Large Language Model Post-Training

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.

Post-training Small Language Models (SLMs) for reasoning typically follows an SFT-then-RL pipeline, yet existing work rarely considers what data should be learned at each stage. We argue that data strategy should be aligned with the distinct roles of SFT and RL: SFT is better suited for acquiring not-yet-mastered reasoning skills, while RL is better suited for consolidating skills that the model can already partially access. Based on this principle, we propose a difficulty-aware SFT-then-RL framework that organizes training data into stage-specific sets. For hard samples in the SFT stage, we introduce a Bridge mechanism that transforms raw teacher-generated reasoning traces into more learnable supervision for SLMs. For hard samples that remain unsolved during RL, we apply Critique Fine-Tuning by converting all-zero-reward failures into diagnostic, repair, and new reasoning trace supervision for the next SFT stage. Experiments on two SLMs across five reasoning benchmarks show that our method consistently improves over representative SFT, distillation, and RL baselines. Our results highlight the importance of coordinating data difficulty across SFT and RL for effective SLM reasoning post-training.

Large Language Models remain plagued by hallucinations. Recent work has sought to tame their prevalence using statistical techniques based on conformal prediction, with both theoretical and empirical success. However, these methods operate in a post-hoc fashion, treating the sampling procedure itself as atomic and then surgically altering samples to remove hallucinated claims. This disconnect between filtering and generation can result in samples that are incoherent, inconsistent, or simply unlikely under the model itself. Moreover, post-hoc surgery is unable to shift probability mass towards more useful and helpful responses. To address these issues, we propose to instead sample from approximations to an LLM posterior, where the conditioning event corresponds to a calibrated, high-scoring region. We develop a calibration procedure tailored to the setting of conditional sequential generation that effectively identifies this region and achieves target risk control. Empirically, we apply our method to case studies focused on open-ended biography generation and mathematical problem solving; compared to prior work, we obtain the same statistical guarantees, with higher downstream utility.

Post-training pruning compresses large language models to high sparsity using a small unlabelled calibration set, and recent work has concluded that the choice of calibration source has only modest impact on averaged post-pruning accuracy. We ask whether this conclusion survives once calibration impact is evaluated separately across distinct capability dimensions rather than aggregated. Decomposing post-pruning capability into General, Commonsense, Code, and Math, and analysing $n{=}15$ calibration sources via Spearman correlations between OIT information metrics and per-dimension retention, we uncover an opposite-sign trade-off: calibration perplexity correlates positively with General retention ($ρ{=}{+}0.71$) but negatively with Math and Code retention ($ρ{=}{-}0.53,\,{-}0.59$; $p{<}0.05$), so no single source can preserve all capabilities. We respond with multi-source calibration mixing, and propose IGSP, an information-guided self-calibration protocol that automates multi-source construction without capability-aligned corpora by minimising 4-gram aggregation and balancing perplexity across dimensions. On LLaMA-3.1-8B at SparseGPT 60% sparsity, a uniform multi-source mix reaches 58.8% total retention, outperforming the best single source (MetaMath, 50.0%) by $+8.8$ and the C4 default (40.0%) by $+18.8$; IGSP improves over Self-Cal by $+2.4$ and SGS by $+4.8$.

Token selection is pivotal for effective LLM post-training. However, existing methods mostly rely on local heuristics and rarely formulate token selection as a principled valuation of individual response tokens. We introduce $\textbf{AlphaToken}$, a response token valuation framework that decouples valuation into $\textbf{adaptation}$ (promoting target-task learning) and $\textbf{stability}$ (preserving pre-trained capabilities), and makes each objective $\textbf{path-aware}$ by combining the direct-path signal from local token gradients with the downstream causal-path signal in autoregressive generation. Since retention data are typically unavailable, AlphaToken approximates stability via a $\textbf{Fisher-drift proxy}$ anchored at the pre-trained reference model. For efficient computation, we extend Ghost Dot-Product to token-level valuation. AlphaToken masks low-value response tokens during fine-tuning and preference optimization, concentrating training signals on more valuable positions. Experiments show that AlphaToken improves post-training performance and mitigates catastrophic forgetting.

Aligning Large Language Models (LLMs) with human preferences is often formulated via Direct Preference Optimization (DPO). However, the standard Bradley-Terry instantiation of DPO is limited in modeling common departures from transitivity in human preferences. To address this, recent work has introduced Self-Play Preference Optimization (SPPO), which iteratively refines the policy by training on self-generated win-lose pairs. Our investigation, however, reveals a critical instability in SPPO: the optimization is prone to policy degeneration when the preference oracle assigns overly confident wins to semantically indistinguishable responses. To mitigate this, we propose S-SPPO, a dual-space semantic calibration framework comprising: i) Supervision Calibration via semantic gating, which anneals win rate targets toward the maximum-entropy baseline as semantic overlap increases; and ii) Representation Calibration via latent repulsion to enforce geometric diversity to prevent manifold collapse and maintain latent diversity between chosen and rejected samples. Theoretically, we show that the calibration preserves the constant-sum game structure, facilitating convergence to a Nash Equilibrium. Empirically, S-SPPO avoids the performance degradation seen in prior methods, achieving 52.19% win rate and 47.46% length-controlled win rate on AlpacaEval 2.0 with Llama-3-8B, without using additional human-annotated preferences during training. The code will be available at https://github.com/xiwenc1/s-sppo.

Deploying Large Language Models (LLMs) in practice incurs substantial memory and computational costs. Post-training pruning (PTP) is an effective approach to reducing these costs by removing weights without additional training. Among existing methods, RIA introduces relative importance scores normalized by row and column sums, achieving state-of-the-art accuracy. However, RIA considers only 1D cross-shaped (row/column) directional information and assigns equal weight to row and column contributions. In this paper, we propose \textbf{CRePE}, which incorporates 2D local neighborhood context and adaptive coefficients into Relative Importance scoring. CRePE consistently outperforms existing PTP methods across diverse models and sparsity settings. However, identifying optimal adaptive coefficients via perplexity (PPL)-based hill climbing requires numerous PPL evaluations and approximately 11 hours of search time. To address this, we propose \textbf{PHO} (Proxy-based Hyperparameter Optimization), which eliminates the need for repeated PPL measurements and reduces the search time to approximately 20 minutes. Furthermore, the optimal hyperparameter configuration found by PHO on one model transfers well to other models, demonstrating strong generalization. Finally, we verify that CRePE can be orthogonally combined with existing techniques including Channel Permutation, non-uniform sparsity allocation, and re-pruning methods.

Post-training of language models is commonly framed as a sample-score-update loop implemented by gradient descent. A recent line of work, exemplified by RandOpt, relocates this loop to weight space, sampling Gaussian perturbations around a pretrained model and ensembling the top-K rewarded specialists at inference. While competitive with PPO and GRPO under matched training compute, this prediction-level ensemble incurs K forward passes per test example and does not extend cleanly to free-form generation. We ask whether the rewarded population can instead be folded into a single deployable model, replacing the inference-time ensemble with one consolidated update. A split-half analysis over 25 model-task pairs reveals reproducible low-rank structure in every case. We turn this geometry into CoRP (Consolidating Rewarded Perturbations), a gradient-free operator that combines reward-weighted aggregation, compatibility-aware reweighting, and a held-out validation gate, with no gradient flowing through the language model. Across five language models from 0.5B to 8B and five tasks covering math, code, and creative writing, CoRP improves the base model by 8.1 points on average. Using one tenth of RandOpt's perturbation budget, CoRP exceeds single-inference RandOpt by 6.5 points and recovers more than half of the gain of the 50-pass majority-vote ensemble, at one forward pass per test example.

