Which Training Data Shapes Large‑Model Abilities? Introducing Mechanistic Data Attribution (MDA)

Recent large language models (LLMs) have demonstrated impressive capabilities such as in‑context learning (ICL), complex reasoning, and code generation, yet the training data that give rise to these abilities remain largely unknown.

Mechanistic Interpretability and Induction Heads

Mechanistic interpretability seeks to uncover the internal computational circuits of LLMs. Induction heads, which copy previously seen patterns to enable "learning from examples," have been identified as a key neural mechanism underlying ICL.

Limitations of Post‑hoc Analyses

Existing work can reverse‑engineer circuits after training but cannot answer how those circuits were formed—i.e., which training data causally shaped them.

Mechanistic Data Attribution (MDA) Framework

The authors from Peking University and Beijing Zhiyuan Institute propose MDA, which extends interpretability from "what mechanisms exist" to "which training data created them," establishing a causal chain training data → internal mechanism → model behavior .

Localizing: Define a monitoring metric (e.g., prefix‑match score for induction heads) to locate interpretable units and their parameter sub‑space.

Computing: Use EK‑FAC (eigenvalue‑corrected Kronecker‑Factored Approximate Curvature) to efficiently estimate influence scores of massive training samples on the targeted sub‑space.

Intervening: Perform data‑deletion and data‑augmentation experiments to causally verify whether the high‑impact samples truly shape the mechanism.

The computational cost of MDA grows sub‑linearly with model size; qualitative validation on OLMo‑2 1B/7B models shows stable pattern capture at larger scales.

High‑Impact Training Samples

Analysis of the Pythia model family (14M–160M) reveals that the top‑ranked influential samples are not high‑quality natural language text but data with repetitive structures:

XML/HTML code with repeated tags

LaTeX source containing abundant symbols and formatting commands

UUIDs and log strings with repetitive patterns

Base64‑encoded strings dense in repeated characters

These high‑impact samples follow a power‑law distribution: roughly 10% of samples contribute about 50% of the cumulative influence, indicating that a small set of "high‑leverage" signals drives induction‑head formation.

Causal Validation: Deletion and Augmentation

Deletion experiment (necessity): Removing the ≤10% high‑impact samples identified by MDA significantly delays or suppresses induction‑head emergence, while randomly deleting an equal number of other samples has negligible effect.

Augmentation experiment (sufficiency): Re‑introducing only these key samples accelerates induction‑head emergence; random augmentation does not.

Linking Mechanisms to In‑Context Learning

Using the same deletion/augmentation settings, the strength of induction heads correlates tightly with ICL scores: suppressing induction heads weakens ICL, while strengthening them improves ICL, providing causal evidence for the long‑standing hypothesis that induction heads underlie ICL.

Mechanistic Data Augmentation

Building on the identified "data recipe," the authors propose a three‑step augmentation pipeline:

Run MDA on a small model (e.g., Pythia‑14M) to discover high‑impact samples.

Use a larger model (e.g., DeepSeek‑V3) to extract common structural features from those samples.

Generate synthetic data matching these structures via automatically generated code.

Cross‑scale experiments show consistent gains: the same synthetic data yields +12.3% / +10.8% / +15.8% / +9.8% induction‑head score improvements on 14M, 31M, 70M, and 160M models respectively. Notably, patterns distilled from the 14M model transfer to the 160M model better than patterns mined directly from the larger model, indicating scale‑independent "structural motifs."

On downstream tasks (Wikitext‑103 language modeling and PopQA factual QA), augmented models match baseline performance, dispelling concerns that targeting specific circuits harms overall capability.

Broader Implications

New perspective on data governance: Traditional "high‑quality" data cleaning may inadvertently discard repetitive data crucial for underlying mechanisms.

More efficient pre‑training: Targeted synthetic data could reduce the compute needed to induce desired abilities.

Mechanistic alignment and unlearning: Precise data‑level interventions enable purposeful activation or suppression of internal circuits, opening pathways for bias mitigation and safety interventions.

Overall, MDA shifts interpretability from merely describing model internals to answering where those internals originate and how we can intervene, paving the way toward a more transparent, "white‑box" approach to large‑model training.