mlsanityData to 14 Oct 2026

Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks

arXiv 2210.13915 ↗First posted 25 Oct 2022cs.LG cs.LOcited by 42

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Abstract (arXiv)

With the rapid growth of machine learning, deep neural networks (DNNs) are now being used in numerous domains. Unfortunately, DNNs are "black-boxes", and cannot be interpreted by humans, which is a substantial concern in safety-critical systems. To mitigate this issue, researchers have begun working on explainable AI (XAI) methods, which can identify a subset of input features that are the cause of a DNN's decision for a given input. Most existing techniques are heuristic, and cannot guarantee the correctness of the explanation provided. In contrast, recent and exciting attempts have shown that formal methods can be used to generate provably correct explanations. Although these methods are sound, the computational complexity of the underlying verification problem limits their scalability; and the explanations they produce might sometimes be overly complex. Here, we propose a novel approach to tackle these limitations. We (1) suggest an efficient, verification-based method for finding minimal explanations, which constitute a provable approximation of the global, minimum explanation; (2) show how DNN verification can assist in calculating lower and upper bounds on the optimal explanation; (3) propose heuristics that significantly improve the scalability of the verification process; and (4) suggest the use of bundles, which allows us to arrive at more succinct and interpretable explanations. Our evaluation shows that our approach significantly outperforms state-of-the-art techniques, and produces explanations that are more useful to humans. We thus regard this work as a step toward leveraging verification technology in producing DNNs that are more reliable and comprehensible.

Key facts. Cited by 42 papers in the map (data through 14 Oct 2026). Builds on 42 of its 72 references that are in the map. First posted on arXiv 25 Oct 2022.

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42 of 72 references.

References · 42

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2016Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localizationcited by 6,733
  3. 2017A Unified Approach to Interpreting Model Predictionscited by 6,555
  4. 2016"Why Should I Trust You?": Explaining the Predictions of Any Classifiercited by 5,070
  5. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,349
  6. 2017SmoothGrad: removing noise by adding noisecited by 1,109
  7. 2016End to End Learning for Self-Driving Carscited by 1,009
  8. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  9. 2017One pixel attack for fooling deep neural networkscited by 582
  10. 2017Adversarial Attacks on Neural Network Policiescited by 320
  11. 2020BAE: BERT-based Adversarial Examples for Text Classificationcited by 316
  12. 2019Algorithms for Verifying Deep Neural Networkscited by 221
30 more
  1. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  2. 2018Abduction-Based Explanations for Machine Learning Modelscited by 160
  3. 2018A Symbolic Approach to Explaining Bayesian Network Classifierscited by 131
  4. 2019"How do I fool you?": Manipulating User Trust via Misleading Black Box Explanationscited by 111
  5. 2019An Abstraction-Based Framework for Neural Network Verificationcited by 68
  6. 2018Deep Neural Network Compression for Aircraft Collision Avoidance Systemscited by 58
  7. 2019Quantitative Verification of Neural Networks And its Security Applicationscited by 56
  8. 2021On Guaranteed Optimal Robust Explanations for NLP Modelscited by 54
  9. 2016Superpixels: An Evaluation of the State-of-the-Artcited by 52
  10. 2020On Explaining Decision Treescited by 49
  11. 2020An SMT-Based Approach for Verifying Binarized Neural Networkscited by 47
  12. 2021SAT-Based Rigorous Explanations for Decision Listscited by 40
  13. 2019Can I Trust the Explainer? Verifying Post-hoc Explanatory Methodscited by 38
  14. 2022Don't Lie to Me! Robust and Efficient Explainability with Verified Perturbation Analysiscited by 38
  15. 2020Parallelization Techniques for Verifying Neural Networkscited by 36
  16. 2020On Tractable Representations of Binary Neural Networkscited by 34
  17. 2021Towards Scalable Verification of Deep Reinforcement Learningcited by 33
  18. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  19. 2019On Validating, Repairing and Refining Heuristic ML Explanationscited by 32
  20. 2020Global Optimization of Objective Functions Represented by ReLU Networkscited by 24
  21. 2022An Abstraction-Refinement Approach to Verifying Convolutional Neural Networkscited by 24
  22. 2022Efficient Neural Network Analysis with Sum-of-Infeasibilitiescited by 24
  23. 2022Neural Network Verification with Proof Productioncited by 22
  24. 2021Pruning and Slicing Neural Networks using Formal Verificationcited by 20
  25. 2022Verification-Aided Deep Ensemble Selectioncited by 18
  26. 2022Neural Network Verification using Residual Reasoningcited by 18
  27. 2021Minimal Multi-Layer Modifications of Deep Neural Networkscited by 14
  28. 2021Efficient Explanations With Relevant Setscited by 12
  29. 2016Propositional Abduction with Implicit Hitting Setscited by 6
  30. 2016The minimal hitting set generation problem: algorithms and computationcited by 5

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Citing papers per year: 2023: 8; 2024: 6; 2025: 14; 2026: 14.

