Supervised Fine-Tuning

Large language model post-training methods such as supervised fine-tuning (SFT), reinforcement learning (RL), and distillation are often analyzed through their loss functions: maximum likelihood, policy gradients, forward KL, reverse KL, or related objective-level variants. We study a complementary factor: the state distribution on which supervision is applied. For an autoregressive policy, a state is a prompt plus generated prefix. SFT trains on fixed dataset states, while RL and on-policy distillation (OPD) train on states induced by the current learner. We formalize post-training as state-distribution shaping and run a controlled smallscale study using Qwen3-0.6B-Base on GSM8K, with TruthfulQA and MMLU as retention evaluations. Our results show three phenomena. First, a mild SFT run improves GSM8K with little forgetting, while a stress SFT run causes substantial retention loss. Second, OPD from a degraded SFT teacher surpasses that teacher on GSM8K, TruthfulQA, and MMLU, despite using the teacher as its only supervision source. Third, a lightweight on-policy RL run improves GSM8K while preserving retention. These results support a state-centric view of post-training: the source and locality of training states can be as important as the form of the supervision signal.

Supervised fine-tuning (SFT) on long teacher trajectories is the dominant way to instill investigation and reasoning in open software-engineering (SWE) agents. Since every retained response becomes an imitation target, the student inherits the final outcome and intermediate flaws, including ungrounded leaps and redundant loops. High-quality training data must be effective(each step is grounded and narrows the agent's epistemic gap to the correct fix) and efficient(each step is information-bearing rather than redundant or looping). Existing recipes filter or relabel teacher rollouts using only a binary terminal verifier, which does not directly target these axes and provides no supervision on instances where the teacher fails. Most real issue includes a developer-authored reference patch, $p^\star$, revealing the file paths, runtime behaviors, and coding conventions presupposed by the correct fix, yet standard pipelines discard it. We propose Patches-to-Trajectories (P2T), which uses $p^\star$ as privileged information during curation and formulates trajectory construction as bi-objective optimization over per-step effectiveness and trajectory length. A reverse phase distills $p^\star$ into a latent process graph, $G^\star$, of contextual facts and solution milestones. A forward phase curates trajectories from blinded teacher continuations by scoring per-step progress against $G^\star$ under a leakage-blocking groundedness check and retaining the shortest effective segments. Using only 1.8k curated SWE-Gym instances, P2T improves effectiveness and efficiency over outcome-filtered SFT and its tool-error-masking variant. On SWE-bench Verified, it raises Pass@1 by up to 10.8 points while reducing per-instance inference cost by ~15%, with consistent gains on SWE-bench Lite. Size-matched ablations and qualitative analysis further isolate trajectory quality from data scale.

Text-to-optimization requires two separable capabilities: modeling -- choosing the right optimization structure -- and binding -- grounding every coefficient, index, and parameter in the concrete problem data. We study this via Text2Opt-Bench, a scalable benchmark of solver-verified optimization problems spanning 12 categories, from textbook linear programs to stochastic and multi-objective formulations with up to thousands of variables. Across 10+ models, we find that accuracy collapses as instance data grows, even when the formulation itself is simple. We call this the effective binding limit. We study it with a family of techniques, BIND, that externalize numeric data to structured files so the model binds data programmatically rather than transcribing from the prompt. When using an oracle for externalizing data, we recover between 12 and 27 accuracy points, confirming binding as a key -- but recoverable -- failure mode. In a deployable setting without oracle access, we validate our hypothesis by finetuning a model exclusively on binding and show that it outperforms end-to-end SFT and RL across three structurally distinct optimization categories, with a 1.5B binding specialist alone matching a 7B end-to-end baseline.

The thinking-while-speaking paradigm aims to make AI communication more human. A key challenge is maintaining fluent speech while performing deep reasoning. Our method, InterRS, tackles this by inserting reasoning steps only during natural speech generation. This requires high-quality data where reasoning and speech are precisely aligned, and the length ratio are under controlled. We introduce a novel pipeline to generate such seamlessly interleaved audio data. To train our model, we combine interleaved SFT with refined data and reinforcement learning with two new rewards: a TA-Balance Reward to manage timing and thinking-answer ratio, and a Linguistic Quality Reward to refine expression. Experiments show our approach achieves 13% better performance on mathmatical and logic benchmarks while generating instant response like a spoken-language instruct model which outputs fast CoT response. Furthermore, our method generates more natural and fluent answers than prior methods.

Text-to-image diffusion models often face a severe trilemma in human portrait generation: text-image alignment, photorealism, and human-perceived aesthetics inherently inhibit one another. Supervised Fine-Tuning (SFT) is an effective method for enhancing the photorealism of image generation. However, it often leads to overfitting to the training dataset, corrupts pre-trained image priors, and degrades alignment or aesthetics. To break this bottleneck, we propose a feature supervision paradigm for Multimodal Diffusion Transformers (MM-DiT). Specifically, we introduce a lightweight cross-modal alignment mechanism that implicitly extracts multi-granularity vision-aligned text representations from SigLIP 2 and applies supervision to the image branch of MM-DiT during the training stage, with zero extra inference overhead. Our method injects vision-aligned text guidance while preserving the base model's original generalization, avoiding degradation caused by SFT. Furthermore, our method directly mines implicit multi-granularity aesthetic signals from pre-trained vision foundation models to optimize human-perceived aesthetics. Extensive experiments on MM-DiTs show that our method pushes the Pareto frontier and achieves synergistic improvements across text-image alignment, photorealism, and human-perceived aesthetics.

This paper explores a scientific question in supervised fine-tuning (SFT): why SFT is broadly effective for small-scale deep neural networks, yet can produce inconsistent or even detrimental effects when applied to large language models (LLMs). Recent advances in interaction-based explanations suggest that interactions between words/tokens provide a faithful metric for quantifying the inference patterns encoded by LLMs. We find that the evolution of interactions during SFT can effectively explain the inconsistent effectiveness of SFT for LLMs. Specifically, we find that (1) SFT primarily removes noise-like interactions, while rarely acquiring reliable new interactions. (2) This denoising stage is extremely brief, after which continued fine-tuning tends to introduce overfitted interactions. We validate these findings across multiple LLMs and datasets. Our findings provide new insights into early stopping and offer practical guidance for LLM training.

