Supervised Fine-Tuning

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.

The frontier of mathematics is defined by problems whose solutions are not yet known. However, whether language models can meaningfully engage with such problems without human intervention remains unclear. A major obstacle is the lack of large-scale research-level math datasets. To this end, we introduce ResearchMath-14k, a set of $14{,}056$ problems curated from academic sources via a multi-agent pipeline. ResearchMath-14k spans 11 mathematical domains and ranks above existing math datasets on knowledge, novelty, and procedural difficulty. To our knowledge, it is the largest research-level mathematical problem set available for training. We additionally generate $220$K teacher trajectories through targeted prompting, followed by behavioral filtering. Notably, however, generating correct trajectories is nontrivial at this level, and two LLM judges label only $3.7\%$ and $4.3\%$ of sampled ResearchMath training trajectories as correct. Nevertheless, across three model families, full-parameter training on ResearchMath improves performance on graduate- and research-level mathematics benchmarks by $2.1$ points over the starting checkpoints. In comparison, training on existing datasets such as DASD and Nemotron-SFT-Math-v4 changes performance by $0.0$ and $-0.5$ points, respectively. Notably, mixing DASD with ResearchMath yields higher scores than token-matched DASD alone on benchmarks covering olympiad short-form ($+2.0$), graduate- and research-level short-form ($+0.8$), graduate- and research-level symbolic ($+2.6$), and proof evaluation ($+5.7$). Further analysis suggests that research-level mathematical content and greater reasoning diversity may help explain why ResearchMath provides complementary supervision to contemporary datasets. We make ResearchMath-14k publicly available for future works on research-level mathematical reasoning.

In-context learning \ -- performing tasks based on examples given in the prompt \ -- is an important capability that has emerged in large language models and has received significant attention in both theory and practice. Existing theoretical work often focuses on settings where the learning uses information purely from the prompt. However, many practical instances of in-context learning require the model to retrieve factual knowledge stored in the model's parameters, with the context serving to identify which knowledge is relevant. In this work, we study how in-context learning leverages factual knowledge recall. We formalize this behavior by introducing the in-context factual recall (IC-recall) task, where a transformer is provided a context of (subject, answer) pairs generated from a hidden relation, along with a query subject, and must both infer this hidden relation and retrieve the corresponding answer. Factual knowledge is modeled by the transformer having access to a simple pre-constructed MLP associative memory storing (subject, relation, answer) triplets. We analyze the supervised fine-tuning dynamics of a one-layer transformer on IC-recall data and prove that the model successfully performs IC-recall by converging to a particular pairwise attention pattern. This fine-tuning stage requires a very small number of samples \ -- only polylogarithmic in the number of stored knowledge triplets. Experiments verify our theoretical predictions and show that the pairwise attention pattern emerges even when the MLP layer is pretrained instead of constructed.

Large language models (LLMs) have achieved remarkable progress, with post-training playing a crucial role in enhancing their reasoning capabilities. Among post-training paradigms, supervised fine-tuning (SFT) is widely used: it leverages external data to provide dense supervision and enables efficient training. However, directly fine-tuning on expert data can hurt generalization when the data distribution is mismatched with the target model's own distribution. In this work, we propose Data Adaptation for Reasoning Tuning (DART), which formulates the use of a fixed, potentially distributionally misaligned SFT dataset as an optimization problem over demonstration transformations. DART trains a mapper model with reinforcement learning to convert original SFT data into model-adapted supervision that better matches the target model's distribution and learning preferences. The transformed data are then used for SFT, allowing the target model to better exploit external supervision. Experiments across multiple models and datasets show that DART improves generalization, achieves higher training efficiency than direct RL, and helps models surpass standard SFT. Our code is available at https://anonymous.4open.science/r/DART525E50D.

Multimodal large language models are typically trained end-to-end to predict ground-truth answers, yet supervision signals are applied exclusively to text tokens. Visual tokens, the core carriers of visual information, are optimized only implicitly as part of the context, leading to coarse-grained visual understanding. Prior works attempt to supervise visual inputs but inevitably rely on auxiliary components such as additional decoders or forward passes, because visual tokens lack readily interpretable labels. This limits their practical applicability. In this work, we propose Direct Vision Supervised Fine-Tuning (DV-SFT), which constructs explicit, token-level supervision for visual tokens and trains them through the same next-token prediction objective used for text. Specifically, we exploit the direct vision--text correspondence in OCR-related scenarios and automatically label each visual token with the word in its corresponding image patch. DV-SFT treats the MLLM as a black box, requiring no architectural modifications or additional forward passes. Extensive experiments demonstrate the superiority of direct vision supervision. DV-SFT consistently outperforms standard SFT across three in-domain and four out-of-domain benchmarks. Further analyses show that vision supervision effectively enhances fine-grained visual understanding and achieves higher multimodal alignment efficiency.

