient solution for model compression and inference acceleration. Yet, the quantized model faces performance degradation due to outlier channels, which are highly sensitive to quantization and substantially impair activation fidelity and task accuracy. To protect these salient channels during quantization, existing PTQ methods leverage modality- or token-level metrics to guide channel-wise scaling (CWS) of LLM decoders. However, these orthogonal measurements fail to capture channel-wise impacts on task-specific loss, and the misalignment between importance and scaling factors ultimately leads to suboptimal performance. To address this issue, we propose C-PTQ, a unified channel-wise PTQ method that harmonizes task-specific loss perturbation and quantization error. Motivated by second-order derivatives, we design a Fisher-weighted objective as a tractable Hessian approximation, seamlessly injecting task sensitivity into the scaling process. Notably, we achieve state-of-the-art performance without auxiliary modules like LoRA, thereby maintaining high efficiency. Experiments on Qwen2.5VL, InternVL2 and LLaVA-OV across 8 benchmarks demonstrate our effectiveness in both weight-only and weight-activation settings.

PPO and the GRPO baseline studied here use clipped surrogate objectives whose favorable-direction saturation introduces an abrupt change in the scalar objective's derivative. We ask whether Output Reset (OR), a smooth one-sided saturation rule, offers a useful alternative for large language model post-training. PPO-OR and GRPO-OR replace the clipped policy term with an OR squared-margin loss in rollout-relative token log-ratio space; the advantage sign determines the update direction, and a token contributes zero direct OR residual after crossing the favorable margin. We compare PPO-clip with PPO-OR under generalized advantage estimation (GAE), and GRPO with GRPO-OR under group-relative advantages, using \texttt{Llama-3.2-1B-Instruct} on Anthropic \texttt{hh-rlhf} with one shared reward model and three seeds per method. Under GAE, PPO-OR has a mean final training-time reward-model score $0.305$ higher than PPO-clip, with a larger observed across-seed spread. Under group-relative advantages, GRPO-OR does not have a higher mean score, but shows a smaller observed spread, a near-zero terminal OR residual, and a declining overshoot fraction, while the matched GRPO clipped-objective trace remains variable. Both group-relative methods exhibit substantially larger rollout-to-current log-ratio displacement than the GAE methods, and OR does not consistently reduce it. Thus, OR changes optimization behavior in both matched comparisons, but the observed reward effect differs between them. At $G=2$, the GRPO-OR diagnostics do not translate into a reward-score gain. Whether larger groups change this outcome remains open. The reported scores are training-time reward-model measurements, not held-out human-preference performance.

We propose Token-Level Off-Policy Labeling (TOPL), an off-policy training paradigm that reframes post-training as a token-level correctness prediction task. Our key intuition is that by training the model to distinguish good and bad tokens in a response, we naturally guide the model towards generating good tokens, while avoiding the pitfalls that come with directly training the model to generate off-policy tokens. Experiments on document summarization tasks show that TOPL achieves strong out-of-distribution generalization across 11 datasets against a diverse set of sequence-level and token-level baselines. We further demonstrate that TOPL transfers effectively to machine translation, suggesting that its benefits generalize across different faithful generation tasks. Through ablation studies, we confirm that our token-level learning signal is critical to good performance; sequence-level analogues do not confer similar benefits. Finally, we show that TOPL induces interpretable model updates: the LoRA adapters learned through TOPL function as linear classification heads and steering vectors.

Diffusion large language models (dLLMs) are a promising alternative to autoregressive generation. However, reasoning-oriented post-training for dLLMs remains challenging. Supervised fine-tuning (SFT) for dLLMs requires dense but often off-policy masked states, while reinforcement learning (RL) relies on sparse rewards or value modeling. This paper proposes \textbf{trace-based on-policy distillation (TOPD)}, a teacher-supervised framework that transfers reasoning ability to a target dLLM without reward estimation. The key idea is to supervise a dLLM on its own denoising trajectory, focusing on the trace-aligned token decisions that form the final response. Specifically, TOPD samples on-policy diffusion trajectories from the target dLLM, obtains teacher token distributions from a teacher model on the corresponding partially denoised states, and updates the target dLLM with a token-level Reverse Kullback-Leibler (Reverse-KL) objective. This design preserves dense teacher supervision while aligning training with the model's own denoising states. On mathematical reasoning benchmarks, TOPD enables SDAR-4B-Chat to match the MATH500 accuracy of its RL-trained counterpart TraDo-4B-Instruct, with gains of +5.7 under static evaluation and +4.5 under dynamic evaluation. Compared with the RL-trained counterpart, TOPD achieves this with 4$\times$ fewer rollout rounds, corresponding to an estimated 96.0$\times$ to-accuracy model-compute speedup.

