On-policy distillation (OPD) combines student-generated rollouts with dense token-level supervision from a teacher. Existing work has mainly studied its algorithmic behavior, leaving the role of training data unclear. We examine this role at the data-minimal limit by training on a single query. One-shot OPD keeps improving for hundreds of steps and recovers most of full-data OPD's gain across task domains and model families. We explain this result through the states visited during training and the rate at which the student aligns with the teacher. We measure \emph{state coverage}, the fraction of the states full-data OPD visits that a query set's rollouts reach. A single query already reaches \(71.5\%\), most of it within the first 100 steps. Adding semantically distinct queries raises coverage and validation accuracy together, until 16 queries reach \(98.9\%\) and match full-data training. Yet alignment slows at a similar pace whether OPD trains on one query or the whole dataset, and even a fixed set of states takes hundreds of steps to absorb. OPD is therefore data-overfed but algorithm-starved. Its rollouts quickly expose broad supervision, while the student absorbs that supervision increasingly slowly. The state-coverage result extends to multi-teacher OPD, where 16 semantically diverse queries per domain match full-data MOPD. As a further stress test, content-light templates and off-domain WildChat queries also approach the real-query baseline. Task content and induced state coverage can therefore come apart. We hope these findings direct future work toward the step efficiency of OPD, and prompt a re-examination of the data and the mechanisms behind its recent successes in frontier post-training.
We show that sequence-level distillation from a capable long-context teacher model is a simple, annotation-free, and data-efficient strategy for improving argument saliency coverage in long legal opinion summarization, where small LLMs often struggle to retain the most salient argumentative content. Across student model sizes, distillation consistently surpasses tuning on expert-written summaries in our legal-opinion setting. We further demonstrate that most gains are achieved with as few as ~10 training summaries, highlighting the strong data efficiency of teacher-generated supervision. Finally, we find that summary distillation is sufficient for improvements: reasoning-chain distillation remains competitive with summary-only distillation, but provides marginal benefit when combined with summary supervision.
Iterative preference optimization is essential for aligning Large Language Models on mathematical reasoning tasks, yet its efficiency is often throttled by signal scarcity: as the model improves, static problem sets become increasingly mismatched to the model's evolving competence, producing rollouts that are either too easy or too hard and therefore non-informative, which leads to a scarcity of valid preference pairs. We propose DIAG, a Diagnostic Iterative Alignment and Generation framework that adaptively reshapes the practice distribution to increase informative supervision and focus training near the student's current competence boundary. DIAG consists of two phases: (1) diagnosing valid preference-pair yield to calibrate the exploration-exploitation trade-off and allocate topic quotas via an Empirical Bayes shrinkage estimator, thereby prioritizing high-yield concepts; and (2) generating targeted practice, where a teacher synthesizes variants from the student's failure traces. We further provide a theoretical view interpreting DIAG as a teacher-mediated approximation to KL-regularized reweighting of the practice distribution toward the student's competence boundary, where valid preference-pair yield is maximized. Experiments show that DIAG boosts yield across iterations and delivers stronger reasoning performance under an iso-effective training budget, demonstrating that it can distill more informative preference supervision for mathematical reasoning.
We introduce ReliableTableQA, a framework for training an LLM to annotate the statistical reliability of tabular QA results, not whether the query is answerable, but whether the computed answer is statistically meaningful. In real enterprise analytics, a syntactically correct SQL query can return a value that is based on too small a sample, has an excessively wide confidence interval, or is too confounded to support action. Existing systems answer confidently in all such cases, a failure we quantify as the Unreliable Confident Answer Rate (UCAR). We contribute (1) a ten-category reliability taxonomy (R1-R10) covering hazards such as small-sample aggregates, multiple-comparison inflation, and distribution-tail mismatch; (2) a program-first data pipeline that generates 50,000 reliability-labeled training examples from a context-free grammar over public retail schemas, with schema-stratified SFT/GRPO splits; and (3) a controlled study of how much supervision calibrated reliability annotation actually requires. We find that a small, schema-stratified SFT set is remarkably sufficient: 200 examples raise reliability-flag F1 from 0.61 to 0.98 and parse rate from 0.52 to 1.00, drive UCAR to zero, and yield a model that generalizes to an unseen retail domain (Rel-F1 0.997 on held-out H&M). Against this strong SFT baseline, GRPO, commonly assumed to be essential, helps only when SFT is under-trained (+0.06-0.16 exact-flag-set match at 100 examples, in- and out-of-distribution) and provides no measurable benefit once SFT is adequate, a null result we confirm across a hard compound-flag slice, a strict exact-match metric, and out-of-distribution evaluation. Our findings reframe reliability annotation as a data-efficiency problem and delineate precisely when reinforcement fine-tuning does and does not pay off.
