# Beyond L2: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures

arXiv: https://arxiv.org/abs/2608.16773 · HTML: https://mlsanity.com/paper/2608.16773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 30 of 30)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Explainable Artificial Intelligence (XAI): Concepts, Taxonomies, Opportunities and Challenges toward Responsible AI](https://mlsanity.com/paper/1910.10045/) (2019)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [From Anecdotal Evidence to Quantitative Evaluation Methods: A Systematic Review on Evaluating Explainable AI](https://mlsanity.com/paper/2201.08164/) (2022)
- [Deep Learning for Case-Based Reasoning through Prototypes: A Neural Network that Explains Its Predictions](https://mlsanity.com/paper/1710.04806/) (2017)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021)
- [Deformable ProtoPNet: An Interpretable Image Classifier Using Deformable Prototypes](https://mlsanity.com/paper/2111.15000/) (2021)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Interpretable Image Classification with Differentiable Prototypes Assignment](https://mlsanity.com/paper/2112.02902/) (2021)
- [ProtoPFormer: Concentrating on Prototypical Parts in Vision Transformers for Interpretable Image Recognition](https://mlsanity.com/paper/2208.10431/) (2022)
- [Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks](https://mlsanity.com/paper/2210.13915/) (2022)
- [VeriX: Towards Verified Explainability of Deep Neural Networks](https://mlsanity.com/paper/2212.01051/) (2022)
- [A Triangle Inequality for Cosine Similarity](https://mlsanity.com/paper/2107.04071/) (2021)
- [Mixture of Gaussian-distributed Prototypes with Generative Modelling for Interpretable and Trustworthy Image Recognition](https://mlsanity.com/paper/2312.00092/) (2023)
- [This Looks Better than That: Better Interpretable Models with ProtoPNeXt](https://mlsanity.com/paper/2406.14675/) (2024)
- [Interpretable Image Classification via Non-parametric Part Prototype Learning](https://mlsanity.com/paper/2503.10247/) (2025)
- [ProtoArgNet: Interpretable Image Classification with Super-Prototypes and Argumentation [Technical Report]](https://mlsanity.com/paper/2311.15438/) (2023)
- [ProtoGMM: Multi-prototype Gaussian-Mixture-based Domain Adaptation Model for Semantic Segmentation](https://mlsanity.com/paper/2406.19225/) (2024)
- [An Overview of Prototype Formulations for Interpretable Deep Learning](https://mlsanity.com/paper/2410.08925/) (2024)
- [Formal Abductive Latent Explanations for Prototype-Based Networks](https://mlsanity.com/paper/2511.16588/) (2025)
- [Efficiently Computing Compact Formal Explanations](https://mlsanity.com/paper/2409.03060/) (2024)
- [Faster Verified Explanations for Neural Networks](https://mlsanity.com/paper/2512.00164/) (2025)
- [This Probably Looks Exactly Like That: An Invertible Prototypical Network](https://mlsanity.com/paper/2407.12200/) (2024)
- [CaBRNet, an open-source library for developing and evaluating Case-Based Reasoning Models](https://mlsanity.com/paper/2409.16693/) (2024)
- [Interpretable Affordance Detection on 3D Point Clouds with Probabilistic Prototypes](https://mlsanity.com/paper/2504.18355/) (2025)
- [FAME: Formal Abstract Minimal Explanation for Neural Networks](https://mlsanity.com/paper/2603.10661/) (2026)

## Abstract (arXiv)

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.