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.

On-policy distillation (OPD) has become a key paradigm in LLM post-training, yet its training dynamics remain poorly understood. We present a systematic study examining the role, pathologies, and regulations of OPD. We first clarify the role of OPD as an exploration catalyst: it steers the student toward correct reasoning paths via dense token-level guidance, without expanding capability ceiling. We confirm this by showing that prompt diversity matters more than per-problem sampling numbers, and critically, that the effectiveness of OPD hinges entirely on the quality of its guiding signal. This dependency exposes two pathologies that derail exploration. The Student-Teacher Mismatch occurs when a large teacher-student distributional gap causes the guiding signal to misalign with task correctness, steering exploration in counterproductive directions. Length Exploitation arises when the aggregated token-level objective creates length-dependent shortcuts, allowing the student to game the reward landscape through response truncation or redundant padding, exploring degenerate length modes rather than reasoning strategies. To tame these pathologies, we investigate lightweight signal regulations: advantage clipping and log-scale compression, ensuring exploration is guided by faithful signals. Experiments across seven benchmarks demonstrate that these regulations alleviate length exploitation and enable effective distillation, stably surpassing OPD variants and RLVR baselines, thereby confirming that well-regulated signal quality, rather than mere teacher scale, governs successful exploration in OPD.

Structured pruning is a hardware-friendly way to compress LLMs, but it is mostly validated on multiple-choice recognition tasks, while the same compressed checkpoints can collapse on the free-form generation that deployment actually requires. Two observations trace this gap. First, greedy \textsc{pass}@$1$ nearly vanishes after compression, yet \textsc{pass}@$k$ recovers substantially under repeated sampling: useful generations are demoted, not erased. Second, the recoverable regime fails mainly through suffix repetition. Recovery should therefore train on the compressed model's own on-policy states with dense token-level supervision, which On-Policy Distillation (OPD) provides by reusing the pre-compression model as a frozen teacher. However, long on-policy rollouts spend early recovery budget on low-information repetitive suffixes, delaying loss descent. To mitigate this waste, we propose \textbf{\shortopd}, a short-to-long OPD schedule that detects teacher-confirmed repetitive suffixes, treats the surviving prefix as each rollout's effective length, and allocates future rollout budgets to the effective lengths the policy can currently use. Across math, code, and open-ended generation, \shortopd\ raises the compressed model's score to about $9\times$ its unrecovered value and $1.6$--$4.4\times$ standard recovery recipes (SFT w/o KD, KD, and SeqKD), and it matches a fixed $8192$-token rollout horizon within two points using a quarter of the training time ($8.5$ vs.\ $35.9$ hours) and $71\%$ fewer rollout tokens. We hope this recipe helps move structured pruning beyond marginal gains on perplexity and multiple-choice benchmarks, a step closer to deployment-ready generation quality.

LLMs can perform language-based quantitative prediction from unstructured inputs, but remain susceptible to hallucinations and overconfident errors, making it critical to know not only what a model predicts, but when its predictions can be trusted. We introduce CARE-PPO, a reinforcement learning framework that establishes a connection between loss prediction for uncertainty estimation and actor-critic PPO fine-tuning, enabling joint learning of accurate numerical estimates and reliable confidence signals in language-based quantitative prediction. CARE-PPO uses a Confidence-Aligned Reward for Estimation, defined as a function of prediction error, to provide dense error-aware feedback to the actor while inducing the critic to learn a value function aligned with prediction quality. During inference, we repurpose the critic as a confidence estimator. Across two real-world tasks in healthcare and finance and two Qwen-3 model scales (4B and 8B), CARE-PPO achieves strong quantitative prediction performance, while producing significantly better-aligned confidence estimates through the critic than logit-based and verbalized baselines. These gains persist under realistic out-of-distribution settings across domains, spanning linguistic and domain shifts. Finally, CARE-PPO reduces task-specific overfitting on general instruction-following prompts, consistent with the broader generalization advantages of RL fine-tuning over supervised approaches.

