In-Run Data Shapley for Adam Optimizer

Reliable data attribution is essential for understanding, debugging, and curating modern machine learning training data, with the Shapley value serving as a principled framework for data valuation. Recent In-Run Data Shapley methods avoid the prohibitive cost of retraining by decomposing data value into step-wise contributions along a single realized training trajectory. However, existing scalable in-run estimators are derived from the linear update structure of stochastic gradient descent (SGD), while modern deep learning pipelines are widely trained with adaptive optimizers such as Adam and AdamW. In this work, we show that data attribution is optimizer-dependent: SGD-induced and Adam-induced data values exhibit extremely low agreement in both magnitude and ranking, indicating that SGD-based attribution can lead to misleading rank-based decisions under Adam training. To address this mismatch, we propose Adam-Aware In-Run Data Shapley, an optimizer-consistent attribution framework for Adam training. We define a fixed-state Adam local utility and derive a first-order approximation that explicitly accounts for momentum and coordinate-wise variance normalization. To make the estimator scalable, we introduce a Linearized Ghost Approximation, which restores an additive dot-product form without materializing per-sample gradients. Experiments show that our method achieves near-perfect fidelity to exact local Shapley values under the fixed-state Adam utility ($R>0.99$), substantially improves efficiency over direct per-sample Adam-aware computation, and improves downstream rank-based attribution tasks including semantic source identification and data pruning.