Hybrid post-training combining supervised fine-tuning (SFT) and reinforcement learning (RL) is the standard paradigm for aligning large language models, yet fixed mixing schedules cannot adapt when the relative noise of the two signals evolves. We derive a noise-aware mixing weight mu* by minimizing an MSE upper bound on the mixed stochastic gradient, yielding a closed-form that balances gradient noise variance and SFT-RL disagreement. Building on the token-wise reweighting of CHORD, the practical Guided Adaptive Controller (GAC) adds EMA smoothing, a schedule prior, and capped updates around this estimator, with all statistics estimated online from existing training tensors. The noise-aware controller alone outperforms the best rule-based controller by +3.0 percentage points on AMC; the full system reaches +3.8 points over HPT across math, code, science, and logic benchmarks, while reducing KL-drift area by 28% and large absolute mixing-weight changes by more than 70%, at less than 1% overhead. Gains grow with model size from 1.5B to 14B. Resources: Qwen3.5-4B compact-backbone release: https://huggingface.co/YueLinHu/GAC-Qwen3.5-4B; reference implementation: https://github.com/deepnovacore/GAC; GAC project page: https://deepnovacore.github.io/GAC/

Fine-tuning large language models (LLMs) frequently induces catastrophic forgetting of prior capabilities. Recent work has shown that reinforcement learning (RL) retains prior capabilities more effectively than supervised fine-tuning (SFT), attributing this to policy-gradient updates remaining closer to the base policy \cite{shenfeld2025rl}. We extend this behavioral account to the mechanistic level and ask whether RL's advantage is mirrored by stronger preservation of internal computational circuits. We introduce differential circuit vulnerability, a head-level measure of how much a circuit degrades under fine-tuning, and use it to compare RL and SFT on Qwen2.5-3B-Instruct adapted to scientific question-answering. We find a clear mechanistic trade-off: SFT adapts more rapidly to the target task but produces substantially greater circuit disruption and forgetting of prior capabilities, whereas RL preserves a larger fraction of the base circuit at the cost of slower task adaptation. These findings suggest that circuit preservation may help explain why RL is more robust to catastrophic forgetting. We released our code here: https://github.com/rl-sft-circuit-research/differential-circuit-vulnerability.

We aim to improve the reasoning capabilities of diffusion language models (DLMs). While SFT is a popular post-training recipe for autoregressive models, its use in DLMs faces challenges and can even hurt performance, though the underlying causes remain understudied. Our analysis reveals that vanilla SFT overlooks learnability, namely what and when tokens are learned. Specifically, rare tokens are difficult to learn when most of the input is masked, whereas it is straightforward and thus of little value to learn common tokens when most of the input is unmasked. Motivated by our analysis, we propose LIFT, an efficient SFT-based post-training algorithm for DLMs. LIFT learns easy tokens when most of the input is masked and hard tokens when more context is available, thus aligning the training with the information available at different diffusion time steps. Our results show that LIFT outperforms existing SFT baselines across six reasoning benchmarks, achieving up to a 3x relative gain on AIME'24 and AIME'25. Our code is publicly available at https://github.com/divelab/LIFT.

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.

Recent development of agents has renewed demand for long-context reasoning capacity of LLMs. However, training LLMs for this capacity requires costly long-document curation or heuristic context synthesis. We observe that agents produce massive trajectories when solving problems, invoking tools and receiving environment observations across many turns. The evidence needed to answer the original question is thus scattered throughout these turns, requiring integration of distant context segments. Nevertheless, standard agent SFT masks tool responses and only trains turn-level tool selection, creating a supervision blind spot where these scattered signals go unused. We propose Agent Context Compilation (ACC), which converts trajectories from search, software engineering, and database querying agents into long-context QA pairs that combine the original question with tool responses and environment observations gathered across multiple turns, training the model to answer directly without tool use. This makes the dependencies between the question and the evidence explicit, enabling direct supervision of long-context reasoning over distant segments without additional annotation. ACC is a simple but effective approach that can be combined with any existing long-context extension or training method, providing scalable supervised fine-tuning data. We validate ACC on long-range dependency modeling tasks through MRCR and GraphWalks, challenging benchmarks requiring cross-turn coreference resolution and graph traversal over extended contexts. Training Qwen3-30B-A3B with ACC achieves 68.3 on MRCR (+18.1) and 77.5 on GraphWalks (+7.6), results comparable to Qwen3-235B-A22B, while preserving general capabilities on GPQA, MMLU-Pro, AIME, and IFEval. Further mechanism analysis reveals that the ACC-trained model exhibits task-adaptive attention restructuring and expert specialization.

