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arxiv: 2604.08510 · v1 · submitted 2026-04-09 · 💻 cs.CL

What do Language Models Learn and When? The Implicit Curriculum Hypothesis

Emmy Liu , Kaiser Sun , Millicent Li , Isabelle Lee , Lindia Tjuatja , Jen-tse Huang , Graham Neubig This is my paper

Pith reviewed 2026-05-10 17:49 UTC · model grok-4.3

classification 💻 cs.CL
keywords language modelspretrainingemergencecompositional taskscurriculummodel representationspredicting trajectoriesscaling
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The pith

Language models acquire skills in a consistent compositional order during pretraining, predictable from their internal representations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper advances the Implicit Curriculum Hypothesis that pretraining imposes a structured, compositional sequence on skill acquisition that holds across model sizes and families. The authors build a collection of basic tasks in areas such as retrieval and logical reasoning, then measure the point at which different models first reach fixed accuracy levels on each task. Emergence sequences turn out highly consistent, with composite tasks appearing after their building-block components. Task similarities captured in function-vector representations also align with shared training trajectories, which in turn support accurate forecasts of when held-out tasks will be learned. If the pattern holds, training progress contains more readable structure than loss curves alone indicate.

Core claim

The Implicit Curriculum Hypothesis claims that pretraining follows a compositional and predictable curriculum across models and data mixtures. Tracking a suite of simple composable tasks across four model families from 410M to 13B parameters shows emergence orderings that remain stable with Spearman rank correlation of 0.81 across 45 model pairs, while composite tasks emerge after their components. Similarities among tasks in function-vector space further correspond to aligned learning curves, allowing the authors to predict trajectories for held-out compositional tasks with R-squared values between 0.68 and 0.84 without ever evaluating those tasks directly.

What carries the argument

The Implicit Curriculum Hypothesis, tested via a suite of simple composable tasks whose emergence orderings and function-vector representations encode predictable training trajectories.

If this is right

  • Skill emergence order remains similar across model sizes and families.
  • Composite tasks reliably appear after their component tasks.
  • Model representations encode information sufficient to forecast future task performance.
  • Held-out compositional tasks can be tracked without direct evaluation during training.
  • Pretraining dynamics contain compositional structure beyond what aggregate loss reveals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Training data mixtures could be adjusted to accelerate or reorder specific capability development.
  • The same representation space might be used to monitor real-time progress on abilities not yet directly tested.
  • Extending the task suite to more complex or open-ended problems could reveal whether the curriculum persists at larger scales.
  • This structure may help explain why certain capabilities remain absent in smaller models even after extensive training.

Load-bearing premise

The suite of simple composable tasks accurately reflects the compositional structure of capabilities that arise during pretraining on natural language.

What would settle it

Running the same task suite on a new model family or data mixture and finding emergence orderings that differ markedly from the previously observed consistent pattern, or finding that representation-based predictions no longer match measured trajectories.

Figures

Figures reproduced from arXiv: 2604.08510 by Emmy Liu, Graham Neubig, Isabelle Lee, Jen-tse Huang, Kaiser Sun, Lindia Tjuatja, Millicent Li.

Figure 1
Figure 1. Figure 1: Emergence order across model families and sizes, smoothed with a Gaussian [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Emergence order heatmap of selected tasks across models (absolute threshold = [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example composite task predictions for OLMo2-7B between 0-1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Complete trajectories for Pythia-410M over 300B tokens. [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Complete trajectories for OLMo2-1B over 1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Complete trajectories for Pythia-1.4B over 300B tokens. [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Complete trajectories for OLMo-2 7B over 1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Complete trajectories for OLMo-3 7B over 1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p023_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Complete trajectories for Amber (7B) over 1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Complete trajectories for CrystalCoder (7B) over 1T tokens. [PITH_FULL_IMAGE:figures/full_fig_p025_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Complete trajectories for Pythia-12B over 300B tokens. Note that this model [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Complete trajectories for OLMo2-13b over 1T tokens. Note that this model [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Predictions of held-out compositional tasks for Pythia-410M. [PITH_FULL_IMAGE:figures/full_fig_p032_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Predictions of held-out compositional tasks for OLMo2-1B. [PITH_FULL_IMAGE:figures/full_fig_p033_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Predictions of held-out compositional tasks for Pythia-1.4B. [PITH_FULL_IMAGE:figures/full_fig_p034_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Predictions of held-out compositional tasks for OLMo2-7B. [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Predictions of held-out compositional tasks for OLMo3-7B. [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Predictions of held-out compositional tasks for Amber. [PITH_FULL_IMAGE:figures/full_fig_p037_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Predictions of held-out compositional tasks for CrystalCoder. [PITH_FULL_IMAGE:figures/full_fig_p038_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Predictions of held-out compositional tasks for Pythia-12B. [PITH_FULL_IMAGE:figures/full_fig_p039_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Predictions of held-out compositional tasks for OLMo2-13B. [PITH_FULL_IMAGE:figures/full_fig_p040_21.png] view at source ↗
read the original abstract

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 ($\rho = .81$ 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes the Implicit Curriculum Hypothesis that pretraining of large language models follows a compositional and predictable curriculum across models and data mixtures. The authors design a suite of simple composable tasks spanning retrieval, morphological transformations, coreference, logical reasoning, and mathematics; they track emergence points (fixed accuracy thresholds) across four model families (410M–13B parameters), report consistent emergence orderings (Spearman’s ρ = .81 across 45 model pairs), show that composite tasks typically emerge after their components, and demonstrate that task function-vector representations allow prediction of held-out compositional task trajectories (R² = .68–.84) without prior evaluation.

