# Formal Abductive Latent Explanations for Prototype-Based Networks

arXiv: https://arxiv.org/abs/2511.16588 · HTML: https://mlsanity.com/paper/2511.16588/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 57 references that are in the map.
- First posted on arXiv 20 Nov 2025.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [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)
- [Concept Whitening for Interpretable Image Recognition](https://mlsanity.com/paper/2002.01650/) (2020)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Neural Prototype Trees for Interpretable Fine-grained Image Recognition](https://mlsanity.com/paper/2012.02046/) (2020)
- [CRAFT: Concept Recursive Activation FacTorization for Explainability](https://mlsanity.com/paper/2211.10154/) (2022)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [What I Cannot Predict, I Do Not Understand: A Human-Centered Evaluation Framework for Explainability Methods](https://mlsanity.com/paper/2112.04417/) (2021)
- [Interpretable Image Classification with Differentiable Prototypes Assignment](https://mlsanity.com/paper/2112.02902/) (2021)
- [ProtoPShare: Prototype Sharing for Interpretable Image Classification and Similarity Discovery](https://mlsanity.com/paper/2011.14340/) (2020)
- [ConceptAttention: Diffusion Transformers Learn Highly Interpretable Features](https://mlsanity.com/paper/2502.04320/) (2025)
- [Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks](https://mlsanity.com/paper/2210.13915/) (2022)
- [On Tractable Representations of Binary Neural Networks](https://mlsanity.com/paper/2004.02082/) (2020)
- [On Validating, Repairing and Refining Heuristic ML Explanations](https://mlsanity.com/paper/1907.02509/) (2019)
- [Interpretability Benchmark for Evaluating Spatial Misalignment of Prototypical Parts Explanations](https://mlsanity.com/paper/2308.08162/) (2023)
- [The Semi-Supervised iNaturalist Challenge at the FGVC8 Workshop](https://mlsanity.com/paper/2106.01364/) (2021)
- [On the Interpretability of Part-Prototype Based Classifiers: A Human Centric Analysis](https://mlsanity.com/paper/2310.06966/) (2023)
- [This Looks Better than That: Better Interpretable Models with ProtoPNeXt](https://mlsanity.com/paper/2406.14675/) (2024)
- [A Formal Approach to Explainability](https://mlsanity.com/paper/2001.05207/) (2020)
- [A Fresh Look at Sanity Checks for Saliency Maps](https://mlsanity.com/paper/2405.02383/) (2024)

## Built on by (most cited first, 5 of 5)

- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks](https://mlsanity.com/paper/2605.24084/) (2026)
- [OPTIMUS-Prime: Minimal and Sufficient Concept Explanations for Deep Vision Models](https://mlsanity.com/paper/2606.07180/) (2026)
- [Beyond L2: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures](https://mlsanity.com/paper/2608.16773/) (2026)

## Abstract (arXiv)

Case-based reasoning networks are machine-learning models that make predictions based on similarity between the input and prototypical parts of training samples, called prototypes. Such models are able to explain each decision by pointing to the prototypes that contributed the most to the final outcome. As the explanation is a core part of the prediction, they are often qualified as ``interpretable by design". While promising, we show that such explanations are sometimes misleading, which hampers their usefulness in safety-critical contexts. In particular, several instances may lead to different predictions and yet have the same explanation. Drawing inspiration from the field of formal eXplainable AI (FXAI), we propose Abductive Latent Explanations (ALEs), a formalism to express sufficient conditions on the intermediate (latent) representation of the instance that imply the prediction. Our approach combines the inherent interpretability of case-based reasoning models and the guarantees provided by formal XAI. We propose a solver-free and scalable algorithm for generating ALEs based on three distinct paradigms, compare them, and present the feasibility of our approach on diverse datasets for both standard and fine-grained image classification. The associated code can be found at https://github.com/julsoria/ale