Entropy-Based Data Selection for Language Models

Not all training samples contribute equally to large language model fine-tuning. Selecting informative training samples can reduce the computational cost while preserving downstream performance. Many existing data selection methods rely on indirect heuristics, such as data quality, diversity or reasoning trace length. However, the effectiveness of these fixed criteria is task-dependent and difficult to generalize across diverse downstream tasks. Perplexity-based data selection provides a simple and model-aware solution to estimate the sample difficulty, but existing approaches typically score the entire training sequence and ignore the difference in learning objectives of language modeling and reasoning tasks. In this paper, we propose PPL-Factory, a simple and interpretable data selection framework that combines task-aware perplexity-based scores and data budget-aware selection criteria. Experiments on GSM8K demonstrate that PPL-Factory outperforms other state-of-the-art data selection methods using only $1\%$ of the training set. With $10\%$ of the data, PPL-Factory exceeds full-data fine-tuning accuracy by 0.9 on GSM8K and 4.8 on MATH. Overall, our results demonstrate that task-aware and budget-aware perplexity-based selection provides an effective and applicable approach for efficient fine-tuning.

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 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.

Resource constraints increasingly determine what can be trained, fine-tuned, and deployed in large language models (LLMs), yet efficiency is often studied through isolated techniques rather than as an interacting system of limits. This survey adopts a constraint-centric perspective and organizes recent progress around three coupled bottlenecks: data efficiency (what to train on), memory efficiency (how to fit training), and compute budget awareness (when and where to spend FLOPs). On the data axis, we review selection and pruning methods that maximize learning per token, ranging from scalable proxy signals based on learning dynamics to gradient- and influence-based scoring, as well as difficulty-aware and curriculum-style strategies. We highlight emerging evidence that different notions of good data dominate in different regimes, implying that optimal subsets depend on the task objective and resource budget rather than being universal. On the systems side, we show that GPU memory, not raw compute, is often the dominant bottleneck in fine-tuning, and that effective scaling requires jointly reducing weight storage, optimizer states, and activation memory rather than optimizing any single component in isolation. Beyond memory, we frame training and inference as compute-governed processes in which optimization, data selection, and decoding must explicitly account for finite FLOP budgets. We review evidence for compute-optimal allocation and stopping rules, where computation should be halted or reallocated once marginal performance gains fall below a budget-dependent threshold. Together, these results unify compute-aware data selection, scaling laws, and adaptive inference under a common principle of resource-conditioned decision-making.