Autoregressive language models execute Transformer layers sequentially, creating a latency bottleneck that is not removed by conventional tensor or pipeline parallelism. We study whether this layerwise dependency can be relaxed by treating the hidden-state trace across layers as the solution of a nonlinear residual equation and solving it with parallel Newton-style updates. While this view is principled, exact Newton corrections require expensive Jacobian-vector products and naive fixed-point iterations are unstable on trained Transformers. We introduce Structured Newton Layer Parallelism (SNLP), a training and inference framework that replaces exact layer Jacobians with cheap architecture-induced surrogate dynamics. In residual Transformers, this yields Identity Newton (IDN), where the correction reduces to a prefix-sum-like update; in mHC-style architectures, HC Newton (HCN) uses the model's residual mixing matrix. We also study SNLP-aware training, including pretraining regularization and direct SNLP-forward SFT. Experiments on Nanochat-scale Transformers show that SNLP exposes a practical speed-quality frontier: on 0.5B models, it reaches up to 2.58x wall-clock speedup, and a less aggressive configuration reaches 1.40x speedup without increasing PPL. The useful tradeoff comes from the biased finite-iteration computation induced by IDN/HCN rather than exact recovery of the sequential trace. We further show that SNLP-forward SFT can preserve downstream task accuracy, and that SNLP can serve as a drafter for self-speculative decoding while a sequential verifier preserves output correctness.

Text classification models are typically trained via supervised fine-tuning (SFT). However, SFT essentially performs behavior cloning from instance-wise labels and thus fails to adequately capture relative preference relations among samples, which limits the model's ability to shape decision boundaries and calibrate predictive confidence. In this paper, we propose ClaHF, a human feedback-inspired reinforcement learning (RL) framework for text classification that integrates preference modeling and RL optimization into the classification pipeline without requiring additional human annotations. Unlike prior work that relies solely on instance-wise supervision, ClaHF constructs multiple candidate predictions together with their relative ranking relations, and jointly models the Top-1 preference and the ordering among non-optimal candidates within a reward model (RM). This design converts conventional label supervision into preference signals that are directly applicable to policy optimization. We conduct systematic evaluations on eight classification tasks spanning three categories of scenarios. Results demonstrate that ClaHF consistently improves both classification performance and confidence calibration across diverse language models (LMs). The data and code are available at https://anonymous.4open.science/r/ClaHF.

Supervised fine-tuning (SFT) is widely used to inject new knowledge into language models, but it often degrades pretrained capabilities such as reasoning and general-domain performance. We argue this forgetting arises because fine-tuning targets from humans or external systems diverge from the model's autoregressive distribution, forcing the optimizer to imitate low-probability token sequences. To address this problem, we propose MixSD, a simple external-teacher-free method for distribution-aligned knowledge injection. Instead of training on fixed targets, MixSD constructs supervision dynamically by mixing tokens from two conditionals of the base model itself: an expert conditional that observes the injected fact in context, and a naive conditional that reflects the model's original prior. The resulting supervision sequences preserve the factual learning signal while remaining substantially closer to the base model's distribution. We evaluate MixSD on two synthetic corpora that we construct to study factual recall and arithmetic function acquisition in a controlled setting, together with established benchmarks for open-domain factual question answering and knowledge editing. Across multiple model scales and settings, MixSD consistently achieves a better memorization-retention trade-off compared to SFT and on-policy self distillation baselines, retaining up to 100% of the base model's held-out capability while maintaining near-perfect training accuracy, whereas standard SFT retains as little as 1%. We further show that MixSD produces substantially lower-NLL supervision targets under the base model and reduces harmful movement along Fisher-sensitive parameter directions. These results suggest that aligning supervision with the model's native generation distribution is a simple and effective principle for knowledge injection that mitigates catastrophic forgetting.

Large-scale pre-trained vision-language models like CLIP demonstrate remarkable zero-shot performance across diverse tasks. However, fine-tuning these models to improve downstream performance often degrades robustness against distribution shifts. Recent approaches have attempted to mitigate this trade-off, but often rely on computationally expensive text-guidance. We propose a novel method for robust fine-tuning, SAE-FT, which operates only on the model's visual representations. SAE-FT regularizes changes to these representations by penalizing the addition and removal of semantically meaningful features identified by a Sparse Autoencoder trained on the pre-trained model. This constraint prevents catastrophic forgetting and makes the fine-tuning process interpretable, enabling direct analysis of semantic changes. SAE-FT is both mechanistically transparent and computationally efficient, matching or exceeding state-of-the-art performance on ImageNet and its associated distribution shift benchmarks. Code is publicly available at: https://github.com/Fabian-Mor/sae-ft.

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved great success in developing Large Language Models (LLMs) with chain-of-thought rollouts for many tasks such as math and coding. Nevertheless, RLVR struggles with sample efficiency on difficult problems where correct rollouts are hard to generate. Prior works propose to address this issue via demonstration-guided RLVR, i.e., to conduct Supervised FineTuning (SFT) when RL fails; however, SFT often requires a lot of data, which can be expensive to acquire. In this paper, we propose FEST, a FEw-ShoT demonstration-guided RLVR algorithm. It attains compelling results with only 128 demonstrations randomly selected from an SFT dataset. We find that three components are vital for the success: supervised signal, on-policy signal, and decaying weights on the few-shot SFT dataset to prevent overfitting from multiple-epoch training. On several benchmarks, FEST outperforms baselines with magnitudes less SFT data, even matching their performance with full dataset.

Supervised fine-tuning (SFT) provides the standard approach for teaching LLMs new behaviors from offline expert demonstrations. However, standard SFT uniformly fits all samples -- including those with low likelihood under the base model -- which can disproportionately drive training updates toward overfitting specific samples rather than learning the target behavior. Moreover, adapting to these unlikely samples induces substantial policy shifts that degrade prior capabilities. Existing methods mitigate this by filtering, regenerating, or down-weighting low-likelihood data. In doing so, they often suppress precisely the novel behaviors the base model has yet to learn. We propose InfoSFT, a principled weighting scheme for the SFT objective that concentrates learning signals on maximally informative, medium-confidence tokens -- those neither overly familiar to the base model nor too unlikely to cause instability. Requiring only a one-line modification to the standard token-wise loss, InfoSFT demonstrably improves generalization over vanilla SFT and likelihood-weighted baselines across math, code, and chain-of-thought tasks with diverse model families, while better preserving pre-existing capabilities.