Post-training is essential for refining the domain-specific capabilities of large language models (LLMs), yet existing reward optimization and distribution matching methods tightly couple policy exploration with distribution alignment. This coupling forces expensive exploration directly on the policy model and severely hinders the asynchronous generation, reuse, and cross-model transfer of optimization signals. In this paper, we propose Proxy-guided Update Signal Transfer (PUST), a novel post-training framework that fundamentally decouples update-signal exploration from distribution alignment. Instead of utilizing the primary model for costly exploration, PUST employs a lightweight proxy model as an efficient testbed to discover high-reward behaviors. We extract the relative improvement signal between the proxy's initial and optimized states, transferring this directional update to the primary model to guide its policy alignment. This decoupled pipeline, comprising proxy exploration, update-signal extraction, and signal transfer, significantly reduces computational overhead and enables optimization signals to be asynchronously generated, cached, and reused. Crucially, by transferring relative improvements rather than absolute policy distributions, PUST naturally supports weak-to-strong improvement and seamless cross-model transfer. Systematic evaluations on Qwen3-family models across math and code domains demonstrate that update signals extracted from substantially weaker proxies can robustly and adjustably enhance stronger primary models. Ultimately, PUST transforms post-training from a monolithic online optimization process into a highly modular, reusable, and cost-efficient paradigm.

Direct Preference Optimization (DPO) has become an important method for aligning large language models (LLMs) with human preferences because it removes the need for explicit reward modeling and reinforcement learning optimization. However, its performance depends heavily on the quality of preference data, and noisy preference data in real-world settings can weaken alignment performance. To address this issue, we propose a bilevel optimization framework and prove, under certain assumptions, that this framework can recover the DPO optimum under clean data. We further derive a prior form for the learnable weighting function under asymmetric label-flipping noise. Considering that high-quality metadata may be difficult to obtain, we propose a task-agnostic meta-knowledge-driven method that enables meta-learning even when metadata is completely unavailable. To reduce the high cost of higher-order gradients in LLM meta-learning, we combine central-difference approximation with LoRA fine-tuning and develop a scalable training scheme. Experiments on TL;DR summarization and Anthropic HH single-turn dialogue show that the proposed method improves training performance over multiple DPO baselines under different noise rates.

Diffusion large language models (dLLMs) generate text by iteratively denoising a masked sequence, offering a parallel alternative to autoregressive models, but eliciting strong reasoning through post-training remains difficult: supervised fine-tuning is off-policy and suffers from exposure bias, while reinforcement learning gives only sparse, sequence-level rewards and is hard to apply without tractable sequence likelihoods. On-policy self-distillation (OPSD) offers a promising alternative, using one model as both student and teacher to provide dense, token-level, on-policy supervision, but its effectiveness hinges on giving the teacher privileged information (PI) - typically an instance-specific ground-truth reference unavailable at inference - so the student ends up distilling a weak PI-free consensus policy that yields little improvement on dLLM reasoning. We introduce dOPSD, which instead derives the teacher's privilege directly from the student's own denoising trajectory, evaluating masked positions using later, more-decoded steps of that same trajectory rather than an external label, so the teacher's advantage emerges from the model's own decoding process; on Dream and LLaDA, dOPSD improves both in-domain math reasoning and out-of-domain code generation, outperforming supervised and on-policy baselines.

On-policy self-distillation (OPSD) has emerged as a practical method for training large language models (LLMs) to reason, where a single model acts as both the teacher and the student with different levels of information access. However, recent studies have found that the teacher's dense token-level supervision, conditioned on privileged information, can lead to overfitting to in-domain patterns, suppress exploration, and hurt cross-domain generalization, while also introducing a more fundamental issue: privileged information leakage, where the student encodes answer-dependent shortcuts that are unavailable at test time. We introduce DemoPSD, a novel framework that resolves such problems through the idea of selective adoption of teacher guidance. Instead of fitting the full teacher distribution, DemoPSD steers the student toward a reverse-KL barycenter target, a weighted geometric combination of the teacher and student distributions, that naturally balances learning from the teacher with preserving the student's own reasoning capacity. We measure the difference between their distributions and use such a discrepancy to adaptively control the blending at each token position. We provably show that DemoPSD achieves (1) leakage attenuation, i.e., effective mitigation of privileged information leakage; and (2) exploration preservation, i.e., preservation of exploration capacity under dense token-level distillation. Extensive experiments on SciKnowEval across four scientific fields show that DemoPSD outperforms both GRPO and SDPO while maintaining higher training entropy and robustly generalizing to out-of-distribution GPQA benchmarks.

