Ripple Shapley: Data Influence Attribution in One Federated Training Run

Contribution evaluation is essential for incentivizing high-quality data sharing in federated learning (FL), yet existing Shapley-value-based methods are prohibitively expensive and overlook temporal influence propagation. In this paper, we propose Ripple Shapley, a novel attribution framework that enables accurate, real-time data valuation within a single federated training run. Our method decomposes each sample’s impact into an instantaneous drop term and a recursive ripple term, the latter capturing downstream influence via a Jacobian chain over global updates. To scale computation, we introduce a low-rank approximation of the Jacobian product and construct a shared subspace for efficient ripple accumulation. Extensive experiments on CIFAR-10 and MNIST show that Ripple Shapley achieves up to 62× speedup over existing Shapley-based FL methods while maintaining high attribution fidelity, significantly improving efficiency, robustness, and fairness in federated environments. We further demonstrate its effectiveness in dynamic federated learning scenarios and its potential for real-time data pricing.