Safety alignment often improves robustness to harmful queries at the cost of reasoning ability, a tradeoff known as the safety tax. A common cause is distributional mismatch: supervised fine-tuning trains the target model on safety demonstrations produced by humans, external models, or fixed self-generated traces, rather than on trajectories sampled from its own policy. We identify off-policy training mismatch as a second source of this tax and study on-policy self-distillation for safety alignment, which we call OPSA. The model generates its own rollouts and receives dense per-token KL supervision from a frozen teacher copy of itself conditioned on a privileged safety context. Because this teacher must be safer than the sampled student trajectory, we introduce \emph{teacher flip rate}: a criterion that measures how often a privileged context converts unsafe responses into safe ones. We use this signal to search for contexts that activate latent safety reasoning rather than merely elicit safe-looking demonstrations. Across two reasoning-model families and five model scales, OPSA achieves a stronger safety--reasoning tradeoff than off-policy self-distillation and external-teacher distillation under matched data and full-parameter fine-tuning, with the largest gains on smaller models (+8.85 points on R1-Distill-1.5B and +5.49 points on Qwen3-0.6B). The gains persist across training-set sizes and adaptive jailbreak evaluations. Token-level analyses further show that OPSA concentrates updates near early compliance-decision tokens, providing a mechanism for improving safety while preserving general reasoning.

Large Language Models (LLMs) are widely applied in educational practices, such as for generating children's stories. However, the generated stories are often too difficult for children to read, and the operational cost of LLMs hinders their widespread adoption in educational settings. We used an existing expert-designed children's reading curriculum and its corresponding generated stories from GPT-4o and Llama 3.3 70B to design different experiments for fine-tuning three 8B-parameter LLMs, which then generated new English reading stories that were subjected to quantitative and qualitative evaluation. Our method prioritizes controllability over scale, enabling educators to target reading levels and error patterns with a compact, affordable model. Our evaluation results show that with appropriate fine-tuning designs, children's English reading stories generated by 8B LLMs perform better on difficulty-related metrics than those from zero-shot GPT-4o and Llama 3.3 70B, with almost no discernible safety issues. Such fine-tuned LLMs could be more broadly used by teachers, parents, and children in classrooms and at home to generate engaging English reading stories with children's interests, controllable difficulty and safety.

Supervised fine-tuning (SFT) data selection is commonly formulated as instance ranking: score each example and retain a top-$k$ subset. However, effective SFT training subsets are often produced through ordered curation recipes, where filtering, mixing, and deduplication operators jointly shape the final data distribution. We formulate this problem as fixed-pool data recipe search: given a raw instruction pool and a library of grounded operators, the goal is to discover an executable recipe that constructs a high-quality selected subset under a limited budget of full SFT evaluations, without generating, rewriting, or augmenting training samples. We introduce AutoSelection, a two-layer solver that decouples fixed-pool materialization based on cached task-, data-, and model-side signals from expensive full evaluation, using warmup probes, realized subset states, local recipe edits, Gaussian-process-assisted ranking, and stagnation-triggered reseeding. Experiments on a 90K instruction pool show that AutoSelection achieves the strongest in-distribution reasoning average across three base models, outperforming full-data training, random recipe search, random top-$k$, and single-operator selectors. Additional Out-of-distribution graph-reasoning results, search-stability analyses, structural ablations, and 1.5B-to-7B transfer checks further show that recipe structure matters beyond individual selection operators. Code is available at https://github.com/w253/AutoSelection.

Data selection during supervised fine-tuning (SFT) can critically change the behavior of large language models (LLMs). Although existing work has studied the effect of selecting data based on heuristics such as perplexity, difficulty, or length, the reported findings are often inconsistent or context-dependent. In this work, we systematically study the role of data difficulty in fine-tuning from both empirical and theoretical perspectives, and find that there is no universally optimal difficulty level; rather, its effectiveness depends on the dataset size. We show that for a fixed data budget, there exists an optimal data difficulty for SFT, and that this optimal difficulty shifts toward harder data as the data budget increases. To explain this phenomenon, we conduct controlled synthetic experiments that reveal a simple underlying mechanism: the interplay between the (in-distribution) generalization gap and the extrapolation gap. We further support this mechanism through a theoretical analysis using PAC-Bayesian generalization bounds. Overall, our results clarify how data size and difficulty jointly affect the trade-off between generalization and extrapolation in SFT, providing guidance for difficulty-based data selection under certain model and data conditions.

Supervised Finetuning (SFT) has become one of the primary methods for adapting a large language model (LLM) with extensive pre-trained knowledge to domain-specific, instruction-following tasks. SFT datasets, composed of instruction-response pairs, often include user-provided information that may contain sensitive data such as personally identifiable information (PII), raising privacy concerns. This paper studies the problem of PII reconstruction from SFT models for the first time. We construct multi-turn, user-centric Q&A datasets in sensitive domains, specifically medical and legal settings, that incorporate PII to enable realistic evaluation of leakage. Using these datasets, we evaluate the extent to which an adversary, with varying levels of knowledge about the fine-tuning dataset, can infer sensitive information about individuals whose data was used during SFT. In the reconstruction setting, we propose COVA, a novel decoding algorithm to reconstruct PII under prefix-based attacks, consistently outperforming existing extraction methods. Our results show that even partial attacker knowledge can significantly improve reconstruction success, while leakage varies substantially across PII types.

The cosine similarity between a large language model's hidden activations before and after Supervised Fine-Tuning (SFT) remains very high. This, at first glance, suggests that SFT leaves the model's activation geometry largely undisturbed. However, projecting both sets of activations through a Sparse Autoencoder (SAE) pretrained on the base model reveals that the underlying sparse latents diverge significantly. We introduce a novel investigative pipeline which utilizes these pretrained SAEs as a high-resolution diagnostic tool to mechanistically investigate the drivers of this representational divergence. Through our analytical pipeline, we discover task-specific and layer-specific distributions of the precise semantic features that are systematically altered during supervised fine-tuning. We additionally identify a layer-wise update profile specific to safety alignment. All code, experimental scripts, and analysis files associated with this work are publicly available at: https://github.com/ruhzi/sae-investigation.

