Beyond $L_2$: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures
2026-08-17 • Machine Learning
Machine Learning
AI summaryⓘ
The authors work on making certain types of neural networks easier to understand by using explanations called Abductive Latent Explanations (ALEs). These explanations were originally only possible when the network’s inner workings used simple, flat (Euclidean) spaces. The authors expanded ALEs to also work with more complex, curved or unusual spaces that modern networks sometimes use. They tested their new approach on image classifiers and showed it allows comparing different network designs fairly. This helps make interpreting advanced neural networks more reliable and consistent.
Prototype-based neural networksAbductive Latent Explanations (ALE)Euclidean latent spaceNon-Euclidean geometryLatent space distancesImage classifiersInterpretabilityFormal explanationsSubset-minimal explanations
Authors
Jules Soria, Alban Grastien, Romain Xu-Darme, Julien Girard-Satabin, Zakaria Chihani, Daniela Cancila
Abstract
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.