The rapid development of large language models (LLMs) has raised concerns on the use of inappropriate data for training, which has led to a growing interest in LLM unlearning. Many existing LLM unlearning approaches rely on optimizing prediction loss(es), such as maximizing the loss on the forget set, but often face critical issues like over-forgetting and poor model utility. To address them, this paper novelly frames the optimization objective for LLM unlearning as one of zeroing out data attribution instead. In particular, we propose the first LLM unlearning framework based on data attribution rewards called DareU that performs reinforcement learning to update the LLM by reducing the attribution score of its generated responses (i.e., de-attributing) to the forget data owners. Empirical evaluation using an LLM classifier as an efficient approximation of attribution shows that DareU outperforms existing baselines by achieving effective unlearning while balancing forget quality and model utility well.

Preference alignment is a crucial post-training step for large language models (LLMs) to ensure their outputs align with human values. However, post-training on real human preference data raises privacy concerns, as these datasets often contain sensitive user prompts and human judgments. To address this, we propose DPPrefSyn, a novel algorithm for generating differentially private (DP) synthetic preference data to enable privacy-preserving preference alignment. DPPrefSyn is a principled framework grounded in the Bradley-Terry preference model and the intrinsic geometric structure of pairwise human preference data. It first learns an underlying preference model from private data with formal differential privacy guarantees, and then leverages the learned model together with public prompts to synthesize high-quality preference data. It exploits the shared linear structure of per-cluster reward models to effectively capture heterogeneous human preferences in private datasets, and leverages DP Principal Component Analysis (DP-PCA) to improve learning accuracy. Extensive experimental results demonstrate that DPPrefSyn achieves competitive alignment performance under strong DP guarantees. These findings highlight the potential of synthetic preference data as a practical alternative for privacy-preserving preference alignment across a broad range of applications. To the best of our knowledge, this is the first work to generate DP synthetic preference data for LLM alignment. Our code is available at https://github.com/gfengyu/Differentially-Private-Preference-Data-Synthesis.

Large language models are now adapted through chains of post-training stages rather than through a single instruction-tuning pass. This paper studies whether such sequential post-training gradually compresses internal representations into low-rank, anisotropic, and homogeneous feature spaces. We define a measurement suite for hidden states, logits, token trajectories, and LoRA updates, and we use it to analyze supervised fine-tuning, preference optimization, safety/refusal tuning, math and code specialization, and long chain-of-thought tuning under controlled stage orderings. The central hypothesis is that excessive representation concentration is not merely a geometric curiosity: it predicts reduced plasticity during later adaptation, weaker out-of-domain generalization, and poorer calibration. We further evaluate lightweight interventions, including mixed-domain replay, feature refresh, representation diversity regularization, and LoRA update decorrelation, as ways to preserve future learnability without giving up the behavioral gains of post-training.

Many open-ended instructions have multiple valid answers that users can benefit from seeing, but post-training often narrows an LLM's output space toward a small set of canonical responses. We introduce REDIPO, an offline DPO data-construction pipeline for recovering distinct valid answer modes while preserving the alignment benefits of the instruct model. For each prompt, REDIPO samples responses from both base and instruct models, rewrites base-model responses with the instruct model, filters candidates for safety and instruction-following quality, and builds preference pairs that favor marginally diverse responses among candidates with similar instruction-following reward. Across Qwen3-4B, OLMo-3-7B, and LLaMA-3.1-8B, REDIPO improves NoveltyBench distinct_k by 134%, 33%, and 44% relative to the instruct checkpoints, while DivPO changes diversity by 0%, -6%, and -4% on the same models. These gains largely maintain MTBench, IFEval, and Arena-Hard performance, and reduce direct-category HarmBench attack success rate. Ablations show that marginal-diversity pair selection and base-response rewriting drive the diversity gains, while filtering and quality-bounded pairing help maintain alignment. Overall, our results show that diverse valid answers from base-model generations can be reintroduced through carefully constructed preference data while retaining the alignment benefits of post-training. We release our code and data at https://github.com/vsamuel2003/ReDiPO.

Long chain-of-thought (CoT) traces are widely used as supervision for reasoning-oriented LLM SFT, yet answer-correct traces can still lead to markedly different fine-tuning outcomes. We study post-conclusion continuation in answer-correct long-CoT data: a continuation where the answer appears sufficiently supported, but the trace continues with additional reasoning that remains in the supervised target. To test its training effect, we use a delete-only editor to construct answer-preserving suffix removal and compare CoT-based SFT on the original and processed traces. We observe improved SFT outcomes after removing the editor-identified post-conclusion continuation, suggesting that this continuation is harmful to training in our setting. We therefore refer to this empirically supported phenomenon as harmful continuation. Beyond this intervention, we further characterize the removed post-conclusion continuation through uncertainty and hidden-state progress. We observe persistent local uncertainty together with weakened terminal-directional progress, forming an uncertainty--geometry mismatch. Finally, we instantiate Harmful Continuation Cut (HCC), a lightweight boundary proxy that approximates the editor-identified post-conclusion continuation boundary.

Pointwise reward modeling offers critical signals for LLM post-training, yet struggles with absolute scoring in subjective, non-verifiable settings. Rubric-based methods address this by decomposing evaluation into explicit criteria, but existing approaches typically depend on frontier LLMs and suffer from ties caused by hard Boolean aggregation. We present RUBRIC-ARROW, an alternating framework that jointly trains a rubric generator and a rubric-conditioned judge, with its RL stage using only pairwise preference data. Our method couples a probability-based scoring rule that reduces ties with phase-specific preference-based rewards and an alternating GRPO scheme that together train the pointwise evaluator. Extensive experiments show that RUBRIC-ARROW achieves competitive reward-modeling accuracy and yields consistent gains for downstream policy post-training.

DPO has become a widely adopted alternative to RLHF for aligning LLMs with human preferences, eliminating the need for a separate reward model or RL loop. Recent theoretical analysis uncovers an asymmetric gradient behavior in DPO: the loss suppresses dispreferred responses substantially faster than it promotes preferred ones, causing the model to learn to avoid bad answers rather than to generate good ones. We propose AdaDPO, a Self-Adaptive variant of the DPO algorithm that introduces per-preference-pair, stop-gradient-based coefficients derived directly from the policy model's generation probabilities, with the reference model's probabilities as an optional component. AdaDPO is constructed to enforce equality of gradient magnitudes between preferred and dispreferred probabilities; the practical implementation balances per-token gradients and applies a numerical clipping bound for stability, while retaining DPO's original hyperparameter structure. On Llama-3-8B-Instruct trained on UltraFeedback under a SimPO similar setup, AdaDPO consistently outperforms DPO on AlpacaEval 2: it achieves higher length-controlled win rates (LC) in 81% of hyperparameter combinations, attains the global best LC (48.3%) and raw win rate (46.1%), and enlarges the LC-over-WR margin in 88% of combinations, indicating effective mitigation of length bias. Additional analyses on KL divergence, reward margin, and reward accuracy confirm that AdaDPO rectifies the gradient imbalance and yields more efficient optimization. Because it operates purely at the loss level, AdaDPO can be dropped into existing preference-based alignment pipelines without changing data collection or model architectures. The method requires only a few lines of code, and the same self-adaptive principle generalizes to a broad family of pairwise contrastive preference losses including SimPO, R-DPO, IPO, CPO, and ORPO.