This paper proposes a novel approach to address the challenge that pretrained VLA models often fail to effectively improve performance and reduce adaptation costs during standard supervised finetuning (SFT). Some advanced finetuning methods with auxiliary training objectives can improve performance and reduce the number of convergence steps. However, they typically incur significant computational overhead due to the additional losses from auxiliary objectives. To simultaneously achieve the enhanced capabilities of auxiliary training with the simplicity of standard SFT, we decouple the two objectives of auxiliary-objective SFT within the parameter space, namely, enhancing general capabilities and fitting task-specific action distributions. To deliver the goal, we only need to train the model to converge on a small-scale task set using two distinct training strategies, resulting in two finetuned models. The parameters' difference between the two models can then be interpreted as capability vectors provided by auxiliary objectives. These vectors are then merged with pretrained parameters to form a capability-enhanced meta model. Moreover, when standard SFT is augmented with a lightweight orthogonal regularization loss, the merged model attains performance comparable to auxiliary finetuned baselines with reduced computational overhead. Internal and external experiments demonstrate that our capability vectors (1) are effective and versatile across diverse models, (2) can generalize to novel environments and embodiments out of the box.

Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives models to exploit and memorize spurious surface correlations in problem-solution pairs, leaving them brittle to superficial input variations. To address this, we propose Theorem-SFT, which reorients supervision toward explicit theorem application by teaching models how rules are invoked rather than what answers look like. Theorem-SFT yields consistent gains across benchmarks and model families: +8.8% on MATH (LLaMA3.2-3B-Instruct) and +20.27% on GeoQA (Qwen2.5-VL-7B-Instruct) without modality-specific re-training. Fine-tuning MLP layers alone matches full-layers performance, implicating feed-forward components as the primary locus of reasoning rules. Our findings reframe the debate: Generalization failures stem not from memorization as a mechanism, but from memorizing the wrong inductive targets.

Teaching language models to use search tools is not only a question of whether they search, but also of whether they issue good queries. This is especially important in open-domain question answering, where broad or copied queries often waste retrieval budget and derail later reasoning. We propose \Ours, a framework that makes query planning explicit through reusable search skills. At each step, the model first selects a skill, then generates a search or answer action conditioned on the selected skill card. The skill inventory itself is not fixed: SearchSkill maintains an evolving SkillBank, expands or refines it from recurrent failure patterns, and reconstructs affected trajectories before supervised training. The resulting two-stage SFT recipe aligns training with the inference-time protocol of skill selection followed by skill-grounded execution. Across open-source and closed-source models, SearchSkill improves exact match on knowledge-intensive QA benchmarks and yields better retrieval behavior, including fewer copied first queries, more atomic hop-focused queries, and more correct answers within a small search budget. These results suggest that explicit skill-conditioned query planning is a lightweight alternative to treating search as an undifferentiated action.

Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities, yet their potential for sequential decision-making remains underexplored. In this paper, we study the ICL capabilities of LLMs in sequential decision-making settings, including Markov Decision Processes (MDPs), Partially Observable MDPs (POMDPs), and Ambiguous POMDPs (APOMDPs). We fine-tune pretrained LLMs to perform few-shot decision-making directly from offline, oracle-labeled trajectories. Our framework enables flexible imitation of policies through supervised fine-tuning (SFT). Theoretically, we focus on linear MDPs and interpret a fine-tuned attention layer as implicitly estimating optimal Q-functions from in-context data. Building on this interpretation, we derive an end-to-end suboptimality bound for the induced policy that separates the in-context estimation error from the training-length bias. Empirically, across synthetic MDP, POMDP, and APOMDP settings, we find that fine-tuned LLMs achieve substantially smaller optimality gaps than in-context-only and random baselines, with especially large gains in longer-horizon, partially observed, and model-ambiguous environments. Together, these results show that supervised fine-tuning provides an effective route to endowing pretrained LLMs with sequential decision-making capabilities from offline data, which is an important advantage in domains such as healthcare where offline data are abundant.

Unconstrained fine-tuning of flow-matching Vision-Language-Action (VLA) models drives dense parameter overwrites, degrading pre-trained capabilities. We present Conservative Supervised Fine-Tuning (ConSFT), an optimization objective that adapts to target distributions while mitigating catastrophic forgetting, requiring zero prior data or architectural overhead. By dynamically scaling learning signals based on model confidence, ConSFT suppresses excessive gradients from low-confidence samples to prevent disproportionate parameter updates, thereby bounding the intrinsic parameter disruption risk. Inspired by reinforcement learning's trust-region clipping, this formulation establishes a progressive learning dynamic to secure target convergence and prior capability retention, maintaining sparse parameter updates without relying on the parallel reference networks required by explicit regularization. We evaluate ConSFT on the LIBERO and RoboTwin benchmarks across state-of-the-art flow-matching VLAs ($π_0$, $π_{0.5}$, and GR00T-N1.6-3B). The method outperforms vanilla SFT in capability retention by an average absolute margin of over 20%, matching the efficacy of data-heavy Experience Replay in a prior-data-free regime. Real-world robotic deployments confirm that ConSFT precludes spatial overfitting during downstream adaptation, preserving pre-trained physical skills while acquiring sequential target tasks.

Supervised fine-tuning (SFT) improves in-domain performance but can degrade out-of-domain (OOD) generalization. Prior work suggests that this degradation is related to changes in dominant singular subspaces of pretrained weight matrices. However, directly identifying loss-sensitive directions with Hessian or Fisher information is computationally expensive at LLM scale. In this work, we propose preserving projected rotations in pretrained singular subspaces as an efficient proxy for Fisher-sensitive directions, which we call Rotation-Preserving Supervised Fine-Tuning (RPSFT). RPSFT penalizes changes in the projected top-$k$ singular-vector block of each pretrained weight matrix, limiting unnecessary rotation while preserving task adaptation. Across model families and sizes trained on math reasoning data, RPSFT improves the in-domain/OOD trade-off over standard SFT and strong SFT baselines, better preserves pretrained representations, and provides stronger initializations for downstream RL fine-tuning. Code is available at \href{https://github.com/jinhangzhan/RPSFT.git}{https://github.com/jinhangzhan/RPSFT}.

Optimizers play an important role in both pretraining and finetuning stages when training large language models (LLMs). In this paper, we present an observation that full finetuning with the same optimizer as in pretraining achieves a better learning-forgetting tradeoff, i.e., forgetting less while achieving the same or better performance on the new task, than other optimizers and, possibly surprisingly, LoRA, during the supervised finetuning (SFT) stage. We term this phenomenon optimizer-model consistency. To better understand it, through controlled experiments and theoretical analysis, we show that: 1) optimizers can shape the models by having regularization effects on the activations, leading to different landscapes around the pretrained checkpoints; 2) in response to this regularization effect, the weight update in SFT should follow some specific structures to lower forgetting of the knowledge learned in pretraining, which can be obtained by using the same optimizer. Moreover, we specifically compare Muon and AdamW when they are employed throughout the pretraining and SFT stages and find that Muon performs worse when finetuned for reasoning tasks. With a synthetic language modeling experiment, we demonstrate that this can come from Muon's strong tendency towards rote memorization, which may hurt pattern acquisition with a small amount of data, as for SFT.