Post-training large language models (LLMs) without real-world interaction feedback or human-labeled supervision remains challenging, particularly in specialized domains where expert annotations are costly to obtain. Recent annotation-free self-evolution methods address this by using the model's own outputs as supervision signals, constructing a teacher via additional context and aggregating predictions across multiple rollouts through majority voting to produce pseudo-labels. However, these approaches are not without drawbacks: SFT- and GRPO-based variants suffer out-of-domain performance degradation, while reward-based on-policy RL inflates calibration error. In this paper, we propose Neuron On-Policy Self-Distillation (Neuron-OPSD), a data-centric framework for annotation-free self-distillation that leverages internal neuron activations to guide both training-data selection and teacher context construction. The model is then trained via on-policy distillation from the teacher distribution, requiring no ground-truth labels at any stage. Across specialized-domain benchmarks, Neuron-OPSD improves in-domain task performance while preserving cross-domain generalization and mitigating calibration collapse over prior annotation-free baselines. This framework is particularly relevant to settings where online interaction or external supervision is costly or infeasible, and is conceptually distinct from offline RL approaches that rely on logged, reward-labeled trajectories.

Scientific Fitness Coaching (SFC) is typically delivered by human professionals, making it costly and inaccessible to many. While recent advances in Large Language Models (LLMs) show considerable promise for more inclusive fitness coaching, directly deploying prevailing general-purpose LLMs in SFC reveals critical limitations. These models often lack sufficient domain-specific knowledge integration, leading to weak performance on complex SFC scenarios. In this paper, we introduce FitOne, a series of fitness LLMs (with 8B and 32B parameters) designed to improve reliability and domain specialization for SFC applications. Built upon the Qwen3 foundation models, FitOne is developed through a three-stage post-training pipeline consisting of continual pre-training, supervised fine-tuning, and reinforcement learning, using large-scale, high-quality datasets derived from rigorous knowledge engineering. We conduct comprehensive evaluations of FitOne on professional fitness certification exams, including ACSM-EP and NSCA-CSCS, as well as general capabilities such as knowledge reasoning and instruction following. Experimental results show that, while retaining strong general capabilities, FitOne-8B/32B achieves average improvements of up to 10.09%/9.29% and 12.73%/7.01% on the ACSM-EP and NSCA-CSCS exams, respectively, compared with the Qwen3 base models. Furthermore, in-depth ablation studies confirm the necessity of each training stage, highlighting the pipeline's effectiveness in balancing domain expertise enhancement with general ability retention. We believe this research advances LLM systems toward more reliable fitness intelligence and will inspire future research on developing domain-specific LLMs.

Online imitation learning (IL), particularly on-policy distillation, has emerged as a strong LLM post-training approach, often outperforming offline supervised fine-tuning (SFT). Yet a principled understanding of when and why online interaction helps remains unclear. In this work, we challenge the view that error accumulation is the main source of online IL's advantage, and instead show that the benefits of online interaction depend critically on whether the setting is realizable, i.e., whether the student policy class can represent the expert policy. Under realizability, we empirically find that offline IL already matches expert performance. In contrast, in non-realizable (misspecified) settings, we prove that offline IL encounters an information-theoretic bottleneck even when horizon $H=1$, and propose a structural characterization of misspecification relative to the reward, under which online IL provably achieves high performance despite a large distributional mismatch between the expert and student policies.

