Organizations: IIIS, Tsinghua University · College of AI, Tsinghua University · Shanghai Qi Zhi Institute · Amazon AGI SF Lab
Abstract
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.
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.
Data selection is increasingly used to reduce the cost of large language model (LLM) fine-tuning, with recent methods prioritizing samples by current utility, diversity, quality, or influence. This paper studies a different question: when fine-tuning occurs over multiple stages, can selection strategies that look optimal now make the model less adaptable later? We introduce a long-horizon view of LLM data selection in which a selector is evaluated not only by immediate task performance, but also by future adaptation speed, forgetting, capability imbalance, and out-of-distribution robustness. We compare representative random, loss-based, gradient-based, diversity-based, quality-based, and utility-diversity selection families under a unified multi-stage protocol. Through controlled experiments designed to instantiate this protocol, we show how short-term selectors can exhibit rank reversal: they improve the current stage while slowing subsequent learning and increasing forgetting. We formalize this behavior as \emph{myopic selection}, provide a simple local analysis of why it can occur, and propose a diagnostic Long-Horizon Aware Selection (LHAS) objective that augments immediate utility with coverage, future-proxy transfer, and anti-concentration terms. The study argues that data selection should be evaluated as a training intervention that shapes the model's learning trajectory, rather than only as a local data-efficiency mechanism.
In Large Language Model (LLM) fine-tuning, parameter and data selection are common strategies for reducing fine-tuning cost, yet they are typically driven by separate scoring mechanisms. When a parameter mask and data subset jointly determine restricted fine-tuning, this separation incurs redundant overhead and makes coordinated selection difficult. We cast parameter and data selection as two bilevel selection problems under a common validation objective and derive a shared local response-surrogate scoring rule. Under first- and second-order validation-improvement approximations, parameter importance and data utility emerge as column-wise and row-wise aggregations of a single gradient interaction matrix, yielding a closed-form row-column correspondence for co-extracting both signals. Building on this structure, we propose DualSFT (Dual-Selection Fine-Tuning), a one-shot dual-scoring algorithm that produces a parameter mask and data subset from shared gradient statistics. On 3B-9B LLMs, single-axis DualSFT variants strengthen target-task performance and stability-plasticity trade-offs within their comparison groups, while full DualSFT yields a more favorable joint-constrained trade-off than sequential hybrid baselines under matched budgets.