# Symbolic Mechanistic Data Attribution: Tracing Training Influence to Learned Behavioral Policies

arXiv: https://arxiv.org/abs/2606.29171 · HTML: https://mlsanity.com/paper/2606.29171/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Circuits and mechanistic analysis, one of 13 directions in Mechanistic interpretability.
- Builds on 13 of its 23 references that are in the map.
- First posted on arXiv 28 Jun 2026.

## Placed in

- Mechanistic interpretability / [Circuits and mechanistic analysis](https://mlsanity.com/mechinterp/circuits-and-mechanistic-analysis/)

## Builds on (most cited first, 13 of 13)

- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [WildGuard: Open One-Stop Moderation Tools for Safety Risks, Jailbreaks, and Refusals of LLMs](https://mlsanity.com/paper/2406.18495/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [Do-Not-Answer: A Dataset for Evaluating Safeguards in LLMs](https://mlsanity.com/paper/2308.13387/) (2023)
- [Mechanistic Data Attribution: Tracing the Training Origins of Interpretable LLM Units](https://mlsanity.com/paper/2601.21996/) (2026)
- [Concept Influence: Leveraging Interpretability to Improve Performance and Efficiency in Training Data Attribution](https://mlsanity.com/paper/2602.14869/) (2026)
- [Beyond Accuracy: Introducing a Symbolic-Mechanistic Approach to Interpretable Evaluation](https://mlsanity.com/paper/2603.23517/) (2026)

## Built on by (most cited first, 1 of 1)

- [What Should Data Teach? Moving Bottlenecks Across Circuit, Store, and Use](https://mlsanity.com/paper/2609.32991/) (2026)

## Abstract (arXiv)

While existing data attribution methods can identify which training examples build specific mechanistic circuits, they cannot explain how training data shapes the behavioral decisions a model learns. We introduce Symbolic Mechanistic Data Attribution (SMDA), a framework that attributes training pairs to the interpretable symbolic policies governing model behavior. SMDA fits a closed-form Ridge regression over sparse autoencoder (SAE) features to model a behavior, then decomposes how each supervised fine-tuning (SFT) example shifts that policy through feature-activation (Delta X) and output-probability (Delta Y) pathways. We distill a symbolic policy for refusal in Llama-3.2-3B-Instruct and analyze 200 SFT pairs. Our analysis reveals (1)~the symbolic policy's coefficients expose systematic gaps in the base model's safety behavior, such as religious stereotyping; (2)~per-feature Delta X/Delta Y decomposition mechanistically explains why harmful and harmless pairs exert qualitatively different influences on certain features; and (3)~individual pairs routinely exhibit cross-feature interference, allowing SMDA to identify pairs whose dominant effect falls on unintended features. Retraining without such pairs improved accuracy by up to 4.5 percentage points over full fine-tuning. These results show that combining mechanistic interpretability with data attribution yields a diagnostic tool both more fine-grained than black-box influence functions and more scalable than manual circuit analysis.