Modern large language models (LLMs) rely on reinforcement learning during post-training to push specific capabilities, yet integrating multiple capabilities into one model remains hard. Existing methods, such as Off-Policy Finetune and Mix-RL, are either inefficient or lose performance. In this work, we propose Multi-teacher On-Policy Distillation (MOPD), a post-training paradigm for combining the capabilities of multiple domain RL teachers: we first run per-domain specialised RL to obtain a set of domain teachers, then distill these teachers into the student on its own rollouts. This eliminates exposure bias and provides a dense optimization signal. On Qwen3-30B-A3B, MOPD outperforms Mix-RL, Cascade RL, Off-Policy Finetune, and Param-Merge baselines, inheriting nearly all of each teacher's capability. MOPD also enables parallel, independent development of domain teachers, removing the cross-domain coupling typical of multi-domain post-training. MOPD has been deployed in the post-training of MiMo-V2-Flash, an industrial-scale frontier model, demonstrating its practical value for capability integration in frontier-scale LLMs.

Post-training alignment determines the reasoning and human preference following capabilities of large language models, yet most existing works withhold detailed data construction, filtering rules and training recipes, which hinders community reproducibility and lightweight model optimization. This work presents NebulaExp, a fully transparent, ablation-driven post-training pipeline built on Qwen3-8B-base, covering two orthogonal model branches: general instruct model and complex reasoning-specialized model. We curate a raw corpus of 3.84M multi-source SFT samples and a 200K verifiable RL candidate pool, and design an end-to-end data processing stack including response distillation, multi-dimensional cross-verification filtering, fine-grained difficulty grading, task classification and diversity-aware sampling. For the Instruct branch, our three-stage optimized supervised fine-tuning approach NebulaExp-Ins-SFT improves the average benchmark score from the 55.01 baseline of Qwen3-8B-nothink to 60.99. GRPO reinforcement learning then further elevates the average score to 61.85. For the Reasoning branch, medium-difficulty GRPO RL improves average reasoning score from 73.88 to 75.17. To address RL's dependency on task verifiers, we systematically investigate single-teacher and multi-teacher OPD (MOPD): utilizing merely 4K instruction-following samples and outperforms RL baseline by 3.26 points on IFEval with +4.43 average overall gain; MOPD fuses four domain-specialist teachers with merely 10K samples, lifting average performance by 4.18 over the base model. This report provides a fully reproducible empirical post-training recipe for 8B-scale LLMs, and comprehensively dissects the capability trade-offs among instruction adherence, mathematical reasoning, code generation and general knowledge.

Large language models (LLMs) achieve strong performance across many tasks, but their high computational cost limits deployment in resource-constrained environments. Knowledge Distillation (KD) offers a practical solution by transferring knowledge from a teacher model of a larger size to a smaller student model. While prior work has mainly examined task-specific or small-scale settings, the post-training stage for building general instruction-following models has received limited attention. In this paper, we conduct a systematic study of KD in post-training using the large-scale Tulu 3 dataset. We find that KD outperforms supervised fine-tuning (SFT) in low-data regimes, but its advantage diminishes as more training data is added. Distilling from a stronger instruction-tuned teacher restores substantial gains even with abundant data, indicating that KD remains effective when the teacher provides knowledge that the student cannot easily acquire from the training data alone. We further study domain-specific, low-resource scenarios and propose a two-stage KD strategy that leverages synthetic teacher-labeled data followed by refinement on human annotations. This method consistently improves student performance, providing practical guidance for building compact models in data-scarce environments.

Reinforcement learning (RL) has become the dominant paradigm for improving the reasoning capabilities of large language models, but it requires expensive training, curated data, and reward signals. Recent work shows that sampling from sharpened base-model distributions at test time recovers much of the RL gain, yet existing methods rely solely on output-layer likelihoods and ignore the transformer's internal forward-pass dynamics. We introduce Depth-Entropy Guided Sampling (DEGS), a training-free, test-time method that exploits layer-wise entropy collapse as an intrinsic quality signal. We observe that stronger reasoners -- including RL-posttrained variants -- exhibit a distinctive "late collapse": logit-lens decoded entropy stays elevated until deeper layers before converging. We define a per-sequence collapse depth $D(\mathbf{x})$ and a joint objective $π(\mathbf{x}) \propto p(\mathbf{x})^α\exp(βD(\mathbf{x}))$ that combines sequence likelihood with this depth-entropy structure, instantiated inside an MCMC power-sampling framework (DEGS-MCMC). Across three open-weight models and four reasoning benchmarks, this near-chance per-candidate signal compounds over the sampling trajectory into state-of-the-art training-free accuracy, with gains largest out of domain and on the harder splits -- exactly where likelihood alone falls short -- at single-digit-percent wall-clock overhead. DEGS narrowly trails an in-house GRPO reference on the math splits GRPO was trained for, yet surpasses it out of domain on GPQA for all three models, without any training, reward model, or labeled data.