As LLMs continue to scale up, improving training efficiency heavily relies on effective data utilization. Data selection mitigates this issue by allocating the limited training budget to high-value examples that optimally facilitate the model's target behavior. Most existing approaches define target behavior via a set of target examples and score candidate training data based on their estimated influence on these samples. However, such methods uniformly treat all target examples as equally important, ignoring the varying relevance of individual examples to model optimization. Specifically, target examples that align closely with the model's inherent behavior deliver stronger supervisory signals, whereas discrepant examples yield only weak and ineffective local guidance. We propose PRISM, a Preference-aware Influence function based Data Selection Method. It leverages model preference to assign weights to target examples and builds a preference-aware target direction. PRISM evaluates candidate training samples according to their influence on this direction, and prioritizes data budget allocation to samples that effectively drive the model to match expected target behavior. Theoretical analysis verifies that weighted preference construction generates a superior first-order gradient direction for boosting target preference, compared with uniform aggregation strategies. Extensive experiments covering diverse model architectures and parameter scales demonstrate that PRISM achieves better performance in efficient fine-tuning and safety-aligned supervised fine-tuning rectification. The results validate that accurate characterization of target behavior serves as the core of cost-effective data selection.

Explicit reasoning models are trained to produce intermediate reasoning traces before final answers, but downstream fine-tuning is often performed on ordinary instruction--response data that contains no such traces. We show that this mismatch can induce reasoning-trace collapse: a fine-tuned model continues to produce plausible final answers while losing the structurally valid explicit reasoning traces that made it a reasoning model in the first place. We introduce a structural evaluation framework that separates answer correctness from reasoning-trace validity, measuring valid, empty, missing, and truncated reasoning alongside reasoning-conditioned task performance. Using this framework, we study four open-weight reasoning models and find that standard supervised fine-tuning can rapidly suppress valid reasoning traces, and that answer-only metrics can substantially obscure this failure: in several settings, performance conditional on valid reasoning remains high while the rate of valid reasoning falls sharply. We further show that simple loss-masking strategies can substantially mitigate collapse without requiring teacher-generated reasoning traces. These results suggest that evaluations of fine-tuned reasoning models should report structural reasoning reliability metrics in addition to final-answer performance, especially when adaptation data does not contain explicit reasoning traces.

Automatic evaluation of long-form literary writing remains challenging, as generic LLM-as-Judge approaches may not fully capture creativity-related dimensions such as originality and flexibility. Although the Torrance Test of Creative Writing (TTCW) provides a structured creativity framework, and prior work has demonstrated reference-based TTCW evaluation at the pairwise level, no large-scale dataset exists for long-form TTCW-based literary review generation. We address this gap by constructing a dataset of 263,911 long-form stories, each annotated with scalar scores and meta-synthesised review comments across 14 TTCW-based dimensions. Using this dataset, we fine-tune Qwen3 models at two scales, 4B and 8B, under two conditions: with and without reasoning content. Results show that non-reasoning fine-tuning achieves stronger and more stable performance, with the best setting reaching an evaluation score of 0.6820. Further analysis shows that reasoning-supervised models are more prone to parse failures, often continuing with irrelevant or repetitive reasoning-style text rather than completing the required 14-metric review report. These results suggest that, for fixed-format rubric-based review generation, reasoning supervision is not straightforwardly beneficial, and precise metric-aligned scoring remains challenging even after task-specific fine-tuning.

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.

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.

We propose last-mile fine-tuning, or Lift, a pipeline in which a pre-trained large language model extracts an initial table from unstructured clipboard text, and a fine-tuned small language model (1B-24B parameters SLM) repairs errors in the extracted table. On a benchmark of 2,596 tables from three datasets, Lift matches or exceeds end-to-end SLM fine-tuning on tree-edit-distance-based similarity (TEDS) metric while requiring as little as 1,000 training examples - where it outperforms end-to-end fine-tuning by up to 0.144 TEDS points. We term this approach last-mile fine-tuning and show it also more robust to input format variability. Comparisons with self-debug and end-to-end fine-tuning approaches show that last-mile fine-tuning provides an attractive option when training data is limited or when robustness to input variation is sought without compromising on accuracy.

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.