Large language models (LLMs) can now solve complex problems through long chain-of-thought (CoT) reasoning, but the trade-off between performance and token cost remains a central challenge. To address this issue, supervised fine-tuning (SFT) often uses compressed reasoning data, where CoT traces are shortened into compact forms. However, the effect of such compressed reasoning data on post-training remains poorly understood. In this paper, we propose a taxonomy of CoT consisting of Explicit CoT, which outputs all operations without aggregation, Composed CoT, which combines multiple operations into a single step, and Implicit CoT, which omits intermediate operations. As a controlled mechanistic study, we construct a synthetic compositional reasoning task that allows controlled variation of difficulty, compression granularity, and data size, and conducted a comprehensive set of experiments across different model families and sizes. Notably, we find that (i) coarser CoT requires more SFT data, (ii) compared with Explicit CoT, Composed CoT and Implicit CoT benefit more from data scaling, while Composed CoT benefits from data repetition and Implicit CoT tends to lead to memorization, (iii) unlike SFT, subsequent reinforcement learning (RL) with verifiable rewards (RLVR) decomposes compressed steps learned during SFT, and (iv) unidirectional CoT ordering shows stronger generalization on longer sequential tasks. Our findings provide implications for CoT design under data resource constraints and offer important insights into the mechanisms of SFT and RL in LLM post-training.

Large language models produce fluent fiction, yet their creative output is widely seen as flat. We ask where this quality originates in the training and whether it affects different domains of human fiction equally. We construct a matched story-continuation paradigm across StoryStar (public-platform), TMAS (prompt-guided), and The New Yorker (professional literary)-and compare continuations from four OLMo 32B checkpoints (Base, SFT, DPO, RLVR) against matched human text. Because these checkpoints share architecture, scale, tokenizer, and pretraining, the design isolates the post-training effect. We measure each continuation along three sentence-level dimensions: thematic motion, affective prevalence, and linguistic diversity. Across all three, post-training compresses dynamic variation: thematic transitions become more uniform, high-intensity emotions give way to neutrality, and stylistic diversity across stories shrinks. We term this progressive loss narrative flattening. The effect is directionally stable across story domains but gap size depends on the human baseline: professional literary fiction is compressed most, while public-platform and prompt-guided stories show smaller gaps, consistent with their human baselines sitting closer to the model's default rhythm. Post-trained endpoints converge across domains, suggesting alignment produces a continuation regime largely insensitive to the source domain's narrative texture.

Existing training approaches for large language models learn a single set of parameters, based on large volumes of data, which is typically heterogeneous, conflicting and often outright contradictory. As a result, the model is forced to compress conflicting goals, and inherent uncertainties into a single, averaged pattern of behaviour. We propose an $α$-Rényi variational framework for learning distributions over post-training parameters, offering an uncertainty-aware alternative to deep ensemble approaches. The resulting variational objective interpolates between classical variational Bayes and predictively oriented posterior learning, balancing between globally plausible individual models against systems of complementary specialists. We identify local stability criteria, demonstrating how model misspecification can make non-degenerate posterior spread locally favourable, manifesting contradictory or conflicting data as epistemic uncertainty. We apply our framework to LLM post-training, learning an ensemble of LoRA adapters attached to a shared, frozen base model, providing a scalable training procedure for both supervised fine-tuning and preference optimisation. Our approach enables training examples to be softly routed across ensemble members, promoting model specialisation and providing actionable uncertainty estimates across different tasks.

Model internals encode rich information about how a large language model (LLM) processes its training data; however, post-training data engineering largely relies on external signals and ignores rich intrinsic signals lying in model internals. We propose SAERL, a data engineering framework for LLM reinforcement learning (RL). It models three intrinsic data properties: diversity, difficulty, and quality, using model internals extracted with Sparse Autoencoder (SAE), an advanced mechanistic interpretability tool. Each property grounds a concrete data engineering operation: SAE-space clustering with moderate batch mixing for batch diversity control, a difficulty proxy for easy-to-hard curriculum ordering, and a quality probe for data filtering. SAERL improves average accuracy by 3.00% over vanilla GRPO and reaches target accuracy with 20% fewer training steps on Qwen2.5-Math-1.5B, with consistent gains across model scales and RL algorithms. Experiments show that SAE transfers effectively across model families and scales, serving as a lightweight and reusable data engineering tool. These results demonstrate that model internals are a powerful and practical source of signals for post-training data engineering.

Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable. Yet, many real-world reasoning problems are inductive: agents must infer uncertain beliefs from sparse, ambiguous observations. There are challenges to using standard fine-tuning methods for inductive reasoning, including difficulties in curating large-scale, high-quality labeled datasets and in handling targets that are inherently distributional. In this work, we introduce a novel approach, called Program-based Posterior Training (PPT), to address these limitations: we use an LLM to generate diverse open-world scenarios as probabilistic programs, run probabilistic inference to produce distributional target responses to queries, and then fine-tune on these probabilistic soft labels. Using this approach, we fine-tune LLMs on 10,000 programmatically generated scenarios and evaluate on held-out motifs, human-labeled judgments, and external benchmarks. Overall, PPT substantially improves estimation accuracy on held-out inductive tasks, increases alignment with human judgments, and transfers to external benchmarks for estimation and calibration. Additionally, the gains in raw calibration are not subsumed by post-hoc temperature scaling, showing that the models have more deeply internalized uncertainty compared to output rescaling. Together, these results suggest that probabilistic-program-mediated fine-tuning is a promising approach for post-training LLMs to reliably perform approximate inductive inference.

Domain specialization can improve LLM behavior, but often weakens the general capabilities inherited from the original model. Recent Multi-Teacher On-Policy Distillation (MOPD) pipelines recover model capabilities by supervising student-generated trajectories with teacher feedback, but typically assume teacher-aligned prompt coverage, requiring prompts to match the teachers' training distributions. This assumption is difficult to satisfy when the general teacher is an open-source model whose post-training data are unknown. Instead of attempting to reconstruct this hidden distribution, we study general capability recovery with readily available proxy general prompts. We identify two failure modes of vanilla MOPD in this incomplete-coverage situation: recovery-preservation counteraction from mixing conflicting recovery and preservation gradients, and weak-signal flattening from uniformly averaging samples with unequal correction demand. We propose \textbf{Counteraction-Aware Multi-Teacher On-Policy Distillation} (\textbf{CaMOPD}), which addresses these issues with decoupled alternating training and gap-based sample selection. CaMOPD allocates dedicated updates to general recovery, periodically performs domain-preservation updates, and selects samples with larger averaged token-level teacher-student log-probability gaps to concentrate correction signals. Across role-play dialogue and medical reasoning QA scenarios, CaMOPD outperforms all baselines in general capability recovery while maintaining domain-specific behavior. Gradient coherence analyses further support the intended effect of CaMOPD in producing more coherent correction signals.

High-quality expert chain-of-thought (CoT) data is one of the core bottlenecks in large language model (LLM) post-training. Existing data production methods each have structural limitations: crowdsourced annotation lacks deep reasoning paths; expert solo writing is constrained by the "expert blind spot" -- experts structurally skip reasoning steps they consider obvious; RLHF only produces preference signals rather than reasoning chains. This paper proposes the BC Protocol -- a structured dual-expert elicitation method for LLM post-training data production. The method carefully pairs a domain expert (crystallized intelligence) with a knowledge engineer (fluid intelligence), systematically externalizing the expert's implicit judgments as natural language reasoning chains. We introduce the Participant Aptitude Model, which defines six participant characteristic dimensions that affect elicitation quality. "Calibrated Ignorance" is an original concept proposed in this paper. We further propose "Selection-over-Prescription" as a methodological principle: for implicit knowledge elicitation tasks, investing quality-control resources in personnel selection yields a higher return than investing the same resources in process design. In a controlled experiment in the narrative fiction domain, we directly compared CoT produced by BC Protocol dual dialogue (Group A, (n=20)) against CoT written independently by the same domain expert (Group B, (n=20)). Three cross-vendor judge models -- GPT-4o, Claude Opus 4.5, and Gemini 2.5 Pro -- conducted blind evaluation across five dimensions (600 ratings total). Results show that the BC Protocol achieves an overwhelming advantage in "naturalness of reasoning process" (Group A mean 4.80 vs. Group B mean 1.30, (p=2.4\times10^{-8}), Cliff's (δ=1.0)).