Massive unstructured multimodal streams suffer from high "data entropy," impeding both efficient human knowledge acquisition and high-quality AI post-training. Existing passive annotation paradigms, heavily reliant on heuristic rules or general VLMs, are costly, monotonous, and fail to unlock the deep procedural logic embedded in raw data. We elevate data processing to a learnable capability, proposing a paradigm shift towards Agentic Data Tailoring, which actively refining and structuring data to align with diverse user and downstream intents. To overcome the data scarcity bottleneck in training such high-order capabilities, we design a two-stage pipeline grounding generative semantic synthesis in deterministic Factual Anchors, yielding a large-scale dataset spanning five core physical and digital domains. Building upon this, $\text{DataClaw}_0$-9B model synergizes Supervised Fine-Tuning (SFT) with Group Relative Policy Optimization (GRPO), achieving robust alignment with complex refinement and tailoring intents. To systematically quantify this capability, we construct $\text{DataClaw}_0$-val, the first benchmark dedicated to data refinement. Crucially, we adopt downstream post-training as the ultimate validation touchstone. Evaluations on video generation, real-world VQA, and GUI navigation confirm that $\text{DataClaw}_0$ delivers high-information-density tailored data, facilitating efficient model adaptation to new tasks under limited training data regimes. Project page: https://czjdsg.github.io/MakeAnyData

Preference-based post-training has become a central paradigm for aligning language models. A common data-collection strategy is to generate a small set of completions for each prompt and label the resulting comparison pairs. However, human preference labels are often much more expensive than generating additional completions, suggesting a different use of the same labeling budget: generate a larger pool of completions, but label only the most informative comparison pairs. This paper studies which pairs should be compared in preference-based post-training. We formulate comparison curation as a sampling-design problem and evaluate designs by the quality of the final policy under the preference-based post-training objective. We instantiate this framework for Direct Preference Optimization (DPO), analyzing how the choice of labeled pairs propagates through DPO training to downstream policy performance. Our main results provide matching upper and lower bounds on the post-training optimality gap of the DPO-trained policy. The bounds show that comparison selection affects downstream performance through a single design-dependent information matrix, which links label allocation to parameter estimation error and policy suboptimality. This yields an explicit optimization criterion for budgeted comparison curation and motivates practical sampling designs for selecting informative pairs from large generated completion pools. Experiments on synthetic settings and language-model post-training benchmarks show that the proposed designs consistently improve sample efficiency over common comparison-selection heuristics.

On-policy self-distillation (OPSD) has proven effective for post-training large language models (LLMs), yet its application to diffusion LLMs (dLLMs) remains unexplored. Existing OPSD methods are inherently autoregressive-centric. They inject privileged information via left-to-right prefix conditioning with token-level divergence supervision, a design that fundamentally conflicts with the arbitraryorder generation of dLLMs. We introduce d-OPSD, the first OPSD framework tailored for dLLMs. Our approach makes two core contributions. First, we reframe self-teacher construction by using self-generated answers as suffix conditioning, enabling the student model to learn from "self future-experience" rather than privileged prefixes. Second, we shift supervision from token-level to step-level, aligning training with the iterative denoising process of dLLMs. Experiments across four reasoning benchmarks show that d-OPSD consistently outperforms RLVR and SFT baselines with superior sample efficiency, requiring only around 10% of the optimization steps by RLVR and opening a promising pathway for dLLM posttraining. The code is available at https://github.com/xingzhejun/d-OPSD.

