Measuring Task-Agnostic Training Data Influence Across Language Model Pretraining

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 ($13\times$) faster than previous art. We further validate its practical utility through downstream applications including data selection, data contamination, and qualitative 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.

One way to understand LLM behavior is to trace its output back to the training data. Two types of measures are commonly used for output tracing: data-similarity and data-influence. The former is cheaper while the latter is believed to be more accurate. Even though many works have compared them for ground-truth tasks, no such comparisons exist for output tracing. Here, we fill this gap and precisely quantify the commonalities and differences between the two measures. We do this by first ranking the training documents according to each measure and then computing the overlap between the two rankings. Our main finding is that the two rankings agree significantly, but there is an asymmetry between them: The top documents of data-similarity are assigned more consistent ranks by data-influence than the other way around. This result is valid across a range of experiments involving OLMo2-1B, Qwen3-1.7B, LlaMa3.2-1B, Gemma3-1B, and GPT2. We exploit the asymmetry to obtain a favorable cost-accuracy trade-off by using the costly data-influence to refine the results of data-similarity.