Language models are pretrained as passive predictors with no incentive to model the consequences of their own outputs. Post-training changes this: a model producing its own responses can benefit from recognizing that it is on-policy. We present evidence that post-trained models recognize their on-policy generations, and this recognition is implicitly encoded in their output distributions. In particular, on-policy output distribution entropy is 3--4$\times$ lower than off-policy entropy, across model families and size classes. We trace part of this effect to an internal representation of input surprise, tracking the unlikeliness of the most recent input token according to the model's prior predictions, that causally modulates output entropy. One example of these phenomena can be observed in response to open-ended prompts; post-trained models (unlike pretrained models) collapse their uncertainty over the topic of their upcoming response before the first output token; violating this cached intention with a different-topic prefill results in higher output entropy. We also tested whether models can distinguish on-policy contexts from prefills via explicit verbal report. We find that they can, but that interestingly, this explicit recognition routes through a different mechanism than implicit recognition.

Language models must now generalize out of the box to novel environments and work inside inference-scaling search procedures, such as AlphaEvolve, that select rollouts with a variety of task-specific reward functions. Unfortunately, the standard paradigm of LLM post-training optimizes a pre-specified scalar reward, often leading current LLMs to produce low-entropy response distributions and thus to struggle at displaying the diversity that inference-time search will require. We propose Vector Policy Optimization (VPO), an RL algorithm that explicitly trains policies to anticipate diverse downstream reward functions and to produce diverse solutions. VPO exploits that rewards are often vector-valued in practice, like per-test-case correctness in code generation or, say, multiple different user personas or reward models. VPO is essentially a drop-in replacement for the GRPO advantage estimator, but it trains the LLM to output a set of solutions where individual solutions specialize to different trade-offs in the vector reward space. Across four tasks, VPO matches or beats the strongest scalar RL baselines on test-time search (e.g. pass@k and best@k), with the gap widening as the search budget grows. For evolutionary search, VPO models unlock problems that GRPO models cannot solve at all. As test-time search becomes more standardized, optimizing for diversity may need to become the default post-training objective.

Self-distillation bootstraps large language models (LLMs) by training on their own generations. However, existing methods either rely on external signals to curate self-generated outputs (e.g., correctness filtering, execution feedback, and reward search), which are costly and unavailable for the best-performing frontier models, or skip curation entirely and train on all raw outputs, an approach that is often domain-specific and hard to generalize. Both also share a deeper weakness that self-generated outputs entangle task-relevant capability with others, such as stylistic patterns, formatting artifacts, and model-specific errors, diluting the signal for the specific capability one aims to improve. In this paper, we propose Self-Policy Distillation (SPD), which achieves generalizable, capability selective without any external signal. Specifically, SPD extracts a low-rank capability subspace from the model's own gradients on correctness-defining tokens, projects key-value (KV) activations into this subspace during self-generation, and fine-tunes on the resulting raw outputs with standard next-token prediction loss. Through extensive experiments across code generation, mathematical reasoning, and multiple-choice QA, we show that SPD achieves up to 13% improvement over state-of-the-art self-distillation methods without external signals and up to 16% improvement over pre-trained baselines. Notably, SPD demonstrates superior generalizability, achieving 15% better performance under out-of-domain generalization settings.

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose \textbf{Direction-Adaptive Self-Distillation} (\textbf{DASD}), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@$k$, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

Direct Preference Optimization (DPO) aligns Large Language Models with human preferences without the need for a separate reward model. However, DPO treats all tokens in responses equally, neglecting the differing importance of individual tokens. Existing token-level PO methods compute the token weights using either token-position-based heuristic functions or probability estimates given by a separately trained model, which lacks robustness and incurs extra training cost. In contrast, we propose Token-weighted DPO (TwDPO) -- a novel training objective grounded on token-weighted RL -- and AttentionPO -- an instantiation of TwDPO that uses attention from the LLM itself to estimate token weights. AttentionPO prompts the LLM to serve as a pairwise judge and check where the model attends when comparing the responses. This design makes AttentionPO content-aware, adjusting weights based on response content, and efficient, incurring only two extra forward passes per example. Experiment results show that AttentionPO significantly improves performance on AlpacaEval, MT-Bench, and ArenaHard, surpassing existing Preference Optimization methods.

Aligned models can misbehave in several ways: they are often sycophantic, fall victim to jailbreaks, or fail to include appropriate safety warnings. Consistency training is a promising new alignment paradigm to mitigate such failures by training invariants into the model using contrastive input pairs. Existing consistency training procedures generate the supervision signal once, offline, and use supervised fine-tuning (SFT) to update the model. Unfortunately, the resulting models tend to merely memorize the surface forms of the training distribution and thus generalize poorly and regress in their capabilities. We introduce On-Policy Consistency Training (OPCT), a new consistency training approach where the objective is computed over the model's own responses to prompts, supervised by itself conditioned on corresponding contrastive prompts. We evaluate OPCT on three safety axes: sycophancy, jailbreaking, and safety awareness. Across three model families, OPCT outperforms its SFT counterpart on all safety desiderata. It nearly halves the sycophancy rate relative to baseline (8.1% vs. 15.4%, compared to 11.2% for SFT). Under an adaptive per-target attacker, OPCT holds jailbreak defense success near 99% on held-out jailbreak behaviors, whereas SFT achieves 87% on average. On safety awareness, OPCT outperforms SFT in two out of three models, and matches it on the other. OPCT also largely avoids the capability regressions that SFT induces, such as a 28-point drop on MATH-500. Our results suggest that consistency training is best implemented as OPCT rather than as SFT, especially when generalization beyond the training distribution is desired.

Reinforcement learning substantially improves pretrained language models, but it remains understudied why critic-free methods such as PPO and GRPO work as well as they do, and when they should provide the largest gains. We develop a value-gradient perspective of critic-free RL for LLM post-training. First, under a differentiable rollout and additive-noise parameterization, we show that the actor update is value-gradient-like in expectation: the backward pass propagates costates whose conditional expectation equals the value gradient. Second, for discrete transformer policies, we show that autodifferentiation through attention produces empirical costates that approximate this value signal, with an error controlled by the sampling gap and policy entropy. These results motivate a decomposition of RL impact into value gradient signal and reachable reward headroom, yielding a criterion for when RL should be most effective along a pretraining trajectory.

Can post-trained large language models (LLMs) further improve themselves using only unlabeled prompts, without external teachers or feedback from tools? We study this setting starting only from unlabeled seed questions with no ground-truth solutions, across three reasoning domains: math, science, and coding. We propose Self-Verified Distillation, a simple post-training refinement algorithm in which the model generates candidate solutions to these seed questions, filters them using prompt-based self-verification, and trains on the resulting self-curated dataset. Inspired by the UQ benchmark's use of multiple validators to screen candidate answers to hard unsolved questions, we adapt this validation-based filtering idea to self-training: the model filters its own generated solutions through a three-stage cascade of cycle-consistency, factuality, and correctness checks, accepting a solution only if it passes all stages with unanimous judge votes. We find that sampling more candidate generations and using a larger verification budget during training data construction produces higher-quality self-curated data and, in turn, better reasoning models. We then train Qwen3 models at multiple scales with Self-Verified Distillation and obtain gains across all three domains. For Qwen3-4B, our method improves aggregate held-out pass@1 by +16.7 points in math (AIME26 and HMMT), +11.1 points in science (GPQA Diamond and HLE), and +8.3 points in coding (LCBv5 and LCBv6), with gains also extending to 0.6B and 8B models. Compared to our test-time-only baseline (UQ-TTC), which improves performance by spending extra compute at inference time, Self-Verified Distillation achieves better performance in most settings while requiring only a single inference call at test time.

