Unifying Data, Memory, and Compute Efficiency in LLM training: A Survey

Scaling LLMs requires tremendous computational resources, and recent advances in AI have gone hand in hand with massive amounts of capital expenditure. While it is established that scaling up LLMs reliably increases model quality (quantified in terms of loss or downstream evaluations), it is unclear how these quality improvements translate to potential revenue, and whether revenue increases would offset costs of larger-scale training and inference. In this work, we develop an economic model for characterizing the rational behavior of an LLM training firm by combining scaling laws with microeconomic theory. Under our model of firm behavior, LLM quality can be increased with more parameters and training tokens, leading to more potential adoption by consumers, who each have a quality threshold for using the LLM. On the other hand, additional parameters and training tokens both incur additional costs. We analyze the profit maximization problem for this model under compute-bound and data-bound regimes. In the compute-bound regime, optimal model size and token budget track hardware efficiency $E$ (FLOPs/$) at a near-linear rate; total training cost then scales sub-quadratically in $E$. Data efficiency improvements incentivize larger models and training expenditure. When we are limited to $D$ data, profit-optimal training expenditure scales as $D^2/E$, i.e, increase with data and decreases with hardware efficiency (as well as data efficiency). Finally, we analyze practical trends in training expenditure: current trends are consistent with our most permissive model variants in the compute-bound regime, but are not profit-optimal in the data-bound regime or assuming hardware advances will stall. Overall, our results provide a theory of profit-optimal LLM training, providing a foundation for engaging critically with industry statements and supporting long-term economic decision making.

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.

Training compute is increasingly outpacing the availability of high-quality data. This shifts the central challenge from optimal compute allocation to extracting maximum value from limited data. The widely adopted Chinchilla scaling law assumes every training token is unique. This limits its ability to guide pretraining decisions in data-constrained regimes. We model the excess loss under repetition with a simple additive overfitting penalty and find that it accurately describes model behavior. Our scaling law yields qualitatively new compute-optimal allocation advice. Beyond a point, further repetition is counterproductive and compute is better spent on model capacity. We show that following our law's recommended configuration improves performance in data-constrained regimes. Finally, because our one-parameter form isolates overfitting in a single coefficient, it enables direct comparison across training configurations. As a case study, we show that strong weight decay ($λ=1.0$) reduces this coefficient by approximately 70%, providing a scaling-law explanation for recent findings that optimal weight decay in data-constrained regimes is an order of magnitude larger than standard practice.