Rethinking Least-Core Computation in Contextual-Distractor Games

2026-10-05

AI Summary

This study addresses the non-uniqueness of minimum core allocations in game-theoretic attribution and the interference of sampling noise in identifying harmful contributions. We propose the Entropy Minimum Core method, which introduces a continuous temperature path to approximate the nucleolus, achieving smooth approximation and solution uniqueness via entropy regularization. By integrating full coalition constraints with GPU parallel acceleration, the approach efficiently overcomes selector dependency. Experimental results demonstrate that our method significantly outperforms traditional linear programming solvers in computational speed while maintaining minimal error. Furthermore, in rare high-value scenarios and contextually confounded games, it more accurately identifies and ranks harmful features and samples, thereby effectively enhancing model interpretability.

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.

Problem

• least-core attribution
• game-theoretic explanation
• payoff selection
• coalition sampling
• contextual-distractor games

Innovation

• Entropic Least Core
• Nucleolus
• Game-theoretic attribution
• Contextual-distractor games
• Smooth approximation