# OPTIMUS-Prime: Minimal and Sufficient Concept Explanations for Deep Vision Models

arXiv: https://arxiv.org/abs/2606.07180 · HTML: https://mlsanity.com/paper/2606.07180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [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)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [Concept Bottleneck Models](https://mlsanity.com/paper/2007.04612/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [Captum: A unified and generic model interpretability library for PyTorch](https://mlsanity.com/paper/2009.07896/) (2020)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [Convergent Learning: Do different neural networks learn the same representations?](https://mlsanity.com/paper/1511.07543/) (2015)
- [Visualizing Deep Neural Network Decisions: Prediction Difference Analysis](https://mlsanity.com/paper/1702.04595/) (2017)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [Superposition of many models into one](https://mlsanity.com/paper/1902.05522/) (2019)
- [Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay](https://mlsanity.com/paper/2008.05803/) (2020)
- [On the Interpretability of Part-Prototype Based Classifiers: A Human Centric Analysis](https://mlsanity.com/paper/2310.06966/) (2023)
- [Formal Abductive Latent Explanations for Prototype-Based Networks](https://mlsanity.com/paper/2511.16588/) (2025)

## Abstract (arXiv)

The growing demand for transparency in automated decision-making has propelled eXplainable Artificial Intelligence (XAI) to the forefront of machine learning research. In computer vision, however, existing explanation methods often prioritize end-user accessibility at the expense of formal guarantees, leaving a critical gap between practical utility and theoretical rigor. In this paper, we address this gap by introducing OPTIMUS, a novel framework for generating concept-based visual explanations for deep classification models. OPTIMUS explanations take the form of visual heatmaps that not only remain interpretable to end users, but are grounded in the well-established theory of prime implicants, providing formal guarantees that have been largely absent from existing saliency-based methods. Specifically, OPTIMUS explanations satisfy two desirable properties: sufficiency, ensuring that the highlighted concepts provably guarantee the classifier's prediction, and minimality, ensuring that no strict subset of those concepts retains this guarantee. Together, these properties yield explanations that are both logically tight and visually coherent. We validate our approach on a visual classification benchmark, demonstrating that OPTIMUS heatmaps naturally and faithfully surface the decision-relevant concepts underlying model predictions.