Standard on-policy distillation (OPD) for large language models estimates the reverse-KL objective using student-sampled tokens, yielding an unbiased single-sample Monte Carlo estimator that avoids vocabulary-wide computation. However, we show that this estimator suffers from severe training pathologies in practice: sample inefficiency, unstable generation dynamics, and a substantial performance gap compared to exact full-vocabulary OPD. Reward-level diagnosis traces these pathologies to the log-ratio reward, which is unbounded by construction, producing extremely high-variance gradients concentrated at early positions and persisting throughout training; standard post-hoc scaling fail as they operate only after this distortion occurs. To solve this problem, we propose PowerOPD: a family of natively bounded, sign-consistent rewards from the Box-Cox power transformation, parameterized by alpha > 0, of which the log-ratio is the degenerate alpha -> 0 limit. Across six mathematical reasoning benchmarks and four Qwen3 teacher-student pairs, PowerOPD achieves benchmark-averaged Avg@8/Pass@8 gains of up to +6.37/+5.71 over vanilla OPD, +3.01/+3.54 over post-hoc stabilization, and +2.59/+8.90 over full-vocabulary OPD, while reducing wall-clock time by 59.2% and peak GPU memory by 23.1%. Larger alpha generally improves accuracy, consistently shortens responses, and keeps gradient norms more than 3,000x smaller than vanilla OPD.

Continual post-training enables models to absorb emerging knowledge after deployment, but repeatedly updating shared parameters can accumulate weight drift, potentially causing catastrophic forgetting and degrading general capabilities. Retrieval-augmented generation avoids such parameter drift, yet often lacks the depth of parametric knowledge integration. In this paper, we propose ReGrad (Retrievable Gradients), a new paradigm that treats gradients as retrievable units of knowledge. ReGrad pre-computes document-specific gradients offline, stores them in an indexed Gradient Bank, and retrieves only query-relevant gradients at inference time for temporary weight adaptation. However, raw language-modeling gradients are optimized for token-level document reconstruction rather than for query-driven knowledge use. We therefore introduce a bi-level meta-learning objective that reshapes document-derived gradients into generalizable adaptation signals for downstream tasks. Experiments across general and domain-specific settings show that \textsc{ReGrad} outperforms CPT and RAG baselines, enabling scalable and reversible parametric knowledge injection without accumulating weight drift.

We study multi-domain LLM training in which two models, each stronger in a different domain, co-evolve by tutoring each other through on-policy feedback. Unlike one-way distillation or single-model fine-tuning, our goal is mutual Pareto improvement: each model improves across domains without losing its original strength. To this end, we propose On-Policy Co-Distillation (OPCoD), where each student's self-distillation is conditioned on its own correct rollout and feedback from its peer. To make feedback exchange effective, OPCoD uses cognizance-based gating to decide when to give feedback and feedback anchoring to ground feedback in the problem. On Science Q&A tasks, OPCoD consistently outperforms baselines and achieves Pareto improvement across all evaluated domain pairs and students.

Warning: This paper contains several toxic and offensive statements. Modern large language models (LLMs) are typically aligned through large-scale post-training to ensure fair and reliable behavior. In this work, we investigate how easily such guardrails can be broken by Group Relative Policy Optimization (GRPO). We show that one-shot GRPO training on a single biased example is sufficient to induce systematic bias, with stereotype-driven reasoning generalizing across attributes, categories, and benchmarks. We further find that models differ in their susceptibility based on the initial likelihood of producing biased outputs. Our results reveal a critical vulnerability in post-training: alignment can be overridden by a single example.

The ambition behind alignment training is to make large language models safe and useful. The primary mechanisms, reinforcement learning from human feedback (RLHF) and its direct-optimization variants, shape the behavior of deployed language models by aligning them with ``human values.'' Yet the process is opaque. What values are being encoded; whose values are they; and how does alignment training encode them? A growing body of evidence suggests that these methods produce only functional compliance rather than deep alignment. We offer a mechanistic case study of this phenomenon for partisan political orientation with a comparison of the internal representations of Llama 3.1 8B before and after alignment training. We show that alignment training does not remove the structured partisan direction in the base model. Instead, it compresses the variance of the partisan signal to generate consistently balanced and non-partisan output. Sparse autoencoder decomposition reveals that policy-encoding features, which activate sporadically in the base model, are completely inactive in the Instruct model. Feature-level steering experiments confirm the causal disconnect. Alignment training thus encodes a norm of political neutrality, not by erasing the model's knowledge of partisanship, but by severing the causal pathway from partisan geometry to output generation. Importantly, this neutrality is functional, not structural so that the underlying geometry that enables partisan steering remains intact. The mechanisms that bypass RLHF's guardrails, such as inferring and amplifying a user's partisan identity, reactivate partisan generation. If alignment training operates by disconnecting rather than removing value-laden structure, then the same pattern may hold for other value domains, and the aligned model's behavior may be more fragile than its outputs suggest.