Fine-tuning LLMs on narrow harmful datasets can induce Emergent Misalignment (EM), where models exhibit misaligned behavior far beyond the fine-tuning distribution. We argue that emergent misalignment can be better understood as a data-mediated transfer phenomenon: harmful fine-tuning examples do not induce uniform behavioral spillover, but interact with the structural properties of the dataset and the difficulty of the tasks relative to the model. Across our experiments, we find that misalignment appears more readily when fine-tuning and evaluation prompts share similar underlying functional structure, when prompts leave more room for coherent harmful completions, and when the target behavior has been more reliably learned by the model. The training pipeline itself also matters: pretraining composition shapes later misalignment. We further study Subliminal Learning (SL), where misalignment is transmitted by fine-tuning on seemingly benign data generated by a harmful teacher. Moving beyond the standard SFT setting, we for the first time compare this transfer under off-policy and on-policy distillation as well, allowing us to separate the roles of the teacher guidance and the training data distribution in transmitting misalignment. Together, these results argue for a data-centric view: Emergent/subliminal misalignment should not be treated as a simple consequence of isolated harmful fine-tuning examples, but as the result of interactions between fine-tuning data structure, pretraining distributions, and training channels.

Using prompted language models as classifiers enables classification in domains with limited training data, but misses some of the robustness and performance benefits that fine-tuning can bring. We study whether training on multiple classification tasks, each with its own prompt, improves performance on new domains with new classification prompts. We show that such training partially generalizes to adjacent domains, improving classification performance on tasks that are unseen during training. However, we identify specific edge cases where the fine-tuned models fail to follow prompts, such as when the classification prompt changes completely while the data domain remains the same as during training. We show that classification training can be mixed with general instruction following training, and that (when done well) such training keeps the benefits of classification training and mitigates its generalization failures. Surprisingly, we see that this no-thinking supervised classification training can generalize to with-thinking classification and summarization, suggesting that no-thinking classification training might be instrumentally useful in building other kinds of classifiers and monitoring systems.

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.

We measure procedural-skill SFT contribution across three Qwen3.5 dense scales (0.8B, 2B, 4B) on a 200-task / 40-skill holdout, with Claude Haiku 4.5 as a frontier reference. The corpus is 353 rows of (task + procedural-skill block, Opus chain-of-thought, judge-pass) demonstrations. Main finding. Under matched-path LLM-only scoring, the SFT-attributable procedural-$Δ$ lift is roughly uniform across sizes: $+0.070 / +0.040 / +0.075$ at 0.8B / 2B / 4B. Variation in post-SFT $Δ$ ($-0.005$, $+0.100$, $+0.065$) is dominated by a W-shaped pre-SFT base trajectory ($-0.075$, $+0.060$, $-0.010$, Haiku-4-5 at $+0.030$): the 5-step procedure hurts 0.8B and 4B, helps 2B, and helps frontier Haiku modestly. SFT works hardest in absolute terms where the base struggles with the procedure -- a regime-asymmetric pattern with a falsifiable prediction at 8B/14B. Methodology. (i) A bench format-compliance artifact: 83.5% of the holdout uses a deterministic ANSWER-line extractor that under-counts free-form-prose conclusions; our LLM-only re-judge reveals it was systematically biased against the curated condition. (ii) A negative-iteration sequence at 0.8B: three well-formed recipe variants cluster post-SFT curated pass-rate within a 2 pp band, constraining the absolute-pass-rate ceiling to base capacity rather than recipe. Cross-family judge validation. GPT-5.4 via OpenRouter on all 7 configurations (2800 paired episodes) agrees on the direction of every per-student finding: Cohen's $κ\geq 0.754$, agreement $\geq 93.25\%$, max headline $Δ$ shift $\leq 0.035$ pp. Two earlier framings -- "format-only learning at 0.8B" and "SFT contribution shrinks at 4B" -- were path-mismatch artifacts; this paper supersedes both. Single-seed evaluation; threats itemised in the paper.

Automated theorem proving with large language models in Lean 4 is commonly approached through either step-level tactic prediction with tree search or whole-proof generation. These two paradigms represent opposite granularities for constructing supervised training data: the former provides dense local signals but may fragment coherent proof processes, while the latter preserves global structure but requires complex end-to-end generation. In this paper, we revisit supervision granularity as a training set construction problem over proof trajectories and propose segment-level supervision, a training data construction strategy that extracts locally coherent proof segments for training policy models. We further reuse the same strategy at inference time to trigger short rollouts for existing step-level models. When trained with segment-level supervision on STP, LeanWorkbook, and NuminaMath-LEAN, the resulting policy models achieve proof success rates of 64.84%, 60.90%, and 66.31% on miniF2F, respectively, consistently outperforming both step-level and whole-proof baselines. Goal-aware rollout further improves existing step-level provers while reducing inference costs. It increases the proof success rate of BFS-Prover-V2-7B from 68.77% to 70.74% and that of InternLM2.5-StepProver from 59.59% to 60.33%, showing that appropriate supervision granularity better aligns model learning with proof structure and search. Code and models are available at https://github.com/NJUDeepEngine/SEG-ATP.