Supervised fine-tuning (SFT) induces new behaviors in large language models, yet imposes no structural constraint on how these behaviors are distributed within the model. Existing behavior interpretation methods, such as circuit attribution approaches, identify sparse subnetworks correlated with SFT-induced behaviors post-hoc. However, such correlations do not imply causal necessity, limiting the ability to selectively control SFT-induced behaviors at inference time. We pursue an alternative by asking: can an SFT-induced behavior be deliberately compressed into a sparse, mechanistically necessary subnetwork, termed a carrier, while remaining controllable at inference time without weight modification? We propose (a) Loss-Constrained Dual Descent (LCDD), which constructs such carriers by jointly optimizing routing masks and model weights under an explicit utility budget, and (b) SFT-Eraser, a soft prompt optimized via activation matching on extracted carrier channels, to reverse the SFT-induced behavior. Across safety, fixed-response, and style behaviors on multiple model families, LCDD yields sparse carriers that preserve target behaviors while enabling strong reversion when triggered by SFT-Eraser. Ablations further establish that the sparse structure is the key precondition for reversal: the same trigger optimization fails on standard SFT models, confirming that structure rather than trigger design is the operative factor. These results provide direct evidence that the learned carriers are causally necessary for the behaviors, pointing to a new direction for systematically localizing and selectively suppressing SFT-induced behaviors in deployed models.

The web is complex, open-ended, and constantly changing, making it challenging to scale training data for visual web agents. Existing data collection attempts remain limited to offline trajectories for supervised fine-tuning or a handful of simulated environments for RL training, thus failing to capture web diversity. We propose Weblica (Web Replica), a framework for constructing reproducible and scalable web environments. Our framework leverages 1) HTTP-level caching to capture and replay stable visual states while preserving interactive behavior and 2) LLM-based environment synthesis grounded in real-world websites and core web navigation skills. Using this framework, we scale RL training to thousands of diverse environments and tasks. Our best model, Weblica-8B, outperforms open-weight baselines of similar size across multiple web navigation benchmarks while using fewer inference steps, scales favorably with additional test-time compute, and is competitive with API models.

The landscape of high-performance image generation models is currently shifting from the inefficient multi-step ones to the efficient few-step counterparts (e.g, Z-Image-Turbo and FLUX.2-klein). However, these models present significant challenges for direct continuous supervised fine-tuning. For example, applying the commonly used fine-tuning technique would compromise their inherent few-step inference capability. To address this, we propose D-OPSD, a novel training paradigm for step-distilled diffusion models that enables on-policy learning during supervised fine-tuning. We first find that the modern diffusion models, where the LLM/VLM serves as the encoder, can inherit its encoder's in-context capabilities. This enables us to formulate the training as an on-policy self-distillation process. Specifically, during training, we make the model act as both the teacher and the student with different contexts, where the student is conditioned only on the text feature, while the teacher is conditioned on the multimodal feature of both the text prompt and the target image. Training minimizes the two predicted distributions over the student's own roll-outs. By optimizing on the model's own trajectory and under its own supervision, D-OPSD enables the model to learn new concepts, styles, etc., without sacrificing the original few-step capacity.

Post-training large language models (LLMs) often suffers from catastrophic forgetting, where improvements on a target objective degrade previously acquired capabilities. Recent evidence suggests that this phenomenon is primarily driven by excessive distributional drift during optimization. Motivated by this perspective, we propose Anchored Learning, a simple framework that explicitly controls distributional updates during offline fine-tuning via a dynamically evolving moving anchor. Instead of matching a fixed reference distribution, the anchor interpolates between the current model and a frozen reference to construct an intermediate target that the model distills toward, transforming global fine-tuning into a sequence of local trust-region updates in distribution space. Theoretically, we prove this anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions. Extensive experiments on iGSM, MedCalc, and IFEval show that Anchored Learning consistently lies on the Pareto frontier of gain-stability trade-offs, achieving near-optimal performance improvements while substantially reducing degradation compared to strong baselines. For example, while standard SFT suffers from over 53% performance degradation on iGSM and MedCalc, Anchored Learning slashes this drop to under 5% while maintaining near-optimal gains (e.g., 75.2% on iGSM).

Online reinforcement learning with verifiable rewards (RLVR) turns checkable outcomes into a scalable training signal, but it keeps rollout generation, verifier scoring, and reference-policy evaluations on the optimization path. Static weighted supervised fine-tuning (SFT) on precomputed rollouts seems to remove this bottleneck, yet a weighted likelihood is not specified by rewards alone: its sampler and weights induce the policy being fit. This paper identifies the reference-sampled weighted-SFT objective whose induced policy equals the fixed-reference KL-regularized RLVR optimizer. The optimizer is the standard Boltzmann target policy, obtained by exponentially tilting the reference policy by verifier reward. Matching a weighted-SFT induced policy to this target forces density-ratio weights; in the reference-sampled subclass, this reduces uniquely, up to prompt scaling, to the prompt-normalized Boltzmann weight $\exp(r(x,y)/β)/Z(x)$. BOLT, a Boltzmann-Targeted SFT procedure, is the empirical estimator of this projection. The finite one-shot analysis separates the exact stored-support price $β\log(1/π^*(S_N\mid x))$ from partition estimation, effective-sample-size variance, generalization, optimization, and approximation errors. This decomposition explains why extra SFT epochs cannot repair missing reference-policy coverage and exposes the temperature--coverage--variance frontier. When coverage needs adaptive sampling, refreshed Boltzmann projections become KL policy mirror descent; finite inner solves enter as additive drift from the exact mirror step. Single-run Qwen experiments provide projection evidence for the target-matched weight, one-shot saturation, refreshed-sampler gains, and optimization-time savings, within the stated single-run scope.