Latent reasoning has emerged as a promising alternative to discrete Chain-of-Thought (CoT) in large language models (LLMs), enabling more expressive reasoning by operating over continuous representations. However, the inherently deterministic nature of continuous representations limits policy exploration in reinforcement learning (RL). To address this, we propose TARPO (Token-Wise Latent-Explicit Reasoning via Action-Routing Policy Optimization), a pure RL framework that adaptively switches between discrete token generation and continuous latent reasoning at each step. TARPO introduces a lightweight action head router that observes the current hidden state and samples a routing decision from a binary mode-selection space, preserving the stochasticity of discrete token sampling from the vocabulary. The LLM backbone and router are jointly optimized end-to-end with a shared group-relative advantage signal. Extensive experiments across Qwen2.5 (from 1.5B to 7B) and Llama-3.1-8B backbones demonstrate that TARPO consistently outperforms existing explicit and latent reasoning RL baselines across diverse benchmarks. Further analysis shows that TARPO learns adaptive token-wise switching behaviors while maintaining stable training dynamics. Our code is available at https://github.com/NKU-LITI/TARPO-master.

Diffusion Large Language Models (dLLMs) refine tokens iteratively but commit them irreversibly, leading to a "stability lag" where early decisions remain fragile even after being written. We reveal that Post-Training Quantization (PTQ) error easily flips these borderline decisions at the write frontier, which are then permanently locked in and amplified. To address this, we propose Frontier-Aware Instability-Reweighted Calibration (FAIR-Calib), a two-stage PTQ framework for dLLMs. Stage I probes a full-precision teacher to estimate a position prior that combines frontier hits and masked-stage reliability. Stage II performs off-policy, layer-wise calibration by minimizing a reweighted hidden-state MSE, effectively prioritizing the protection of fragile frontier states without requiring expensive end-to-end diffusion rollouts. We further theoretically justify our weighted objective as a surrogate for output KL divergence. Empirically, FAIR-Calib consistently outperforms state-of-the-art baselines on LLaDA and Dream (W4A4), significantly reducing frontier decision flips and suppressing post-commit mismatches across diverse benchmarks.

LLM post-training proceeds through multiple stages, e.g., supervised fine-tuning (SFT) followed by reinforcement learning from human feedback (RLHF) or direct preference optimization (DPO), where each stage draws data from different, potentially untrusted sources. Existing literature assumes data poisoning attacks may occur at each training stage, but neglects the possibility of multiple attackers. To study the trustworthiness of the entire post-training pipeline, we propose the threat model of sequential data poisoning, where multiple adversaries separately poison the SFT and preference datasets. Under this threat model, we identify the single-attacker illusion: each adversary, evaluated in isolation, appears to pose a negligible threat. Yet when adversaries collaborate across stages, the true vulnerability is revealed. In the SFT $\to$ DPO pipeline, their contributions are additive: splitting a fixed poison budget across stages outperforms concentrating it in either stage alone. In the SFT $\to$ PPO pipeline, their contributions are complementary: neither SFT nor reward model poisoning succeeds individually, yet their combination does. These findings show that security analyses of individual post-training stages systematically underestimate compound vulnerabilities that emerge only from their interaction. Code is available at https://github.com/jcksanderson/sequential-poisoning.

Experience internalization converts contextual experience from past interactions into reusable parametric capability, offering a promising path toward continual learning in large language models (LLMs). While prior work has predominantly focused on single-iteration transfer, we discover that under multi-iteration experience learning, existing methods suffer from a progressive capability collapse rather than compounding improvement. We systematically examine this failure through three vital dimensions of experience internalization: (1) Experience Granularity: We find that principle-level experience is more durable than instance-level experience, as it effectively abstracts transferable strategies away from trajectory-specific details. (2) Experience Injection Pattern: Our analysis reveals that step-wise injection significantly outperforms global injection by aligning experience with intermediate decision states, a property that is critical for long-horizon tool use. (3) Internalization Regime: We demonstrate that off-policy context-distillation on high-quality teacher trajectories provides a substantially more stable training signal than on-policy context-distillation, which is inherently limited by local corrections on student-induced flawed states. Together, these insights yield a simple yet robust recipe for stable and sustainable experience internalization, providing concrete guidance for engineering self-evolving and continually learning LLMs.