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

2026-06-27

AI Summary

Existing data attribution methods struggle to elucidate how training samples influence high-level behavioral decisions of models. This work proposes Symbolic Mechanistic Data Attribution (SMDA), a novel framework that integrates mechanistic interpretability with data attribution for the first time. SMDA employs sparse autoencoders to extract intermediate features, models target behaviors via ridge regression, and leverages symbolic policies combined with Delta_X/Delta_Y decomposition to achieve fine-grained, symbolic attribution of how fine-tuning samples shape behavioral strategies. Experiments on Llama-3.2-3B-Instruct successfully recover symbolic policies governing refusal behavior, uncovering systematic deficiencies in safety-critical categories such as religious stereotyping, and precisely identify harmful training samples responsible for undesirable features along with their cross-feature interference mechanisms.

Abstract

While existing data attribution methods can identify which training examples build specific mechanistic circuits, they cannot explain how training data shapes the high-level behavioral decisions a model learns to make. To bridge this gap, 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 target behavior, then analytically decomposes how each supervised fine-tuning example shifts that policy through feature-activation Delta_X and output-probability Delta_Y pathways. We distill a symbolic policy for refusal behavior in Llama-3.2-3B-Instruct and analyze 200 SFT training pairs. Our analysis reveals that (1) the symbolic policy's coefficients expose systematic gaps in the base model's safety behavior for categories like religious stereotyping; (2) per-feature Delta_X/Delta_Y decomposition can mechanistically explain why harmful and harmless pairs exert qualitatively different influences on certain features; and (3) individual training pairs routinely exhibit cross-feature interference, allowing SMDA to identify training pairs whose dominant effect falls on unintended features. These results demonstrate that combining mechanistic interpretability with data attribution yields a diagnostic tool that is both more fine-grained than black-box influence functions and more scalable than manual circuit analysis.

Problem

• data attribution
• behavioral policies
• mechanistic interpretability
• symbolic policies
• training influence

Innovation

• Symbolic Mechanistic Data Attribution
• Sparse Autoencoder
• Ridge Regression
• Feature-Activation Decomposition
• Interpretable Policy