Small Models Scout Bottleneck Order for Large-Model Data Control

Large language models (LLMs) can perform remarkably complex tasks, yet the fine-grained details of how these capabilities emerge during pretraining remain poorly understood. Scaling laws on validation loss tell us how much a model improves with additional compute, but not what skills it acquires in which order. To remedy this, we propose the Implicit Curriculum Hypothesis: pretraining follows a compositional and predictable curriculum across models and data mixtures. We test this by designing a suite of simple, composable tasks spanning retrieval, morphological transformations, coreference, logical reasoning, and mathematics. Using these tasks, we track emergence points across four model families spanning sizes from 410M-13B parameters. We find that emergence orderings of when models reach fixed accuracy thresholds are strikingly consistent ($ρ= .81$ across 45 model pairs), and that composite tasks most often emerge after their component tasks. Furthermore, we find that this structure is encoded in model representations: tasks with similar function vector representations also tend to follow similar trajectories in training. By using the space of representations derived from our task set, we can effectively predict the training trajectories of simple held-out compositional tasks throughout the course of pretraining ($R^2 = .68$-$.84$ across models) without previously evaluating them. Together, these results suggest that pretraining is more structured than loss curves reveal: skills emerge in a compositional order that is consistent across models and readable from their internals.

Data strategy plays a central role in training large language models (LLMs). It governs the selection, weighting, and scheduling of training data, thereby determining the capabilities a model can acquire from a fixed data budget. We treat high-quality data as having high training-dependent utility, which depends on the target objective, the model, and its training state rather than on the text alone. Research in this area now spans pretraining and post-training, but related ideas use inconsistent terminology and evaluation protocols. This work reviews data strategies across the training lifecycle and formulates them as policies that allocate a training budget over candidate examples. We organise methods by their decision granularity, model dependence, and temporal adaptivity, then compare their computational requirements and empirical support. Fine-grained or state-dependent policies offer more control but incur additional scoring, search, or rollout costs. Evidence for transfer across model scales and comparable end-to-end cost remains limited. A continuously updated list of papers, along with their public implementations, is available at https://github.com/xuyj233/data_strategy_survey.

What should data teach a language model at a particular point in training? A circuit view reveals three distinct bottlenecks: forming a computation, making its required content available, and selecting among available routes. A shared diagnosis-to-data principle connects them: localize the missing operation, preserve its causal relation, vary shortcut-bearing context, and re-audit the residual. Formation-sensitive selection and prerequisite ordering accelerate a binding-matching-transport path; a brief early prefix from the same training multiset retains a validation advantage through 100B tokens. Availability counterfactuals then distinguish writing content from invoking available memory, while paired supervision and context-opportunity ranking improve matched route decisions and long-context answer likelihood. A continuous 350M-model experiment connects the three interventions on the same facts: early circuit training improves subsequent learning, and the complete sequence outperforms stage-replacement controls on facts withheld from Use teaching. Independent query surfaces and opposed-source decisions expose conditional arbitration as the remaining frontier. Together, these results show why a change in the limiting operation calls for a change in supervision, not merely a new ranking of difficult examples.