Preference-based post-training aligns LLMs with human intent, yet safety behavior often remains brittle. A model may refuse a harmful request in a standard prompt but comply when the same intent is wrapped in adversarial wording. We suggest that robust safety requires context-invariant alignment, where behavior depends on the underlying intent rather than surface form. Enforcing invariance is difficult in alignment because not all training signals are equally trustworthy; for some prompt variants we can obtain verifiable feedback (e.g., multiple-choice), while for open-ended variants we typically rely on noisy, gameable reward proxies (e.g., learned judges). As a result, standard symmetric invariance regularizers can reduce cross-context discrepancies by lowering performance on reliable variants instead of improving open-ended robustness. To address this, we introduce Anchor Invariance Regularization (AIR), which treats verifiable prompts as anchors and uses a stop-gradient target to regularize only the open-ended variants toward the anchor performance. AIR is implemented as a plug-in auxiliary loss and combined with group-based preference optimization (e.g., GRPO) via heterogeneous prompt grouping. Across Safety, Moral Reasoning, and Math, AIR improves context invariance, boosting in-distribution group accuracy by 12.71% and out-of-distribution consistency by 33.49%, making safety constraints robust to adversarial framings.

Large language models can predict real-valued quantities from heterogeneous inputs such as text, code, and molecular strings, but most training objectives score each decoded floating-point number independently, improving point estimates without ensuring calibrated predictive distributions. This limits applications requiring candidate ranking or uncertainty estimation. We introduce Distribution-Aware Reward, an on-policy reinforcement learning objective whose main contribution is to train language models to produce better predictive distributions for regression tasks, rather than only optimizing individual decoded outputs against scalar targets. Our method treats multiple decoded samples as an empirical predictive distribution, evaluates it with the Continuous Ranked Probability Score, and assigns leave-one-out credit based on each rollout's marginal contribution to distribution quality, rewarding predictions that are both accurate and appropriately dispersed. We evaluate our method on a controlled Gaussian-mixture task, code performance prediction, and molecular property prediction from SMILES strings. Across tasks, our method improves over supervised fine-tuning and pointwise reinforcement learning baselines, with strong rank-correlation gains, including a 6-point Spearman improvement on KBSS. On MoleculeNet, it uses only SMILES strings yet remains competitive with strong graph-based and 3D molecular models. Further analyses show that our method mitigates rollout diversity collapse and improves uncertainty diagnostics, suggesting that directly optimizing predictive distributions makes language model regression more robust and better calibrated.

Improving LLM performance on downstream tasks sometimes requires leveraging auxiliary datasets during post-training. In practice, however, developers face constraints on compute, labeling, and licensing costs that preclude using all available data, necessitating principled dataset-level selection. These constraints are increasingly shaped by dataset marketplaces, where data acquisition is governed by budgets and negotiation. We study dataset valuation as a subset selection problem during LLM post-training. Our goal is to identify and weight auxiliary datasets so as to maximize target task performance given constrained budgets. We first show that commonly used gradient alignment scores provide a reasonable yet incomplete valuation signal, as they ignore redundancy among datasets. To address this, we propose a scalable convex dataset-level valuation method based on kernel mean matching (KMM) in gradient space, which jointly accounts for alignment with the target task and redundancy across auxiliary datasets. Through extensive experiments across diverse post-training settings and tasks, we show that our approach consistently outperforms existing valuation baselines, achieving stronger performance with low computational overhead. Our results position dataset valuation as a practical decision tool for post-training data selection in market-constrained large language model settings. The code is available at https://github.com/uiuctml/convex_data_valuation.

Direct Preference Optimization (DPO) is a widely used RL-free method for aligning language models from pairwise preferences, but it models preferences over full sequences even though generation is driven by per-token decisions. Existing token-level extensions typically decompose a sequence-level Bradley-Terry objective across timesteps, leaving per-prefix (state-wise) optimality implicit. We study how to recover token-level preference optimality using only standard sequence-level pairwise comparisons. We introduce Token-level Bregman Preference Optimization (TBPO), which posits a token-level Bradley-Terry preference model over next-token actions conditioned on the prefix, and derive a Bregman-divergence density-ratio matching objective that generalizes the logistic/DPO loss while preserving the optimal policy induced by the token-level model and maintaining DPO-like simplicity. We introduce two instantiations: TBPO-Q, which explicitly learns a lightweight state baseline, and TBPO-A, which removes the baseline through advantage normalization. Across instruction following, helpfulness/harmlessness, and summarization benchmarks, TBPO improves alignment quality and training stability and increases output diversity relative to strong sequence-level and token-level baselines.

The performance of Large Language Models (LLMs) on downstream tasks is fundamentally constrained by the capabilities acquired during pre-training. However, traditional benchmarks like MMLU often fail to reflect a base model's plasticity in complex open-ended scenarios, leading to inefficient model selection. We address this by introducing a new task of predicting post-training potential - forecasting a base model's performance before post-training. We propose RuDE (Rubric-based Discriminative Evaluation), a unified framework that bypasses the generation gap of base models by leveraging response discrimination. Guided by our systematic 4C Taxonomy, RuDE constructs controlled contrastive pairs across diverse domains by fine-grained rubric violations. Extensive experiments demonstrate a correlation greater than 90% with post-training performance. Crucially, validation via Reinforcement Learning (RL) confirms that RuDE effectively identifies high-potential smaller models that outperform larger counterparts, offering a compute-efficient mechanism for foundation model development.

On-policy distillation (OPD) has emerged as an efficient post-training paradigm for large language models. However, existing studies largely attribute this advantage to denser and more stable supervision, while the parameter-level mechanisms underlying OPD's efficiency remain poorly understood. In this work, we argue that OPD's efficiency stems from a form of ``foresight'': it establishes a stable update trajectory toward the final model early in training. This foresight manifests in two aspects. First, at the \textbf{Module-Allocation Level}, OPD identifies regions with low marginal utility and concentrates updates on modules that are more critical to reasoning. Second, at the \textbf{Update-Direction Level}, OPD exhibits stronger low-rank concentration, with its dominant subspaces aligning closely with the final update subspace early in training. Building on these findings, we propose \textbf{EffOPD}, a plug-and-play acceleration method that speeds up OPD by adaptively selecting an extrapolation step size and moving along the current update direction. EffOPD requires no additional trainable modules or complex hyperparameter tuning, and achieves an average training acceleration of $3\times$ while maintaining comparable final performance. Overall, our findings provide a parameter-dynamics perspective for understanding the efficiency of OPD and offer practical insights for designing more efficient post-training methods for large language models.

Continual post-training aims to extend large language models (LLMs) with new knowledge, skills, and behaviors, yet it remains unclear when sequential updates enable capability transfer and when they cause catastrophic forgetting. Existing methods mitigate forgetting through sequential fine-tuning, replay, regularization, or model merging, but offer limited criteria for determining when incorporating new updates is beneficial or harmful. In this work, we study LLM continual post-training through three questions: What drives forgetting? When do sequentially acquired capabilities transfer or interfere? How can compatibility be used to control update integration? We address these questions through task geometry: we represent each post-training task by its parameter update and study the covariance geometry induced by the update. Our central finding is that: forgetting can be considered as a state-relative update-integration failure, it arises when the covariance geometries induced by tasks misalign with the geometry of the evolving model state. Sequential updates transfer when they remain compatible with the model state shaped by previous updates, and interfere when state-relative geometry conflict becomes high. Motivated by this finding, we propose Geometry-Conflict Wasserstein Merging (GCWM), a data-free update-integration method that constructs a shared Wasserstein metric via Gaussian Wasserstein barycenters and uses geometry conflict to gate geometry-aware correction. Across Qwen3 0.6B--14B on domain-continual and capability-continual settings, GCWM consistently outperforms data-free baselines, improving retention and final performance without replay data. These results identify geometry conflict as both an explanatory signal for forgetting and a practical control signal for LLM continual post-training.

