# MiSS: A Logic-Driven Explanation of Minimal Sufficient Coalitions for Point Cloud Classifiers

arXiv: https://arxiv.org/abs/2607.24074 · HTML: https://mlsanity.com/paper/2607.24074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [PointCloud Saliency Maps](https://mlsanity.com/paper/1812.01687/) (2018)
- [Logic-Based Explainability in Machine Learning](https://mlsanity.com/paper/2211.00541/) (2022)
- [Point Cloud Classification Using Content-based Transformer via Clustering in Feature Space](https://mlsanity.com/paper/2303.04599/) (2023)
- [Metricizing the Euclidean Space towards Desired Distance Relations in Point Clouds](https://mlsanity.com/paper/2211.03674/) (2022)

## Abstract (arXiv)

We present MiSS, a black-box, query-based framework for explaining 3D point cloud classifiers through perturbation-relative sufficiency reasoning. MiSS treats a superpoint partition as an interpretable abstraction layer and asks whether the original prediction can be certified from a minimal coalition of geometric regions under a specified perturbation distribution. Unlike abductive explainers that require Boolean feature spaces or white-box logical encodings of the predictor, MiSS separates candidate proposal from verification: a weighted MaxSAT procedure proposes coalitions using a heuristic adaptive cardinality floor, certified exact-size fallback, a safely tightened upper bound, blocking clauses, and a surrogate acquisition heuristic learned from previous oracle evaluations, while a blackbox statistical oracle decides sufficiency from prediction queries. The system returns a statistically verified sufficient coalition as a binary attribution, with minimum cardinality guaranteed when certified search completes. Experiments on ModelNet40 and ShapeNet with PointNet and PointMLP classifiers show higher precision and coverage than rule-based baselines in most settings, with lower explanation time than exhaustive search.