SFT and RLVR represent two fundamental yet distinct paradigms for LLM post-training, each excelling in distinct dimensions. SFT expands knowledge breadth while RLVR enhances reasoning depth. Yet integrating these complementary strengths remains a formidable challenge. Sequential training can cause catastrophic forgetting, and joint optimization often suffers from severe gradient conflicts. We analyze SFT and RLVR through the lens of task vectors and reveal three structural properties behind these failures: a 30* magnitude disparity, 45* sign interference, and heterogeneous module-wise update distributions. These findings show SFT and RLVR are difficult to integrate directly, but they also suggest that the two paradigms modify partly complementary components of the model. Motivated by these observations, we propose Decoupled Test-time Synthesis (DoTS), a post-hoc framework allows SFT and RLVR checkpoints to be trained independently and synthesizes their capabilities only at inference time via task vector arithmetic, without updating model parameters. To reduce interference, DOTS applies selective sparsification with norm-preserving rescaling. It then uses Bayesian optimization on a small set of unlabeled queries to search for combination coefficients on the Pareto frontier of consistency and perplexity. Empirically, \ours matches or exceeds the performance of training-based SFT--RLVR integration methods across multiple mathematical reasoning benchmarks, incurring only $\sim$3% of the computational cost. When applied to stronger post-trained checkpoints, DOTS surpasses SOTA models and generalizes to out-of-domain benchmarks without re-tuning. Code is available at https://github.com/chaohaoyuan/DoTS.

Supervised Fine-Tuning (SFT) is essential for aligning Large Language Models (LLMs) with user intent, yet it is believed to suppress generative diversity. Although this reduction is frequently referenced, formal empirical testing of the phenomenon remains limited. The expressiveness of LLMs by itself was addressed by multiple prior methods. Their varying perspectives suggest that deeper investigation could yield further improvements. In this study, we attribute the decline to two primary drivers: the neglect of low-frequency patterns within fine-tuning datasets and the forgetting of preexisting knowledge. Motivated by our theoretical analysis, we develop Tempered Focal (TOFU) loss, a novel objective that addresses both stated challenges simultaneously. Our extensive evaluation confirms at scale that generation breadth narrows after SFT and strengthens the hypothesis explaining this effect. Across multiple models and benchmarks, we demonstrate that TOFU enhances output diversity while preserving high response quality, offering a principled approach to SFT.

The standard post-training recipe for large multimodal models (LMMs) applies supervised fine-tuning (SFT) on curated demonstrations followed by reinforcement learning with verifiable rewards (RLVR). However, SFT introduces distributional drift that neither preserves the model's original capabilities nor faithfully matches the supervision distribution. This problem is further amplified in multimodal reasoning, where perception errors and reasoning failures follow distinct drift patterns that compound during subsequent RL. We introduce PRISM, a three-stage pipeline that mitigates this drift by inserting an explicit distribution-alignment stage between SFT and RLVR. Building on the principle of on-policy distillation (OPD), PRISM casts alignment as a black-box, response-level adversarial game between the policy and a Mixture-of-Experts (MoE) discriminator with dedicated perception and reasoning experts, providing disentangled corrective signals that steer the policy toward the supervision distribution without requiring access to teacher logits. While 1.26M public demonstrations suffice for broad SFT initialization, distribution alignment demands higher-fidelity supervision; we therefore curate 113K additional demonstrations from Gemini 3 Flash, featuring dense visual grounding and step-by-step reasoning on the hardest unsolved problems. Experiments on Qwen3-VL show that PRISM consistently improves downstream RLVR performance across multiple RL algorithms (GRPO, DAPO, GSPO) and diverse multimodal benchmarks, improving average accuracy by +4.4 and +6.0 points over the SFT-to-RLVR baseline on 4B and 8B, respectively. Our code, data, and model checkpoints are publicly available at https://github.com/XIAO4579/PRISM.

SFT-then-RLVR is widely used for post-training reasoning models, but why this specific ordering, and why RLVR-only stalls at cold start, have lacked a unifying theoretical account. We provide that account under a unified loss family $J_Q$ using the Tsallis $q$-logarithm. $J_Q$ is a single-parameter family that interpolates between RLVR (at $q{=}0$, the \textit{exploitation pole}) and the log-marginal-likelihood over latent trajectories (at $q{=}1$, the \textit{density-estimation pole}), under which the standard pipeline corresponds to a stepwise $q{=}1 \to 0$ schedule. All members share the same per-example gradient direction, differing only by a per-instance amplification $P_θ^{-q}$ that reweights each instance independently of the learning rate. Under gradient flow analysis, we show that the exploitation pole requires $Ω(\frac{1}{p_0})$ time to escape cold start but is robust to label noise, while the density-estimation pole escapes in $Θ\big(\log(\frac{1}{p_0})\big)$ but memorizes label noise. This separation explains how SFT ($q{=}1$) first moves the model out of the cold-start regime, followed by the more robust RLVR ($q{=}0$), under the SFT-then-RLVR paradigm. We further derive two Monte Carlo estimators that directly optimize fixed-$q$ on the $J_Q$ continuum, without annotated rationales: Gradient-Amplified RL (GARL) and Posterior-Attenuated Fine-Tuning (PAFT), with shared bias $O\big(\frac{q}{M P_θ^q}\big)$ but different variance and stability properties. On FinQA, HotPotQA, and MuSiQue, GARL at sufficiently high $q$ substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low $q$ dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes and PAFT at $q{=}0.75$ remains stable, reaching $47.9$ \texttt{m@16} on HotPotQA ($+13.9$ over GRPO).

Scaling test-time compute has emerged as a powerful mechanism for enhancing Large Language Model (LLM) performance. However, standard post-training paradigms, Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL), optimize the likelihood of individual samples under a base policy, creating a misalignment with test time procedures that rely on aggregated or filtered outputs. In this work, we propose Compute Aligned Training, which aligns training objectives with test-time strategies. By conceptualizing inference strategies as operators on the base policy, we derive new loss functions that maximize performance when said strategies are applied. We instantiate such loss functions for SFT and RL across common test time strategies. Finally, we provide empirical evidence that this training method substantially improves test time scaling over standard training.

Accurate disease classification from radiology reports is essential for many applications. While supervised fine-tuning (SFT) of lightweight LLMs improves accuracy, it can degrade reasoning. We propose a two-stage approach: SFT on disease labels followed by Group Relative Policy Optimization (GRPO) to refine predictions by optimizing accuracy and format without reasoning supervision. Across three radiologist-annotated datasets, SFT outperformed baselines and GRPO further improved classification and enhanced reasoning recall and comprehensiveness.