On-policy distillation (OPD) is widely used for LLM post-training. When pushed with a reward-extrapolation coefficient lambda > 1, the student can lift past the teacher in domain, but past a threshold lambda* the same step violates the output contract on structured-output tasks. In a single-position Bernoulli reduction, we derive a closed-form base-relative clip-safety threshold lambda*(p,b,c) determined by three measurable quantities: the teacher modal probability, the warm-start mass, and the importance-sampling clip strength. Above lambda*, the extrapolated fixed point exits the clip-safe region, changing training from format-preserving to format-collapsing. We extend the rule to calibrated K-ary listwise JSON tasks where a single binding equivalence class dominates the output contract and SFT retains parse headroom. On Amazon Fashion, three pre-registered tests--a fine-grid cliff interval, a budget-extension test, and a small-clip cross-prediction--fall within their locked prediction windows, with the small-clip value matching the closed-form prediction below grid resolution. Operating just below lambda*, ListOPD brings a 1.7B Qwen3 student to in-domain parity with an 8B-SFT baseline at one-fifth the parameters. The gain is driven primarily by format adherence: NDCG@1 on parsed outputs remains flat across lambda, while parse validity sharply changes at the predicted boundary. The cliff diagnostic is rubric-independent, whereas the parity claim uses a Gemini-graded rubric and inherits that evaluator's exposure.

Large language models (LLMs) are increasingly used as surrogates for human participants, but it remains unclear which models best capture human behavior and why. To address this, we introduce Psych-201, a novel dataset that enables us to measure behavioral alignment at scale. We find that post-training -- the stage that turns base models into useful assistants -- consistently reduces alignment with human behavior across model families, sizes, and objectives. Moreover, this misalignment widens in newer model generations even as base models continue to improve. Finally, we find that persona-induction -- a popular technique for eliciting human-like behavior by conditioning models on participant-specific information -- does not improve predictions at the level of individuals. Taken together, our results suggest that the very processes that are currently employed to turn LLMs into useful assistants also make them less accurate models of human behavior.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

Alignment of large language models (LLMs) via SFT and RLHF/DPO typically ignores the global geometry of the representation space, relying instead on local token likelihoods or scalar scores. We view generation as tracing a semantic trajectory in hidden space and propose a topology-enhanced alignment framework that regularizes these trajectories using 0-dimensional persistent homology. First, for SFT, we introduce Trajectory Topology Loss (TTL). Treating prompt and gold-answer embeddings as a mixed point cloud, we use a 0D persistent homology algorithm to extract "prompt-answer bridges." TTL aligns the model's actual update direction with these topological bridges rather than arbitrary directions. Second, for DPO, we propose Topological Preference Optimization (TPO). TPO constructs topic-specific semantic preference vectors and aligns the improvement direction between rejected and chosen responses with these vectors in an intermediate hidden layer. We also introduce a dynamic weighting scheme to balance DPO and TPO losses. Evaluating on Qwen2.5-7B-Instruct using UltraChat and Anthropic HH-RLHF, our topology-enhanced objectives consistently outperform strong non-topological baselines (e.g., per-example, nearest-neighbor, random regularizers) on automatic preference metrics and LLM-judge evaluations, while maintaining or improving toxicity. Results show persistent homology and trajectory geometry offer a promising direction for controllable alignment.

Data selection methods address a critical challenge in LLM post-training: effectively leveraging scarce, high-fidelity target data alongside abundant but imperfectly aligned general training data. In this work, we move beyond the data-selection framing and introduce Dr. Post-Training (Data-Regularized Post-Training), a novel framework that reconceptualizes general training data as a data-induced regularizer that prevents overfitting to the scarce target objective, rather than serving as a pool for selection. Specifically, our framework proposes that at each training step, construct a feasible set of model update directions using the general training data, and project the model update direction specified by the scarce target data onto that feasible set. Standard training and existing data selection methods arise as special cases with different choices of the data-induced regularizer, and these methods correspond to different points on a bias--variance spectrum with different regularization strength. Building on this view, we propose a family of methods offering a richer design space and more flexible bias--variance tradeoffs. For practical LLM-scale use, we introduce careful system optimizations that realize these methods with minimal overhead. Extensive experiments across SFT, RLHF, and RLVR show that our methods consistently outperform state-of-the-art data selection baselines, and system benchmarks confirm their efficiency.

The "Locate-then-Update" paradigm has become a predominant approach in the post-training of large language models (LLMs), identifying critical components via mechanistic interpretability for targeted parameter updates. However, this paradigm rests on a fundamental yet unverified assumption: can mechanisms derived from current static parameters reliably guide future dynamic parameter updates? To investigate this, we systematically track the structural evolution of Transformer circuits throughout the supervised fine-tuning (SFT) process, revealing the underlying dynamics of task mechanisms. We introduce three novel metrics-Circuit Distance, Circuit Stability, and Circuit Conflict-to analyze circuit evolution across three dimensions: neural migration, semantic stability, and cross-task interference. Our empirical results reveal that circuits inherently exhibit "Free Evolution" during parameter updates. Consequently, static mechanisms extracted from current states inevitably suffer from temporal latency, making them fundamentally inadequate for guiding future states. Moreover, by deconstructing the "illusion of effectiveness" in existing methods, this work underscores the necessity of "foresight" in mechanistic localization and proposes a predictive framework for future research.

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose \textbf{LoPT}: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT

Reinforcement fine-tuning (RFT) has become a core paradigm for post-training large language models, yet its training process remains highly fragile. Existing efforts mainly improve reliability at the system level or address specific issues in individual subproblems by modifying RFT algorithms. Despite their effectiveness, they largely overlook the problem of failure management at the training-process level. When training goes wrong, practitioners still rely heavily on expert-driven manual inspection and correction, and automatic failure management for RFT remains largely unexplored. In this paper, we take a first step toward systematic failure management for reinforcement fine-tuning. To understand the empirical structure of RFT failures, we first construct RFT-FaultBench, the first benchmark for fine-grained failures in reinforcement fine-tuning, covering 5 fault families, 16 fault types, 779 training runs, 22,549 train-step records, and 1,457,288 trajectory-level records. Based on this benchmark, we conduct a comprehensive empirical study showing that RFT failures are both observable from training dynamics and distinguishable through their empirical fault fingerprints. Building on these findings, we propose RFT-FM, an automatic failure management framework for reinforcement fine-tuning that unifies anomaly detection, failure diagnosis, and auto remediation in a closed loop. Experimental results show that RFT-FaultBench is neither trivial nor saturated: it exhibits clear anomaly structure while still posing substantial challenges, especially under subtle fault settings. Moreover, RFT-FM shows strong capability in detecting, diagnosing, and mitigating RFT failures.

