ALE以前只支持L2空间，这篇把它扩展到球面、高斯这些新结构，还在图像分类上实测了。
ALE框架原先仅支持L2范数下的欧几里得潜在空间。本研究将ALE推广至球面度量、高斯密度和维度投影三类非欧几里得原型架构。作者针对三类变体推导了映射或新型界算法，并在图像分类器上计算子集最小形式解释。该统一框架在三种架构间首次实现严格的可解释性比较。
Beyond $L_2$: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures
Prototype-based neural networks are hailed as interpretable-by-design architectures. Recently, Abductive Latent Explanations (ALE) were introduced to provide formal, mathematically guaranteed explanations that leverage the intrinsic structure of these networks to ensure both predictive safety and human readability. ALEs rely on computing tight bounds on latent space distances to produce formal explanations. However, existing ALE formulations are rigidly confined to Euclidean latent spaces. This leaves a critical gap: modern state-of-the-art architectures increasingly rely on non-Euclidean representations - such as spherical metrics, Gaussian densities, and dimensional projections - rendering current formal explanation methods incompatible. In this work, we generalize the ALE framework to support non-Euclidean prototype architectures. For each geometric variant, we systematically derive how to either map the architecture to existing bounds or construct novel, architecture-specific bounding algorithms. We validate our theoretical constructions by computing subset-minimal formal explanations on fully trained image classifiers. By unifying these diverse models under a single formal framework, we enable the first rigorous, cross-architecture comparison of their interpretability.