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

arXiv: https://arxiv.org/abs/2604.08510 · HTML: https://mlsanity.com/paper/2604.08510/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 47 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 30 of 43)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [Scaling Data-Constrained Language Models](https://mlsanity.com/paper/2305.16264/) (2023)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [In-Context Learning Creates Task Vectors](https://mlsanity.com/paper/2310.15916/) (2023)
- [Function Vectors in Large Language Models](https://mlsanity.com/paper/2310.15213/) (2023)
- [SGD on Neural Networks Learns Functions of Increasing Complexity](https://mlsanity.com/paper/1905.11604/) (2019)
- [The Quantization Model of Neural Scaling](https://mlsanity.com/paper/2303.13506/) (2023)
- [Sudden Drops in the Loss: Syntax Acquisition, Phase Transitions, and Simplicity Bias in MLMs](https://mlsanity.com/paper/2309.07311/) (2023)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [A Theory for Emergence of Complex Skills in Language Models](https://mlsanity.com/paper/2307.15936/) (2023)
- [Language models scale reliably with over-training and on downstream tasks](https://mlsanity.com/paper/2403.08540/) (2024)
- [Language Model Evaluation Beyond Perplexity](https://mlsanity.com/paper/2106.00085/) (2021)
- [Probing Across Time: What Does RoBERTa Know and When?](https://mlsanity.com/paper/2104.07885/) (2021)
- [Skill-Mix: a Flexible and Expandable Family of Evaluations for AI models](https://mlsanity.com/paper/2310.17567/) (2023)
- [Which Attention Heads Matter for In-Context Learning?](https://mlsanity.com/paper/2502.14010/) (2025)
- [Scaling Laws for Downstream Task Performance of Large Language Models](https://mlsanity.com/paper/2402.04177/) (2024)
- [Revealing the structure of language model capabilities](https://mlsanity.com/paper/2306.10062/) (2023)
- [PolyPythias: Stability and Outliers across Fifty Language Model Pre-Training Runs](https://mlsanity.com/paper/2503.09543/) (2025)
- [Scaling Laws Are Unreliable for Downstream Tasks: A Reality Check](https://mlsanity.com/paper/2507.00885/) (2025)
- [Parallel Structures in Pre-training Data Yield In-Context Learning](https://mlsanity.com/paper/2402.12530/) (2024)
- [Sloth: scaling laws for LLM skills to predict multi-benchmark performance across families](https://mlsanity.com/paper/2412.06540/) (2024)
- [The Dual-Route Model of Induction](https://mlsanity.com/paper/2504.03022/) (2025)

## Built on by (most cited first, 10 of 10)

- [Extracting Small Translation Specialists from LLMs by Aggressively Pruning Experts](https://mlsanity.com/paper/2605.28042/) (2026)
- [Logic Before Language: Pre-pretraining on Formal Derivations Fosters Skill Acquisition and Compressibility](https://mlsanity.com/paper/2608.03930/) (2026)
- [Fast & Faithful Function Vectors](https://mlsanity.com/paper/2606.05079/) (2026)
- [Pretraining Curricula Enable Selective Fine-tuning](https://mlsanity.com/paper/2607.04846/) (2026)
- [Small Models Scout Bottleneck Order for Large-Model Data Control](https://mlsanity.com/paper/2608.14936/) (2026)
- [Coupled Scaling: A Representational Accessibility Framework for Neural Scaling Laws](https://mlsanity.com/paper/2609.03533/) (2026)
- [The Free-Recipe Limit: Every Recipe Effect Measures Which Premise of an Idealised Learner Broke](https://mlsanity.com/paper/2609.26160/) (2026)
- [Neural Dynamics as the Composition of Quantized Units](https://mlsanity.com/paper/2609.32487/) (2026)
- [Conflicting Supervision Moves Commitment, Not Capability: A 12.29σ arrangement effect that is exactly zero under a convention-agnostic score](https://mlsanity.com/paper/2610.00234/) (2026)
- [From Copying to Composition: How Language Models Develop In-Context Learning](https://mlsanity.com/paper/2610.19113/) (2026)

## Abstract (arXiv)

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 (R2 = .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.