Aligning large language models (LLMs) with human preferences is commonly done via reinforcement learning from human feedback (RLHF) with Proximal Policy Optimization (PPO) or, more simply, via Direct Preference Optimization (DPO). While DPO is stable and RL-free, it treats preferences as flat winner vs. loser signals and is sensitive to noisy or brittle preferences arising from fragile chains of thought. We propose TUR-DPO, a topology- and uncertainty-aware variant of DPO that rewards how answers are derived, not only what they say, by eliciting lightweight reasoning topologies and combining semantic faithfulness, utility, and topology quality into a calibrated uncertainty signal. A small learnable reward is factorized over these signals and incorporated into an uncertainty-weighted DPO objective that remains RL-free and relies only on a fixed or moving reference policy. Empirically, across open 7-8B models and benchmarks spanning mathematical reasoning, factual question answering, summarization, and helpful/harmless dialogue, TUR-DPO improves judge win-rates, faithfulness, and calibration relative to DPO while preserving training simplicity and avoiding online rollouts. We further observe consistent gains in multimodal and long-context settings, and show that TUR-DPO matches or exceeds PPO on reasoning-centric tasks while maintaining operational simplicity.

Large language models (LLMs) trained on unfiltered corpora inherently risk retaining sensitive information, necessitating selective knowledge unlearning for regulatory compliance and ethical safety. However, existing parameter-modifying methods face fundamental limitations: high computational costs, uncontrollable forgetting boundaries, and strict dependency on model weight access. These constraints render them impractical for closed-source models, yet current non-invasive alternatives remain unsystematic and reliant on empirical experience. To address these challenges, we propose the Controllable Alignment Prompting for Unlearning (CAP) framework, an end-to-end prompt-driven unlearning paradigm. CAP decouples unlearning into a learnable prompt optimization process via reinforcement learning, where a prompt generator collaborates with the LLM to suppress target knowledge while preserving general capabilities selectively. This approach enables reversible knowledge restoration through prompt revocation. Extensive experiments demonstrate that CAP achieves precise, controllable unlearning without updating model parameters, establishing a dynamic alignment mechanism that overcomes the transferability limitations of prior methods.

Knowledge distillation (KD) is a powerful paradigm for compressing large language models (LLMs), whose effectiveness depends on intertwined choices of divergence direction, optimization strategy, and data regime. We break down the design of existing KD methods and present a unified view that establishes connections between them, reformulating KD as a reweighted log-likelihood objective at the token level. We further propose Hybrid Policy Distillation (HPD), which integrates the complementary advantages of forward and reverse KL to balance mode coverage and mode-seeking, and combines off-policy data with lightweight, approximate on-policy sampling. We validate HPD on long-generation math reasoning as well as short-generation dialogue and code tasks, demonstrating improved optimization stability, computational efficiency, and final performance across diverse model families and scales. The code related to this work is available at https://github.com/zwhong714/Hybrid-Policy-Distillation.

Many applications of LLM-based text regression require predicting a full conditional distribution rather than a single point value. We study distributional regression under empirical-quantile supervision, where each input is paired with multiple observed quantile outcomes, and the target distribution is represented by a dense grid of quantiles. We address two key limitations of current approaches: the lack of local grounding for distribution estimates, and the reliance on shared representations that create an indirect bottleneck between inputs and quantile outputs. In this paper, we introduce Quantile Token Regression, which, to our knowledge, is the first work to insert dedicated quantile tokens into the input sequence, enabling direct input-output pathways for each quantile through self-attention. We further augment these quantile tokens with retrieval, incorporating semantically similar neighbor instances and their empirical distributions to ground predictions with local evidence from similar instances. We also provide the first theoretical analysis of loss functions for quantile regression, clarifying which distributional objectives each optimizes. Experiments on the Inside Airbnb and StackSample benchmark datasets with LLMs ranging from 1.7B to 14B parameters show that quantile tokens with neighbors consistently outperform baselines (~4 points lower MAPE and 2x narrower prediction intervals), with especially large gains on smaller and more challenging datasets where quantile tokens produce substantially sharper and more accurate distributions.

Self-play has recently emerged as a promising paradigm for post-training Large Language Models (LLMs). In self-play, the target LLM creates the task input (e.g., a question), which it then addresses itself by producing a task output (e.g., an answer). A reward model evaluates the output, and the rewards are used to train the LLM, typically via Reinforcement Learning (RL). A key benefit of self-play for post-training LLMs is its minimal supervision costs: self-play avoids the need for high-quality input-output pairs traditionally constructed by humans or expensive proprietary models. Existing work, however, explores self-play only for verifiable tasks, such as math and coding, for which objective ground truth is available and easily checkable. In this paper, we seek to extend self-play to more realistic open-ended tasks. We propose POP, a self-play framework that uses the same LLM to synthesize evaluation rubrics along with each input-output pair. The rubric is used to evaluate outputs and train the model. Crucially, we ground the framework on a content-rich pretraining corpus to (1) enable an exploitable generation-verification gap and reduce reward hacking, and (2) prevent mode collapse. On Qwen-2.5-7B, POP increases performance of both the pretrained base model and instruction-tuned model on multiple tasks ranging from long-form healthcare QA to creative writing and instruction following.

Reinforcement learning (RL) for LLM post-training faces a fundamental design choice: whether to use a learned critic as a baseline for policy optimization. Classical theory favors critic-based methods such as PPO for variance reduction, yet critic-free alternatives like GRPO have gained widespread adoption due to their simplicity and competitive performance. We show that in sparse-reward settings, a learned critic can inject estimation noise that exceeds the state signal it captures, increasing rather than reducing advantage variance. By casting baseline selection as a Kalman filtering problem, we unify PPO and GRPO as two extremes of the Kalman gain and prove that explained variance (EV), computable from a single training batch, identifies the exact boundary: positive EV indicates the critic reduces variance, while zero or negative EV signals that it inflates variance. Building on this insight, we propose Explained Variance Policy Optimization (EVPO), which monitors batch-level EV at each training step and adaptively switches between critic-based and batch-mean advantage estimation, provably achieving no greater variance than the better of the two at every step. Across four tasks spanning classical control, agentic interaction, and mathematical reasoning, EVPO consistently outperforms both PPO and GRPO regardless of which fixed baseline is stronger on a given task. Further analysis confirms that the adaptive gating tracks critic maturation over training and that the theoretically derived zero threshold is empirically optimal.

The prevailing paradigm for training LLMs has evolved to rely on a massive post-training phase consisting of SFT and RL. In this position paper, we argue that this methodology effectively marks a reversion to the pre-train then fine-tune'' approach of the BERT era, explicitly tailoring models to the desired behaviors and specific benchmarks on which they are evaluated. We begin with a historical overview of LLMs, describing the different phases of the LLM evolution. We argue that the current landscape is remarkably similar to the early days of LLMs, where task performance heavily relied on fitting the models to in-distribution datasets. To empirically demonstrate this, we compare pre-trained models to randomly initialized ones, by fine-tuning both variants on modern reasoning datasets and evaluating them on competitive math and code benchmarks. We show that models post-trained from scratch yield highly non-trivial performance. Our findings suggest that current post-training methodologies function primarily as a distribution-fitting mechanism. We finish by positing that developing generally capable models and systems requires moving beyond extensive post-training for predefined behaviors, shifting instead toward training procedures where models learn how to learn''.

Extending the effective context length of large language models (LLMs) remains a central challenge for real-world applications. While recent post-training methods have made progress in long-context scaling, they either rely on high-quality supervision data or sparse sequence-level rewards, leading to unstable and inefficient optimization. We propose OPSDL, an On-Policy Self-Distillation method for enhancing the Long-context capabilities of LLMs. Unlike other recent self-distillation methods that inject privileged information and rely on the model's in-context learning ability to act as a teacher, OPSDL leverages the model's own inherently strong short-context capability as a self-teacher to supervise its own generation in long-context scenarios. The model first generates responses conditioned on the full long-context, then the self-teacher provides per-token supervision signals via point-wise reverse KL divergence under the relevant extracted short-context. This dense token-level signal encourages faithful use of relevant evidence and mitigates hallucinations induced by irrelevant context. We evaluate OPSDL on long-context benchmarks across a range of models from 7B to 32B parameters. Results show consistent and substantial improvements across varying context lengths, outperforming standard post-training approaches such as SFT and DPO with higher sample efficiency. Notably, these gains are achieved without degrading general short-context performance. These findings highlight the effectiveness of OPSDL as a scalable and stable approach for long-context learning.