As available training data approaches its physical limit, gains from Scaling Laws have begun to diminish. Consequently, improving Large Language Models (LLMs) now depends less on data expansion and more on higher-quality data utilization. However, in the context of large-scale corpora, existing refinement methodologies face significant limitations in quality, efficiency, and reliability: Rule-based approaches are constrained by fixed heuristics and struggle with instance-level variations; LLM-based approaches improve quality but fail to meet the efficiency and reliability requirements of large-scale data processing. To address these challenges, we propose UltraX, a function-calling refinement framework for large-scale pre-training data that completes the editing function space by introducing insertion in addition to deletion and modification, enabling fine-grained instance-level editing. Specifically, UltraX builds a reliable program-supervision generation pipeline. In this pipeline, dataset-adaptive prompt optimization first guides an expert LLM to produce high-quality end-to-end refined texts, and Line Alignment Mapping and Dynamic Context Replacement then convert original-refined text pairs into structured program supervision. Meanwhile, UltraX improves supervision quality and stabilizes the training distribution with low-confidence example filtering and ratio-controlled sampling by operation combination. During inference and execution, it normalizes and validates model outputs through sliding-window prediction, global operation aggregation, and systematic post-processing, improving the stability and reliability of large-scale execution. Experiments show that UltraX achieves the highest average performance across all corpora and also matches or surpasses baselines with fewer training tokens, demonstrating stronger data efficiency and refinement reliability.
Multi-epoch training is becoming the standard now that compute is growing faster than the supply of high-quality text. But pretraining a single model saturates within a few passes, long before the compute budget is exhausted. We argue this calls for a conceptual shift from training a single model toward exploring a population of models and aggregating their predictions. We introduce hyper-epoch pretraining (q0), which turns a multi-epoch budget into a population of diverse models whose combined predictions reach a lower validation loss than a single refined model. q0 reduces to three core primitives. A cyclic schedule with anti-correlated learning rate and weight decay collects diverse models from a few parallel trajectories. Chain distillation trains each model against its predecessor so that model quality compounds across the population. A learned prior, fit on a held out set, selects and weights members for any inference budget. On a 1.8B-parameter model trained on 100M FineWeb tokens, q0 matches a strong 256-epoch ensemble baseline using only ~56 epochs (~4.6x fewer), or ~67 epochs (~3.8x fewer) when matched to the baseline's ensemble size, and continues to improve beyond it. These gains reach cumulative ~12.9x data efficiency under the Slowrun setting and transfer to downstream benchmarks. Crucially, the optimal allocation shifts with the budget, so we give prescriptive recipes for how to spend a given epoch budget to maximize generalization, from a single epoch up to the largest budgets.
While mechanistic interpretability tools like Sparse Autoencoders (SAEs) can uncover meaningful features within Large Language Models (LLMs), a critical gap remains in transforming these insights into practical actions for model optimization. We bridge this gap with the hypothesis that data selection guided by a model's internal task features is a effective training strategy. Inspired by this, we propose Interpretability-Guided Data Selection (IGDS), a framework that first identifies these causal task features through frequency recall and interventional filtering, then selects ``Feature-Resonant Data'' that maximally activates task features for fine-tuning. We validate IGDS on mathematical reasoning, summarization, and translation tasks within Gemma-2, LLaMA-3.1, and Qwen3 models. Our experiments demonstrate exceptional data efficiency: on the Math task, IGDS surpasses full-dataset fine-tuning by a remarkable 17.4% on Gemma-2-2B while using only 50% of the data, and outperforms established baselines focused on data quality and diversity. Analysis confirms a strong positive correlation between feature amplification and task performance improvement. IGDS thus provides a direct and effective framework to enhance LLMs by leveraging their internal mechanisms, validating our core hypothesis.