# Rethinking Least-Core Computation in Contextual-Distractor Games

arXiv: https://arxiv.org/abs/2610.06087 · HTML: https://mlsanity.com/paper/2610.06087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Explaining individual predictions when features are dependent: More accurate approximations to Shapley values](https://mlsanity.com/paper/1903.10464/) (2019)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [FastSHAP: Real-Time Shapley Value Estimation](https://mlsanity.com/paper/2107.07436/) (2021)
- [PredDiff: Explanations and Interactions from Conditional Expectations](https://mlsanity.com/paper/2102.13519/) (2021)
- [Identifying Important Group of Pixels using Interactions](https://mlsanity.com/paper/2401.03785/) (2024)
- [Approximating the Core via Iterative Coalition Sampling](https://mlsanity.com/paper/2402.03928/) (2024)
- [Explaining Object Detectors via Collective Contribution of Pixels](https://mlsanity.com/paper/2412.00666/) (2024)
- [Game-Theoretic Understanding of Misclassification](https://mlsanity.com/paper/2210.03349/) (2022)
- [In-Context Credit Assignment via the Core](https://mlsanity.com/paper/2605.06920/) (2026)
- [Lexicographic Optimization: Algorithms and Stability](https://mlsanity.com/paper/2405.01387/) (2024)

## Abstract (arXiv)

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.