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.

Rejection Fine-Tuning (RFT) is a standard method for training LLM agents, where unsuccessful trajectories are discarded from the training set. In the context of SWE-bench tasks, this corresponds to filtering out runs where the submitted patch does not pass the tests. However, this approach discards unresolved trajectories, even though they form a large portion of all trajectories for hard tasks and even then may be partially correct. In this work, we propose Step Rejection Fine-Tuning (SRFT) - a practical way to leverage these unresolved trajectories. For this, we employ a critic LLM to assess the correctness of each step in a trajectory. Consequently, during training, we mask the loss for erroneous steps while retaining them in the context window. This way we ensure the model learns to recover from errors without reproducing them. Evaluation on SWE-bench Verified shows that while RFT improves the resolution rate by 2.4% by excluding unresolved trajectories, SRFT improves it by 3.7% by filtering them instead of discarding completely, reaching the total resolution rate of 32.2%.

Post-training (via supervised fine-tuning) improves instruction-following, but often induces semantic mode collapse by biasing models toward low-entropy fine-tuning data at the expense of the high-entropy pretraining distribution. Crucially, we find this trade-off worsens with scale. To close this semantic diversity gap, we propose annotation-anchored training, a principled method that enables models to adopt the preference-following behaviors of post-training without sacrificing the inherent diversity of pretraining. Our approach is simple: we pretrain on documents paired with semantic annotations, inducing a rich annotation distribution that reflects the full breadth of pretraining data, and we preserve this distribution during post-training. This lets us sample diverse annotations at inference time and use them as anchors to guide generation, effectively transferring pretraining's semantic richness into post-trained models. We find that models trained with annotation-anchored training can attain $6 \times$ less diversity collapse than models trained with SFT, and improve with scale.

Large language models can now process increasingly long inputs, yet their ability to effectively use information spread across long contexts remains limited. We trace this gap to how attention budget is spent during supervised fine-tuning (SFT) on long sequences: positional biases and attention sinks cause the model to allocate most of its attention to positionally privileged tokens rather than semantically relevant content. This training-time attention dilution (the starvation of content tokens in the attention distribution) weakens the gradient signal, limiting the model's ability to learn robust long-context capabilities. We introduce FocuSFT, a bilevel optimization framework that addresses this problem at training time. An inner loop adapts lightweight fast-weight parameters on the training context to form a parametric memory that concentrates attention on relevant content, and the outer loop performs SFT conditioned on this sharpened representation. Both loops apply bidirectional attention over context tokens while preserving causal masking for responses, reducing the causal asymmetry that gives rise to attention sinks and aligning inner-outer behavior. On BABILong, FocuSFT improves accuracy by up to +14pp across 4K--32K context lengths; on RULER, it raises CWE aggregation from 72.9% to 81.1% at 16K; and on GPQA with agentic tool use, it yields a 24% relative gain in pass@1. Attention analysis shows that FocuSFT reduces attention sink mass by 529$\times$ and triples context engagement during training. Code: https://github.com/JarvisPei/FocuSFT

Knowledge of a protein's atomic conformational ensemble is critical to determining its function, yet state-of-the-art ensemble prediction models are limited by lack of high-quality conformational data from simulation or experiment. Recent advances in heterogeneous reconstruction for cryo-electron microscopy (cryo-EM) have enabled scientists to visualize ensembles of density maps for larger proteins and complexes not typically accessible through simulation, but building atomic models into these maps remains a challenge. Traditionally, ensemble prediction models are trained via a two-stage process: experimental density maps are converted into atomic structural ensembles through model building, after which these structures are used to train sequence-to-atomic ensemble predictors. In this work, we propose a new principle for fine-tuning pre-trained static structure prediction models such as Boltz-2 directly on raw cryo-EM maps, bypassing the two-stage process. We apply this technique to the problem of atomic model building by fine-tuning Boltz-2 to generate atomic conformations from an input ensemble of cryo-EM maps, achieving superior model building accuracy compared to prior work. Beyond overfitting to individual map ensembles, our method, CryoSampler, also shows preliminary evidence of in-domain generalization after fine-tuning, sampling diverse atomic conformations for an unseen sequences within the same protein family without requiring cryo-EM data. These capabilities indicate that CryoSampler holds the potential to train next-generation atomic ensemble prediction models directly on raw cryo-EM measurements.

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.