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文章背景与核心概要

当前的后验可解释人工智能（XAI）方法——如 GradCAM、SHAP、LIME 和集成梯度（Integrated Gradients）——通常依赖于截然不同的理论基础，这使得它们之间很难进行直接比较。经验证据表明，基于联盟的方法和基于梯度的方法具有互补性，但长期以来它们缺乏一个统一的框架。

GRALIS（Gradient-Riesz Averaged Locally-Integrated Shapley，梯度-里斯平均局部集成 Shapley）通过将这两种机制融为一个单一的估计器来解决这一问题。通过将 Shapley 联盟权重和局部性核与连续的条件路径（类似于集成梯度）相结合，GRALIS 提供了两个关键保证：1. 闭式完整性缺陷：对交互归因误差的精确量化；2. 有限样本界限：针对算法返回的自归一化比率提供了严密的 \(O(1/\sqrt{m}) + O(1/k^2)\) 界限。该框架以里斯表示定理（Riesz Representation Theorem）为基础，为加法、线性、连续的归因泛函建立了唯一的典型表示。

GRALIS: Fusing Coalition and Gradient Attribution with Closed-Form Conservation Error and Finite-Sample Guarantees

Author: Raimondo Fanale
arXiv: 2605.05480 [cs.LG]
Submitted: 6 May 2026 (v1); Last revised: 21 Aug 2026 (v3)

Summary

Current post-hoc Explainable AI (XAI) methods—such as GradCAM, SHAP, LIME, and Integrated Gradients—often rely on disparate theoretical foundations, making them difficult to compare. Empirical evidence suggests that coalition-based methods and gradient-based methods are complementary, yet they have historically lacked a unified framework.

GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley) addresses this by fusing these two mechanisms into a single estimator. By combining Shapley coalition weights and locality kernels with a continuous, conditioned path (similar to Integrated Gradients), GRALIS provides two critical guarantees: 1. Closed-form completeness deficit: An exact quantification of interaction attribution errors. 2. Finite-sample bounds: A rigorous \(O(1/\sqrt{m}) + O(1/k^2)\) bound for the self-normalized ratio returned by the algorithm.

The framework is underpinned by the Riesz Representation Theorem, establishing a unique canonical representation for additive, linear, continuous attribution functionals.

主要贡献

  • 统一的估计器：将基于联盟和基于梯度的归因整合为一个连贯的单一机制。
  • 理论严密性：提供了七个定理，确立了与 Shapley 交互值的确切对应关系，以及与 Hoeffding/Sobol 分解的仿射区制对应关系。
  • 认证保证：提供了完整性和样本效率的数学界限，这是以往任何单一机制都无法独自提供的。
  • 多尺度扩展：包含用于多尺度分析的最小方差扩展。
  • 经验验证：通过乳腺组织学成像的初步实验展示了其实用性，并在伴随论文中提供了广泛的验证（Fanale, 2026）。

Key Contributions

  • Unified Estimator: Integrates coalition-based and gradient-based attribution into a single, cohesive mechanism.
  • Theoretical Rigor: Provides seven theorems establishing exact correspondences with Shapley Interaction Values and affine-regime correspondences with Hoeffding/Sobol decompositions.
  • Certified Guarantees: Offers mathematical bounds for completeness and sample efficiency that neither mechanism could previously provide in isolation.
  • Multi-scale Extension: Includes a minimum-variance extension for multi-scale analysis.
  • Empirical Validation: Demonstrates utility through preliminary experiments in breast histology imaging, with extended validation provided in a companion paper (Fanale, 2026).

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元数据

  • 学科分类：机器学习 (cs.LG)；人工智能 (cs.AI)；机器学习 (stat.ML)
  • MSC 类别：68T07, 46C05, 62-07, 68T20
  • ACM 类别：I.2.6; I.5.1; G.3
  • DOI：10.48550/arXiv.2605.05480

Metadata

  • Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
  • MSC Classes: 68T07, 46C05, 62-07, 68T20
  • ACM Classes: I.2.6; I.5.1; G.3
  • DOI: 10.48550/arXiv.2605.05480