We present a generative method for texture filtering, which exhibits surprisingly good performance and generalizability. Our core idea is to empower texture filtering by taking full advantage of the strong learned image prior of pre-trained generative models. To this end, we propose to fine-tune a pre-trained generative model via a two-stage strategy. Specifically, we first conduct supervised fine-tuning on a very small set of paired images, and then perform reinforcement fine-tuning on a large-scale unlabeled dataset under the guidance of a reward function that quantifies the quality of texture removal and structure preservation. Extensive experiments show that our method clearly outperforms previous methods, and is effective to deal with previously challenging cases. Our code is available at https://github.com/OnlyZZZZ/Generative_Texture_Filtering.

Large Language Models (LLMs) show promise in lyric-to-melody generation, but models trained with Supervised Fine-Tuning (SFT) often produce musically implausible melodies with issues like poor rhythm and unsuitable vocal ranges, a phenomenon we term "constraint violation". To address this, we propose a novel alignment framework that instills musical knowledge without human annotation. We define rule-based musical constraints to automatically generate a preference dataset from an SFT model's outputs. The model is then aligned through a sequential process, first using Direct Preference Optimization (DPO) on paired preference data, followed by Kahneman-Tversky Optimization (KTO) on unpaired negative samples. Experimental results demonstrate that our aligned model substantially reduces rule violations and outperforms strong baselines in both objective and subjective evaluations, generating melodies with substantially improved musicality and coherence. An interactive demo with audio comparisons is available at https://arain233.github.io/AligningMelody-demo.

Supervised fine-tuning of large language models relies on human-annotated data, yet annotation pipelines routinely involve multiple crowdworkers of heterogeneous expertise. Standard practice aggregates labels via majority vote or simple averaging, discarding annotator identity and causing the model to absorb the errors of unreliable annotators into its parameters. We propose REALM, which jointly learns the model parameters and a scalar expertise value for each annotator, entirely unsupervised and requiring nothing beyond annotator identity. The key idea is to model each observed label as a mixture between the model's prediction and a uniform random guess, weighted by the annotator's learned expertise. REALM applies to any task with a fixed label set, and extends to multiple tasks via a learned expertise matrix. On four text-classification datasets with \emph{real} crowdsourced annotations, REALM is the best method in all $12$ configurations of the three heterogeneous-annotator datasets, improving on the strongest applicable baseline, including majority vote and Dawid--Skene aggregation, by $+2.9$ points on average. On five question answering benchmarks with simulated noisy labels, it outperforms naive noisy fine-tuning in $152$ of $162$ configurations, by $+5.0$ points on average, with gains that grow with model capacity. The learned expertise additionally recovers annotator reliability without ever observing it. Our code is available at https://github.com/sajjad-ucsb/REALM

Supervised Fine-Tuning (SFT) accelerates taskspecific large language models (LLMs) development, but the resulting proliferation of finetuned models incurs substantial memory overhead. Delta compression addresses this by retaining a single pre-trained LLM with multiple compressed delta weights. However, existing methods fail on models fine-tuned with largescale datasets. We find that larger SFT data scale amplifies delta parameter magnitude, singular values, and entropy, exacerbating compression errors. To tackle this, we propose DQRELO (Delta Compression via Quantization and Residual Low-Rank), a novel training- and data-free delta compression method. It combines coarse-grained one-bit quantization to capture the dominant structure of the delta, followed by compensated residual low-rank approximation to recover fine-grained details from the smaller residual error. Experiments on various LLMs spanning dense and MoE architectures across multiple domains under this challenging setting demonstrate that DQRELO outperforms existing methods. Moreover, we establish key design principles for delta compression through extensive empirical analysis, demonstrating how task difficulty, architecture, and layer positioning create predictable patterns that can guide optimal compression strategies in production systems.

Recent video diffusion models have achieved impressive capabilities as large-scale generative world models. However, these models often struggle with fine-grained physical consistency, exhibiting physically implausible dynamics over time. In this work, we present \textbf{Phys4D}, a pipeline for learning physics-consistent 4D world representations from video diffusion models. Phys4D adopts \textbf{a three-stage training paradigm} that progressively lifts appearance-driven video diffusion models into physics-consistent 4D world representations. We first bootstrap robust geometry and motion representations through large-scale pseudo-supervised pretraining, establishing a foundation for 4D scene modeling. We then perform physics-grounded supervised fine-tuning using simulation-generated data, enforcing temporally consistent 4D dynamics. Finally, we apply simulation-grounded reinforcement learning to correct residual physical violations that are difficult to capture through explicit supervision. To evaluate fine-grained physical consistency beyond appearance-based metrics, we introduce a set of \textbf{4D world consistency evaluation} that probe geometric coherence, motion stability, and long-horizon physical plausibility. Experimental results demonstrate that Phys4D substantially improves fine-grained spatiotemporal and physical consistency compared to appearance-driven baselines, while maintaining strong generative performance. Our project page is available at https://sensational-brioche-7657e7.netlify.app/

Post-training of flow matching models-aligning the output distribution with a high-quality target-is mathematically equivalent to imitation learning. While Supervised Fine-Tuning mimics expert demonstrations effectively, it cannot correct policy drift in unseen states. Preference optimization methods address this but require costly preference pairs or reward modeling. We propose Flow Matching Adversarial Imitation Learning (FAIL), which minimizes policy-expert divergence through adversarial training without explicit rewards or pairwise comparisons. We derive two algorithms: FAIL-PD exploits differentiable ODE solvers for low-variance pathwise gradients, while FAIL-PG provides a black-box alternative for discrete or computationally constrained settings. Fine-tuning FLUX with only 13,000 demonstrations from Nano Banana pro, FAIL achieves competitive performance on prompt following and aesthetic benchmarks. Furthermore, the framework generalizes effectively to discrete image and video generation, and functions as a robust regularizer to mitigate reward hacking in reward-based optimization. Code and data are available at https://github.com/HansPolo113/FAIL.