Significance. If the hand-designed task suite is shown to instantiate the same compositional dependencies that drive emergence on natural data, the results would provide a concrete, falsifiable framework for studying fine-grained capability acquisition beyond aggregate scaling laws. The reported consistency of orderings across model families and the predictive use of internal representations are notable empirical strengths that could inform both mechanistic interpretability and training interventions.

major comments (2)
  1. [Abstract and experimental design] The central claim concerns the structure of pretraining on natural language data, yet all quantitative support (ρ = .81, composite-after-component ordering, R² = .68–.84) is obtained exclusively on the authors’ hand-designed suite; no experiment or analysis is presented that tests whether the observed orderings or representational similarities align with capabilities that actually emerge from natural pretraining distributions (e.g., by probing for known emergent skills such as multi-step arithmetic or coreference in naturally occurring contexts). This assumption is load-bearing for the Implicit Curriculum Hypothesis.
  2. [Methods and results sections] The manuscript provides insufficient detail on task construction, accuracy-threshold selection, and controls for confounds such as task difficulty, token overlap with pretraining data, or prompt sensitivity; without these, it is impossible to determine whether the reported consistency and predictability are robust properties of the pretraining process or artifacts of the particular task definitions and evaluation protocol.
minor comments (2)
  1. [Representation analysis] The description of how function vectors are extracted and how similarity is quantified could be expanded with an explicit equation or pseudocode to improve reproducibility.
  2. [Figures] Figure legends and axis labels should explicitly state the accuracy threshold used for each emergence curve and the number of seeds or runs averaged.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which highlights important considerations for strengthening the manuscript. We address each major comment below with clarifications on our design choices and commitments to revisions where the concerns are valid.

read point-by-point responses

  1. Referee: [Abstract and experimental design] The central claim concerns the structure of pretraining on natural language data, yet all quantitative support (ρ = .81, composite-after-component ordering, R² = .68–.84) is obtained exclusively on the authors’ hand-designed suite; no experiment or analysis is presented that tests whether the observed orderings or representational similarities align with capabilities that actually emerge from natural pretraining distributions (e.g., by probing for known emergent skills such as multi-step arithmetic or coreference in naturally occurring contexts). This assumption is load-bearing for the Implicit Curriculum Hypothesis.

    Authors: We agree that the central claim targets the structure of natural pretraining, and our experiments rely on a controlled hand-designed suite as a proxy. This choice enables precise isolation of compositional dependencies (retrieval, morphology, coreference, logic, math) and exact measurement of emergence orderings and function-vector predictability—analyses that are difficult to perform cleanly on noisy natural data. The suite was constructed to instantiate core compositional patterns known to underlie many emergent capabilities in language. While we have not conducted direct alignment experiments (e.g., probing natural contexts for multi-step arithmetic or coreference), the high consistency of orderings across four model families and the ability to predict held-out trajectories from representations provide evidence that the observed structure is not an artifact of the suite alone. In revision we will (a) explicitly qualify the scope in the abstract and introduction, (b) add a dedicated limitations subsection discussing the proxy nature of the tasks and their relation to documented natural emergent skills, and (c) outline concrete future directions for validating the orderings against natural pretraining distributions. We maintain that the current results constitute a necessary, falsifiable first step toward the hypothesis. revision: partial

  2. Referee: [Methods and results sections] The manuscript provides insufficient detail on task construction, accuracy-threshold selection, and controls for confounds such as task difficulty, token overlap with pretraining data, or prompt sensitivity; without these, it is impossible to determine whether the reported consistency and predictability are robust properties of the pretraining process or artifacts of the particular task definitions and evaluation protocol.

    Authors: We accept this criticism and will substantially expand the Methods and Results sections. Specifically, we will add: (1) full task-construction details, including primitive definitions, composition rules, and example prompts for every task; (2) explicit justification and sensitivity analysis for the accuracy thresholds used to mark emergence (currently 70 %); (3) quantitative controls for task difficulty via random-model baselines and length-matched controls; (4) token-overlap statistics between task prompts and common pretraining corpora (e.g., The Pile, C4); and (5) prompt-sensitivity results across at least three prompt templates per task. These additions will appear in the main text where space permits and in a new appendix containing complete task specifications, code snippets, and robustness tables. We believe these revisions will allow readers to evaluate whether the reported consistency (ρ = .81) and predictive R² values reflect genuine pretraining structure. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on direct empirical measurements of held-out tasks

full rationale

The paper designs a task suite, measures emergence orderings across models (ρ = .81), observes composite-after-component patterns, and reports R² = .68-.84 for predicting trajectories of held-out compositional tasks from representation spaces. These steps are empirical evaluations and cross-task predictions on explicitly held-out items; they do not reduce by construction to fitted parameters, self-definitions, or self-citation chains. No equations or derivations are presented that equate outputs to inputs tautologically. The central results remain falsifiable against external benchmarks and do not rely on renaming or ansatz smuggling.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the chosen task suite captures meaningful compositional structure in LLM capabilities and that representation similarity reflects functional relatedness relevant to emergence timing.

axioms (1)
  • domain assumption The selected tasks are representative of compositional capabilities in language models.
    The paper relies on performance patterns on these tasks to infer a general curriculum in pretraining.

pith-pipeline@v0.9.0 · 5572 in / 1285 out tokens · 78012 ms · 2026-05-10T17:49:04.086639+00:00 · methodology

discussion (0)

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Reference graph

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