# VeriX: Towards Verified Explainability of Deep Neural Networks

arXiv: https://arxiv.org/abs/2212.01051 · HTML: https://mlsanity.com/paper/2212.01051/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 74 references that are in the map.
- First posted on arXiv 2 Dec 2022.

## Builds on (most cited first, 30 of 39)

- [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)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [A Survey of Deep Learning Techniques for Autonomous Driving](https://mlsanity.com/paper/1910.07738/) (2019)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Evaluating Deep Neural Networks Trained on Clinical Images in Dermatology with the Fitzpatrick 17k Dataset](https://mlsanity.com/paper/2104.09957/) (2021)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [A Symbolic Approach to Explaining Bayesian Network Classifiers](https://mlsanity.com/paper/1805.03364/) (2018)
- [On The Reasons Behind Decisions](https://mlsanity.com/paper/2002.09284/) (2020)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [Explaining Naive Bayes and Other Linear Classifiers with Polynomial Time and Delay](https://mlsanity.com/paper/2008.05803/) (2020)
- [On Explaining Random Forests with SAT](https://mlsanity.com/paper/2105.10278/) (2021)
- [On Guaranteed Optimal Robust Explanations for NLP Models](https://mlsanity.com/paper/2105.03640/) (2021)
- [On Tackling Explanation Redundancy in Decision Trees](https://mlsanity.com/paper/2205.09971/) (2022)
- [Optimization and Abstraction: A Synergistic Approach for Analyzing Neural Network Robustness](https://mlsanity.com/paper/1904.09959/) (2019)
- [Parallelization Techniques for Verifying Neural Networks](https://mlsanity.com/paper/2004.08440/) (2020)
- [A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1807.03571/) (2018)
- [ASTERYX : A model-Agnostic SaT-basEd appRoach for sYmbolic and score-based eXplanations](https://mlsanity.com/paper/2206.11900/) (2022)

## Built on by (most cited first, 30 of 30)

- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [Formally Explaining Neural Networks within Reactive Systems](https://mlsanity.com/paper/2308.00143/) (2023)
- [From Robustness to Explainability and Back Again](https://mlsanity.com/paper/2306.03048/) (2023)
- [Explain Yourself, Briefly! Self-Explaining Neural Networks with Concise Sufficient Reasons](https://mlsanity.com/paper/2502.03391/) (2025)
- [Hard to Explain: On the Computational Hardness of In-Distribution Model Interpretation](https://mlsanity.com/paper/2408.03915/) (2024)
- [Formal Mechanistic Interpretability: Automated Circuit Discovery with Provable Guarantees](https://mlsanity.com/paper/2602.16823/) (2026)
- [Formal Explanations for Neuro-Symbolic AI](https://mlsanity.com/paper/2410.14219/) (2024)
- [Self-Explaining Neural Networks for Business Process Monitoring](https://mlsanity.com/paper/2503.18067/) (2025)
- [Space Explanations of Neural Network Classification](https://mlsanity.com/paper/2511.22498/) (2025)
- [Faster Verified Explanations for Neural Networks](https://mlsanity.com/paper/2512.00164/) (2025)
- [Additive Models Explained: A Computational Complexity Approach](https://mlsanity.com/paper/2510.21292/) (2025)
- [FAME: Formal Abstract Minimal Explanation for Neural Networks](https://mlsanity.com/paper/2603.10661/) (2026)
- [Unifying Formal Explanations: A Complexity-Theoretic Perspective](https://mlsanity.com/paper/2602.18160/) (2026)
- [Incremental Neural Network Verification via Learned Conflicts](https://mlsanity.com/paper/2603.12232/) (2026)
- [Efficient Contrastive Explanations on Demand](https://mlsanity.com/paper/2412.18262/) (2024)
- [Uncovering Bugs in Formal Explainers: A Case Study with PyXAI](https://mlsanity.com/paper/2511.03169/) (2025)
- [Neurosymbolic Inference On Foundation Models For Remote Sensing Text-to-image Retrieval With Complex Queries](https://mlsanity.com/paper/2512.14102/) (2025)
- [Provably Explaining Neural Additive Models](https://mlsanity.com/paper/2602.17530/) (2026)
- [Unveiling Transformer Perception by Exploring Input Manifolds](https://mlsanity.com/paper/2410.06019/) (2024)
- [Fixed Point Explainability](https://mlsanity.com/paper/2505.12421/) (2025)
- [Comparing Neural Network Encodings for Logic-based Explainability](https://mlsanity.com/paper/2505.20269/) (2025)
- [The CAISAR Platform: Extending the Reach of Machine Learning Specification and Verification](https://mlsanity.com/paper/2506.12084/) (2025)
- [Rigorous Feature Importance Scores based on Shapley Value and Banzhaf Index](https://mlsanity.com/paper/2508.11959/) (2025)
- [Efficient & Correct Predictive Equivalence for Decision Trees](https://mlsanity.com/paper/2509.17774/) (2025)
- [Towards Rigorous Explainability by Feature Attribution](https://mlsanity.com/paper/2604.15898/) (2026)
- [Are Safety Guarantees in Neural Networks Safe? How to Compute Trustworthy Robustness Certifications](https://mlsanity.com/paper/2606.23858/) (2026)
- [Mining Verdict Boundaries for Neural Network Verification](https://mlsanity.com/paper/2607.28954/) (2026)
- [Beyond L2: Generalizing Abductive Latent Explanations to Diverse Prototype-Based Architectures](https://mlsanity.com/paper/2608.16773/) (2026)
- [Neuron Activation-based Computation of Logical Explanations for Deep Neural Networks](https://mlsanity.com/paper/2609.14099/) (2026)
- [The Misery of Mechanistic Interpretability: A Formal Perspective](https://mlsanity.com/paper/2609.15533/) (2026)

## Abstract (arXiv)

We present VeriX (Verified eXplainability), a system for producing optimal robust explanations and generating counterfactuals along decision boundaries of machine learning models. We build such explanations and counterfactuals iteratively using constraint solving techniques and a heuristic based on feature-level sensitivity ranking. We evaluate our method on image recognition benchmarks and a real-world scenario of autonomous aircraft taxiing.