Large language models are commonly adapted to downstream tasks through supervised fine-tuning (SFT), but substantial distribution mismatch between downstream supervision and a model's generation distribution can intensify catastrophic forgetting. Data rewriting offers a data-centric way to narrow this mismatch before SFT. Existing methods, however, typically sample rewrites from a prompt-induced conditional distribution, which need not align with the backbone's natural question-answering generation distribution, and fixed templates can reduce output diversity. We formulate data rewriting as a policy-learning problem and train a lightweight LoRA rewriting policy with reinforcement learning. The policy optimizes question-answering-style distributional alignment and semantic diversity under a hard task-consistency gate, producing verified supervision for downstream SFT. Across three instruction-tuned backbones, the resulting models attain downstream gains broadly comparable to standard SFT while reducing degradation on non-downstream benchmarks in every evaluated setting. Additional experiments on logical reasoning and medical question answering provide preliminary evidence that a rewriting policy can be reused across domains for the same backbone.

The standard post-training recipe for large reasoning models, supervised fine-tuning followed by reinforcement learning (SFT-then-RL), may limit the benefits of the RL stage: while SFT imitates expert demonstrations, it often causes overconfidence and reduces generation diversity, leaving RL with a narrowed solution space to explore. Adding entropy regularization during SFT is not a cure-all; it tends to flatten token distributions toward uniformity, increasing entropy without improving meaningful exploration capability. In this paper, we propose CurioSFT, an entropy-preserving SFT method designed to enhance exploration capabilities through intrinsic curiosity. It consists of (a) Self-Exploratory Distillation, which distills the model toward a self-generated, temperature-scaled teacher to encourage exploration within its capability; and (b) Entropy-Guided Temperature Selection, which adaptively adjusts distillation strength to mitigate knowledge forgetting by amplifying exploration at reasoning tokens while stabilizing factual tokens. Extensive experiments on mathematical reasoning tasks demonstrate that, in SFT stage, CurioSFT outperforms the vanilla SFT by 2.5 points on in-distribution tasks and 2.9 points on out-of-distribution tasks. We also verify that exploration capabilities preserved during SFT successfully translate into concrete gains in RL stage, yielding an average improvement of 5.0 points.

Can language models improve their accuracy without external supervision? Methods such as debate, bootstrap, and internal coherence maximization achieve this surprising feat, even matching golden finetuning performance. Yet why they work remains theoretically unclear. We show that they can all be understood as coherence optimization, the search for a context-to-behavior mapping that is most compressible and jointly predictable, with debate an exact instance and bootstrap and internal coherence maximization closely related to it. We prove that coherence optimization is equivalent to description-length regularization, and that among all such regularization schemes, coherence regularization with a prior derived from a pretrained model optimizes a lower bound of worst-case accuracy for semi-supervised learning. Our theory, supported by preliminary experiments, explains why feedback-free self-improvement works and predicts when it should succeed or fail.

Semi-supervised few-shot learning (SSFSL) resembles real-world applications such as auto-annotation, as it aims to learn a model from a few labeled and abundant unlabeled task-specific examples to annotate the unlabeled ones. Despite the availability of powerful open-source Vision-Language Models (VLMs) and open-world data, existing SSFSL literature largely neglects these resources. In contrast, the related area few-shot learning (FSL) has already exploited them to boost performance. Arguably, to solve real-world auto-annotation, SSFSL should leverage such open resources. To bridge this gap, we explore established SSL methods to finetune a VLM. Unexpectedly, they significantly underperform FSL baselines that do not use unlabeled data. Our in-depth analysis reveals the root cause of failure: VLMs produce flat distributions of softmax probabilities, resulting in zero utilization of unlabeled data and weak supervision signals. To address this challenge, we propose an embarrassingly simple solution that uses temperatures to sharpen the softmax output, which not only increases the confidence scores of pseudo-labels to improve the utilization of unlabeled data, but also strengthens training supervision for effective finetuning. Furthermore, we exploit task-relevant open data, e.g., those retrieved from VLMs' publicly available pretraining set. To mitigate the imbalance and domain gaps in retrieved data, we employ a stage-wise training strategy. Building on the successful finetuning of VLMs and the exploitation of open data, we present a simple yet effective SSFSL method, Stage-Wise Finetuning with Temperatures (SWIFT). Across five benchmarks, SWIFT outperforms recent FSL and SSL methods by $\sim$5 accuracy points. SWIFT even rivals supervised learning, which finetunes a VLM assuming unlabeled data having ground-truth labels!

Large language models (LLMs) are increasingly released under restricted licenses, creating a growing need for robust model ownership verification. Existing fingerprinting methods are often fragile under downstream finetuning, require invasive training modifications, or fail in black-box settings. We introduce RAFP, a robust framework for identifying LLM lineages via rare-region fingerprints. Our key insight is that downstream finetuning primarily updates common high-density language behaviors, while low-probability prompt regions receive weak optimization signal and limited gradient alignment under finetuned distribution. As a result, rare prompt-response behaviors remain stable across common model adaptations. RAFP is non-invasive, constructing fingerprints via discrete gradient-based optimization over rare prompts without modifying model weights. We provide a theoretical analysis showing that the likelihood change of rare-region fingerprints under finetuning remains bounded. Experiments across four LLM families and multiple downstream adaptations, including supervised finetuning, LoRA, quantization, prompt-template variation, and decoding changes, show that RAFP achieves strong fingerprint persistence and substantially outperforms prior fingerprinting baselines in black-box settings.

Palmyra x6 is a large language model optimized for use with enterprise-oriented agentic tasks. The model was built by post-training a Mixture-of-Experts base model with Anchored Supervised Fine-Tuning on a compact corpus of verified, synthetic tool-use trajectories, optimized with a Muon + Adam hybrid. The recipe is deliberately conservative and deliberately controlled: 626 trajectories, a single epoch, a low learning rate, and a KL anchor to the frozen base. The model shows substantial gains over the previous default model for Writer Agent, and compares favorably with several recent models on public benchmarks, scoring the highest on BFCL Core at $0.785$ and posts the highest six-benchmark mean of the cohort. Furthermore, the model has shown itself to be competitive or leading relative to comparators in our bias and safety evaluations.

We introduce a novel method that averages the logits of a frozen reference policy (e.g., SFT) and a trainable policy, and incorporate the method into Group Relative Policy Optimization (GRPO). In contrast to Reinforcement Learning with Verifiable Rewards (RLVR) methods, our proposal does not involve a Kullback Leibler (KL) regularization or critic; the trainable policy and the reference anchor are coupled through the logit averaging structure to leverage the reasoning expertise of the trainable policy while maintaining the formatting advantage of SFT. Our method is evaluated on MATH, cn-k12, and MMLU, and the results show a higher accuracy or at least comparable accuracy relative to the canonical KL-regularized GRPO.