GRASP: Geometry-aware Residual Alignment for Scalable Pretraining Data Attribution

Scalable data attribution methods typically assign isolated utility scores to individual training examples. This prevalent additive assumption fundamentally fails to capture critical subset dynamics, including data redundancy and complementary coverage. In this work, we reframe attribution as subset-level counterfactual utility prediction and introduce GRASP, an interaction-aware surrogate. Grounded in a theoretical smoothness lower bound, GRASP explicitly models subset interactions through a quadratic geometric penalty. To achieve pretraining-scale efficiency without relying on hidden oracle tuning, we couple low-dimensional feature sketches with a strictly finite lower-confidence bound selection protocol. Extensive subset-retraining evaluations demonstrate that GRASP decisively outperforms existing scalable baselines. It more than doubles the task-level rank correlation for counterfactual subset fidelity while reducing upfront artifact construction costs by nearly an order of magnitude. Downstream diagnostics further show that this scoring mechanism transfers to language model curation and cross-domain vision selection, establishing a robust foundation for optimizing massive pretraining corpora.