# What Should Data Teach? Moving Bottlenecks Across Circuit, Store, and Use

arXiv: https://arxiv.org/abs/2609.32991 · HTML: https://mlsanity.com/paper/2609.32991/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 34)

- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [RULER: What's the Real Context Size of Your Long-Context Language Models?](https://mlsanity.com/paper/2404.06654/) (2024)
- [Transformer Feed-Forward Layers Are Key-Value Memories](https://mlsanity.com/paper/2012.14913/) (2020)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [Extending Context Window of Large Language Models via Positional Interpolation](https://mlsanity.com/paper/2306.15595/) (2023)
- [Large Language Models Struggle to Learn Long-Tail Knowledge](https://mlsanity.com/paper/2211.08411/) (2022)
- [Knowledge Conflicts for LLMs: A Survey](https://mlsanity.com/paper/2403.08319/) (2024)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [QuRating: Selecting High-Quality Data for Training Language Models](https://mlsanity.com/paper/2402.09739/) (2024)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Physics of Language Models: Part 3.2, Knowledge Manipulation](https://mlsanity.com/paper/2309.14402/) (2023)
- [Skill-it! A Data-Driven Skills Framework for Understanding and Training Language Models](https://mlsanity.com/paper/2307.14430/) (2023)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formation](https://mlsanity.com/paper/2404.07129/) (2024)
- [What is Wrong with Perplexity for Long-context Language Modeling?](https://mlsanity.com/paper/2410.23771/) (2024)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Studying Large Language Model Behaviors Under Context-Memory Conflicts With Real Documents](https://mlsanity.com/paper/2404.16032/) (2024)
- [Beyond Random Sampling: Efficient Language Model Pretraining via Curriculum Learning](https://mlsanity.com/paper/2506.11300/) (2025)
- [Preference Curriculum: LLMs Should Always Be Pretrained on Their Preferred Data](https://mlsanity.com/paper/2501.13126/) (2025)
- [Task Matters: Knowledge Requirements Shape LLM Responses to Context-Memory Conflict](https://mlsanity.com/paper/2506.06485/) (2025)
- [Group-Level Data Selection for Efficient Pretraining](https://mlsanity.com/paper/2502.14709/) (2025)
- [LADM: Long-context Training Data Selection with Attention-based Dependency Measurement for LLMs](https://mlsanity.com/paper/2503.02502/) (2025)
- [Mechanistic Data Attribution: Tracing the Training Origins of Interpretable LLM Units](https://mlsanity.com/paper/2601.21996/) (2026)
- [LongAttn: Selecting Long-context Training Data via Token-level Attention](https://mlsanity.com/paper/2502.16860/) (2025)
- [Why Supervised Fine-Tuning Fails to Learn: A Systematic Study of Incomplete Learning in Large Language Models](https://mlsanity.com/paper/2604.10079/) (2026)
- [Influence Dynamics and Stagewise Data Attribution](https://mlsanity.com/paper/2510.12071/) (2025)
- [From Shortcut to Induction Head: How Data Diversity Shapes Algorithm Selection in Transformers](https://mlsanity.com/paper/2512.18634/) (2025)
- [Beyond Length: Quantifying Long-Range Information for Long-Context LLM Pretraining Data](https://mlsanity.com/paper/2510.25804/) (2025)
- [CASCADE Your Datasets for Cross-Mode Knowledge Retrieval of Language Models](https://mlsanity.com/paper/2504.01450/) (2025)

## Abstract (arXiv)

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.