Post-trained language models produce less varied outputs than their base counterparts. This output diversity collapse undermines inference-time scaling methods that rely on varied samples, and risks homogenizing model outputs on creative and value-laden tasks. Prior work attributes collapse to specific post-training methods, without separating the role of training data composition from the method, or the generation format from the model weights. We trace output diversity through three parallel post-training lineages of Olmo 3, Think (chain-of-thought distillation), Instruct (broad multi-source data), and RL-Zero, across 15 tasks and four text diversity metrics. We find that the location of collapse co-varies with data composition: the Think lineage loses most semantic diversity at supervised fine-tuning, and the effect of DPO is larger in Instruct than in Think. Suppressing chain-of-thought reasoning at inference in Think models drops accuracy on hard tasks, yet leaves answer-level diversity unchanged, showing that the collapse is embedded in the model weights by training data, not imposed by the generation format. Decomposing diversity loss on six verifiable tasks into a quality-control component (removal of incorrect outputs) and a residual component (genuine narrowing among correct outputs) reveals that the split is task-dependent, and Think models retain more correct-answer diversity than Instruct despite collapsing more in aggregate. Our results indicate that diversity collapse is determined during training by data composition and cannot be addressed at inference time alone.

Machine unlearning has gained increasing attention in recent years, as a promising technique to selectively remove unwanted privacy or copyrighted information from Large Language Models that are trained on a massive scale of human data. However, the emergence of Large Reasoning Models (LRMs), which emphasize long chain-of-thought (CoT) reasoning to address complex questions, presents a dilemma to unlearning: existing methods either struggle to completely eliminate undesired knowledge from the CoT traces or degrade the reasoning performances due to the interference with the reasoning process. To this end, we introduce Counterfactual Unlearning through iterative Preference Optimization (CiPO), a novel framework that redefines unlearning as the targeted intervention of the CoT reasoning in LRMs. More specifically, given a desired unlearning target answer, CiPO instructs LRMs to generate a logically valid counterfactual reasoning trace for preference tuning. As the LRM adjusts to the counterfactual trace, CiPO iteratively updates the preference learning data to increase the discrepancy from the original model. This iterative loop ensures both desirable unlearning and smooth optimization, effectively mitigating the dilemma. Experiments on challenging benchmarks demonstrate that CiPO excels at unlearning, completely removing knowledge from both the intermediate CoT steps and the final answer, while preserving the reasoning abilities of LRMs.

Large Language Models (LLMs) have shown strong promise in healthcare applications. Yet deploying general-purpose models in real-world settings remains difficult due to data privacy constraints, inference costs, and limited suitability for edge or on-device use. These challenges motivate the development of smaller, more efficient models that require robust post-training strategies to ensure reliable medical reasoning. In this work, we investigate Group Relative Policy Optimization (GRPO) for post-training LLMs on heart-focused medical question answering with rubric-based supervision derived from RaR-Medicine. We propose a Variance-Aware Reward Framework that extends the Explicit Aggregation and Implicit Aggregation strategies of Rubrics as Rewards by replacing weighted binary criterion aggregation and single overall Likert-style scoring with continuous analytical reward functions derived from criterion-level rubric outcomes. This formulation provides richer optimization signals for feedback that is sparse, multi-criteria, and difficult to verify automatically, and enables more stable on-policy reinforcement learning. On a held-out heart-related subset of HealthBench, our best GRPO variant improves accuracy from 0.362 to 0.502 and F1 from 0.532 to 0.668 relative to the Qwen3-14B base model, while remaining competitive with GPT-OSS-120B (0.508 accuracy, 0.674 F1). Our findings show that carefully designed rubric-based rewards provide a practical strategy for improving heart-focused medical question answering in LLMs, with potential to extend to other rubric-based tasks.

Preference optimization is widely used to align Large Language Models (LLMs) with preference feedback. However, most existing methods train on a single positive-negative pair per prompt, discarding additional supervision available in preference datasets that typically contain multiple candidate responses. Motivated by this limitation, recent work explores group-wise preference optimization, which jointly contrasts multiple responses for the same prompt, but its empirical behavior and scalability remain underexplored due to the memory overhead of group-coupled objectives. In this work, we present a unified empirical and systems study of group-wise preference optimization and develop a memory-efficient implementation for group-coupled objectives. By instantiating first-order linearization with objective-specific per-response coefficients, our implementation preserves first-order gradients while decoupling samples during backpropagation, substantially reducing peak memory usage and enabling scalable training with larger groups. Across offline and online settings, we show that leveraging multiple responses consistently outperforms single-pair training. Furthermore, incorporating a negative log-likelihood (NLL) term on positive responses is critical for both performance gains and training stability.

Machine unlearning for large language models (LLMs) aims to remove targeted knowledge while preserving general capability. In this paper, we recast LLM unlearning as an asymmetric two-task problem: retention is the primary objective and forgetting is an auxiliary. From this perspective, we propose a retention-prioritized gradient synthesis framework that decouples task-specific gradient extraction from conflict-aware combination. Instantiating the framework, we adapt established PCGrad to resolve gradient conflicts, and introduce SAGO, a novel retention-prioritized gradient synthesis method. Theoretically, both variants ensure non-negative cosine similarity with the retain gradient, while SAGO achieves strictly tighter alignment through constructive sign-constrained synthesis. Empirically, on WMDP Bio/Cyber and RWKU benchmarks, SAGO consistently pushes the Pareto frontier: e.g., on WMDP Bio (SimNPO+GD), recovery of target model MMLU performance progresses from 44.6% (naive) to 94.0% (+PCGrad) and further to 96.0% (+SAGO), while maintaining comparable forgetting strength. Our results show that re-shaping gradient geometry, rather than re-balancing losses, is the key to mitigating unlearning-retention trade-offs.

The inability to filter out in advance all potentially problematic data from the pre-training of large language models has given rise to the need for methods for unlearning specific pieces of knowledge after training. Existing techniques overlook the need for continuous and immediate action, causing them to suffer from degraded utility as updates accumulate and protracted exposure of sensitive information. To address these issues, we propose Continual Unlearning in Real Time with Ensured Preservation of LLM Knowledge (CURaTE). Our method begins by training a sentence embedding model on a dataset designed to enable the formation of sharp decision boundaries for determining whether a given input prompt corresponds to any stored forget requests. The similarity of a given input to the forget requests is then used to determine whether to answer or return a refusal response. We show that even with such a simple approach, not only does CURaTE achieve more effective forgetting than existing methods, but by avoiding modification of the language model parameters, it also maintains near perfect knowledge preservation over any number of updates and is the only method capable of continual unlearning in real-time.

Large Language Models (LLMs) are widely used across many domains, but their scale makes deployment challenging. Post-Training Quantization (PTQ) reduces memory footprint without retraining by leveraging a small calibration set. Recent Hessian-based PTQ methods compensate quantization error via cross-channel dependencies, but such approaches degrade at low bit-widths due to noisy curvature estimates from limited calibration data. We propose DASH-Q, a robust PTQ framework using diagonal Hessian approximation and iterative weighted least squares. By discarding noise-prone dependencies, DASH-Q filters sampling noise while prioritizing the preservation of salient feature power. We outperform other PTQ baselines in ultra low-bit regime, improving zero-shot accuracy by 7.01% on average and up to 14.01% over the strongest baselines across five baseline LLM models, while showing robust and stable performance with very small calibration data.