Abstract
Classical data valuation defines a data point's value through the finite marginal contribution U(C∪{i})−U(C), but estimating this quantity over coalitions requires repeated training and does not describe the contribution made along a stochastic training path. We ask whether marginal contributions of data points can be estimated from one coupled trajectory while retaining a verifiable relation to coalition-based values. To this end, we introduce Neural Dynamic Data Valuation (NDDV), which models each data point as a controlled stochastic state and computes a first-order marginal-contribution score via the adjoint equation of the Stochastic Maximum Principle (SMP). This raw sensitivity is then calibrated by a mass-preserving redistribution that increases one data point's participation while redistributing the same total weight over the remaining data points. We prove that the resulting backward adjoint recursion is the exact reverse-mode adjoint of the frozen-aggregate Euler system, bound its discrepancy from the mean-field sensitivity, and express each finite coalition marginal as an integral of local sample-weight sensitivities. These results yield pair-specific error bounds and sufficient conditions for ordering agreement with Shapley, Banzhaf, and leave-one-out values. Experiments on existing benchmarks evaluate marginal-contribution fidelity, score-release cost, corrupted-sample detection, ablations, and failure regimes. NDDV is a one-run, trajectory-conditioned estimator, not an unconditional replacement for cooperative-game values.
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May 20, 2026cs.LG
Shapley-based data valuation provides a principled way to quantify the contribution of training data, but its high computational cost makes it impractical in dynamic settings where tasks and training players evolve. Existing methods treat Shapley computation as a one-shot process and collapse contributions into aggregated scores, preventing reuse and requiring recomputation under any change. We introduce a new perspective that represents Shapley values as a player-by-task matrix and formulates dynamic valuation as a structured matrix maintenance problem. We exploit the fact that each task depends on a small subset of training players and that similar tasks yield similar valuations, leading to utility locality and coalition locality. Based on these insights, we propose D-Shap, a dynamic valuation framework that enables efficient updates by modifying only a small portion of the matrix: new task valuations are inferred via structure-aware interpolation, while updates induced by new players are confined to affected local matrix blocks. To eliminate the need for pre-specified evaluation tasks, we introduce self-valuation, which constructs the initial matrix directly from training data, supported by scalable subset reuse and coverage-aware anchor selection. Experiments across diverse models show that D-Shap performs task updates in milliseconds and reduces the cost of player updates by up to three orders of magnitude, while achieving valuation quality competitive with full recomputation.
Xuan Yang, Hsi-Wen Chen, Ming-Syan Chen +1
Jul 4, 2026cs.LG
Shapley values are widely used to attribute value to training data based on their marginal contribution to performance on a validation set. Existing practice often assumes these values are stable once the training data and model are fixed. In this work, we uncover a systematic vulnerability: even modest changes to the validation set, such as introducing noises, cause directional shifts in Shapley distributions. As noises are added, Shapley values of training samples compress toward zero. We trace this to a noise-induced neighborhood reshuffling effect: perturbations alter the local rank order between validation and training samples, flattening the valuation landscape. Using the KNN-Shapley framework, we show through synthetic and real data that these shifts are consistent and reproducible. Our findings challenge the assumption of Shapley stability and reveal a new axis of fragility in data valuation. We propose normalization and boundary-aware validation strategies to mitigate these distortions and enable more robust, interpretable valuation in machine learning marketplaces.
Yinan Shen, Ziao Yang, Hongfu Liu
May 7, 2026cs.LG
We study the efficient computation of Shapley values for \emph{product games} -- cooperative games in which the coalition value factorizes as a product of per-player terms. Such games arise in machine learning explainability whenever the value function inherits a multiplicative structure from the underlying model, as in kernel methods with product kernels and tree-based models. Our key result is that the Shapley value of each player in a product game admits an exact one-dimensional integral representation: the weighted sum over exponentially many feature coalitions collapses to the integral of a degree-
(d−1) polynomial over
[0,1], where
d is the total number of features. This yields a Gauss--Legendre quadrature scheme that is \emph{provably exact} whenever the number of nodes satisfies
mq≥⌈d/2⌉, and otherwise provides a \emph{near-exact} approximation with error provably decaying geometrically in
mq. In practice, a few hundred nodes can achieve highly precise estimates even with thousands of features. Building on this formulation, we derive a numerically stable implementation via log-space evaluation, together with an efficient parallel implementation based on associative scan primitives that achieves
O(dmq) total work and
O(logd) parallel time. Experiments show that \textsc{QuadraSHAP} is the fastest numerically stable method across all tested configurations.
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