# Gradient Atoms: Unsupervised Discovery, Attribution and Steering of Model Behaviors via Sparse Decomposition of Training Gradients

arXiv: https://arxiv.org/abs/2603.14665 · HTML: https://mlsanity.com/paper/2603.14665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 13 references that are in the map.
- First posted on arXiv 15 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Progress measures for grokking via mechanistic interpretability](https://mlsanity.com/paper/2301.05217/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Procedural Knowledge in Pretraining Drives Reasoning in Large Language Models](https://mlsanity.com/paper/2411.12580/) (2024)
- [Training Data Attribution via Approximate Unrolled Differentiation](https://mlsanity.com/paper/2405.12186/) (2024)
- [Mode-Conditioning Unlocks Superior Test-Time Scaling](https://mlsanity.com/paper/2512.01127/) (2025)
- [Patterning: The Dual of Interpretability](https://mlsanity.com/paper/2601.13548/) (2026)
- [Features that Make a Difference: Leveraging Gradients for Improved Dictionary Learning](https://mlsanity.com/paper/2411.10397/) (2024)
- [CrispEdit: Low-Curvature Projections for Scalable Non-Destructive LLM Editing](https://mlsanity.com/paper/2602.15823/) (2026)
- [Beyond Input Activations: Identifying Influential Latents by Gradient Sparse Autoencoders](https://mlsanity.com/paper/2505.08080/) (2025)
- [GradientSpace: Unsupervised Data Clustering for Improved Instruction Tuning](https://mlsanity.com/paper/2512.06678/) (2025)
- [ELROND: Exploring and decomposing intrinsic capabilities of diffusion models](https://mlsanity.com/paper/2602.10216/) (2026)

## Abstract (arXiv)

Training data attribution (TDA) methods ask which training documents are responsible for a model behavior. However, models often learn broad concepts shared across many examples. Moreover, existing TDA methods are supervised -- they require a predefined query behavior, then score every training document against it -- making them both expensive and unable to surface behaviors the user did not think to ask about. We present Gradient Atoms, an unsupervised method that decomposes per-document training gradients into sparse components ("atoms") via dictionary learning in a preconditioned eigenspace. Each atom captures a shared update direction induced by a cluster of functionally similar documents, directly recovering the collective structure that per-document methods do not address. Among 500 discovered atoms, the highest-coherence ones recover interpretable task-type behaviors -- refusal, arithmetic, yes/no classification, trivia QA -- without any behavioral labels. These atoms double as effective steering vectors: applying them as weight-space perturbations produces large, controllable shifts in model behavior (e.g., bulleted-list generation 33% to 94%; systematic refusal 50% to 0%). The method requires no query--document scoring stage, and scales independently of the number of query behaviors of interest. Code is available at https://github.com/jrosseruk/gradient_atoms.