42 papers.

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  1. 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
  2. 2024Local vs. Global Interpretability: A Computational Complexity Perspectivecited by 23
  3. 2024Distance-Restricted Explanations: Theoretical Underpinnings & Efficient Implementationcited by 21
  4. 2023Delivering Inflated Explanationscited by 16
  5. 2023From Robustness to Explainability and Back Againcited by 14
  6. 2023Stability Guarantees for Feature Attributions with Multiplicative Smoothingcited by 14
  7. 2025Explaining, Fast and Slow: Abstraction and Refinement of Provable Explanationscited by 13
  8. 2025Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasonscited by 12
  9. 2026Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guaranteescited by 11
  10. 2025Probabilistic Stability Guarantees for Feature Attributionscited by 9
  11. 2024Auditing Local Explanations is Hardcited by 8
  12. 2025SHAP Meets Tensor Networks: Provably Tractable Explanations with Parallelismcited by 8
30 more
  1. 2024Analyzing Adversarial Inputs in Deep Reinforcement Learningcited by 7
  2. 2025Most General Explanations of Tree Ensembles (Extended Version)cited by 7
  3. 2026Interpretability Can Be Actionablecited by 7
  4. 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
  5. 2023Sum-of-Parts: Self-Attributing Neural Networks with End-to-End Learning of Feature Groupscited by 6
  6. 2023Bridging Dimensions: Confident Reachability for High-Dimensional Controllerscited by 5
  7. 2025Self-Explaining Neural Networks for Business Process Monitoringcited by 5
  8. 2025Formal Abductive Latent Explanations for Prototype-Based Networkscited by 5
  9. 2024Towards Formal Verification of Deep Neural Networks for Object Detectioncited by 4
  10. 2025PICID: Proof-Driven Clause Learning in Neural Network Verificationcited by 3
  11. 2025Additive Models Explained: A Computational Complexity Approachcited by 3
  12. 2026FAME: Formal Abstract Minimal Explanation for Neural Networkscited by 3
  13. 2025Interactive Explanations for Reinforcement-Learning Agentscited by 2
  14. 2026Unifying Formal Explanations: A Complexity-Theoretic Perspectivecited by 2
  15. 2026Incremental Neural Network Verification via Learned Conflictscited by 2
  16. 2023Finding Minimum-Cost Explanations for Predictions made by Tree Ensemblescited by 1
  17. 2025Uncovering Bugs in Formal Explainers: A Case Study with PyXAIcited by 1
  18. 2026Provably Explaining Neural Additive Modelscited by 1
  19. 2026Bound Propagation meets Constraint Simplification: Improving Logic-based XAI for Neural Networkscited by 1
  20. 2026Missingness Bias Calibration in Feature Attribution Explanationscited by 1
  21. 2026Concept-Based Abductive and Contrastive Explanations for Behaviors of Vision Modelscited by 1
  22. 2023ASQ-IT: Interactive Explanations for Reinforcement-Learning Agentscited by 0
  23. 2025The CAISAR Platform: Extending the Reach of Machine Learning Specification and Verificationcited by 0
  24. 2025Feature Attribution in 5G Intrusion Detection: A Statistical vs. Logic-Based Comparisoncited by 0
  25. 2025Efficient & Correct Predictive Equivalence for Decision Treescited by 0
  26. 2026Slice and Explain: Logic-Based Explanations for Neural Networks through Domain Slicingcited by 0
  27. 2026Concisely Explaining the Doubt: Minimum-Size Abductive Explanations for Linear Models with a Reject Optioncited by 0
  28. 2026Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networkscited by 0
  29. 2026Beyond L2: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architecturescited by 0
  30. 2026The Misery of Mechanistic Interpretability: A Formal Perspectivecited by 0