Rethinking Least-Core Computation in Contextual-Distractor Games

Abstract:Game-theoretic attribution explains a model by assigning credit to its features or training examples. The least core has attracted interest as an alternative to Shapley-style averaging because it can expose players that cause substantial harm in rare, high-value contexts. However, least-core allocations are generally nonunique, and the choice of allocation can affect the resulting explanation. In this study, we investigate how payoff selection and coalition sampling affect least-core attribution. Our experiments show that selector choice matters for distinguishing useful and harmful contributions, and that sampling can degrade harmful-player identification across the tested selectors even when useful players remain well identified. These observations motivate efficient computation with all coalition constraints and a well-defined selector. We introduce entropic least core (ELC), a smooth approximation whose unique minimizer follows a continuous path along the temperature to the nucleolus, a classical refinement of the least core. Our experiments show that ELC approximates the nucleolus faster than an LP-based nucleolus solver while retaining small payoff errors, with further GPU acceleration at larger problem sizes. In the tested full-coalition contextual-distractor games, ELC matches the minimum-norm selector in identification accuracy and more accurately ranks distractors by harm.

Machine Learning (cs.LG); Computer Science and Game Theory (cs.GT)

arXiv:2610.06087 [cs.LG]

(or arXiv:2610.06087v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06087 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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