Organizations: University of California, Santa Cruz
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.
Large Language Models (LLMs) are increasingly deployed across diverse applications, raising critical questions for governance, accountability, and data provenance. Understanding which training data most influenced a model's output remains a fundamental open problem. We address this challenge through training data attribution (TDA) for auto-regressive LLMs by expanding upon the inverse formulation: How would training data be affected if the model had seen the generated output during training? Our method perturbs the base model using bidirectional gradient optimization (gradient ascent and descent) on a generated text sample and measures the resulting change in loss across training samples. Our framework supports attribution at arbitrary data granularity, enabling both factual and stylistic attribution. We evaluate our method against baselines on pretrained models with known datasets, and show that it outperforms previous work on influence metrics, thereby enhancing model interpretability, an essential requirement for accountable AI systems.
Frédéric Berdoz, Luca A. Lanzendörfer, Kaan Bayraktar +1
With the growth of LLMs' (Large Language Models) capabilities, there has been an increasing push to curate high quality datasets by filtering samples in the training data. In general, Data Attribution (DA) methods aim to estimate how individual samples in a training dataset can precondition a model to generate certain outputs. As an example, one might be interested in which samples in the data could be the source of toxic behavior after training the LLM. Many methods quantify this conditioning through the paradigm of influence functions. While methods of this family are effective in its function, they lack the necessary processing speed and storage compactness to be practically implemented on large datasets. We propose a method, Influcoder, as a quick and cost-effective approach to influence-based Data Attribution at scale.
Training Data Attribution (TDA) seeks to trace a model's predictions back to its training data. The gold standard for TDA relies on causal interventions, observing how a model changes when data is added or removed, but repeated retraining is computationally challenging for Large Language Models (LLMs). Consequently, most approaches approximate this effect in the parameter space using gradients. However, tracking gradients across billions of parameters is not only prohibitively expensive but relies on local approximations. In this work, we propose a shift: rather than estimating parameter changes, we model the functional effect of training data in the activation space. We introduce STRIDE (Steering-based Training Data Influence Decomposition), a framework that formulates TDA as a sparse recovery problem in the spirit of compressive sensing. STRIDE learns lightweight "steering operators" that mimic the behavioral shift caused by training on data subsets. By measuring how these operators perturb test predictions, we recover individual training example influences via sparse linear decomposition. STRIDE achieves state-of-the-art for LLM pre-training attribution while being an order of magnitude (13×) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative analysis.