# When to Trust AI: Advances and Challenges for Certification of Neural Networks

arXiv: https://arxiv.org/abs/2309.11196 · HTML: https://mlsanity.com/paper/2309.11196/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 63 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 30 of 37)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- ["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)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Evasion Attacks against Machine Learning at Test Time](https://mlsanity.com/paper/1708.06131/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [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)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [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)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [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)
- [Globally-Robust Neural Networks](https://mlsanity.com/paper/2102.08452/) (2021)
- [Introduction to Neural Network Verification](https://mlsanity.com/paper/2109.10317/) (2021)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)](https://mlsanity.com/paper/2301.05815/) (2023)
- [On Guaranteed Optimal Robust Explanations for NLP Models](https://mlsanity.com/paper/2105.03640/) (2021)
- [Feature-Guided Black-Box Safety Testing of Deep Neural Networks](https://mlsanity.com/paper/1710.07859/) (2017)
- [Probabilistic Safety for Bayesian Neural Networks](https://mlsanity.com/paper/2004.10281/) (2020)
- [A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1807.03571/) (2018)
- [Scalable Quantitative Verification For Deep Neural Networks](https://mlsanity.com/paper/2002.06864/) (2020)
- [Improving Neural Network Verification through Spurious Region Guided Refinement](https://mlsanity.com/paper/2010.07722/) (2020)
- [Provably Bounding Neural Network Preimages](https://mlsanity.com/paper/2302.01404/) (2023)
- [On the Hardness of Robust Classification](https://mlsanity.com/paper/1909.05822/) (2019)
- [Individual Fairness Guarantees for Neural Networks](https://mlsanity.com/paper/2205.05763/) (2022)

## Built on by (most cited first, 6 of 6)

- [Intersymbolic AI: Interlinking Symbolic AI and Subsymbolic AI](https://mlsanity.com/paper/2406.11563/) (2024)
- [Query languages for neural networks](https://mlsanity.com/paper/2408.10362/) (2024)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Learning Polynomial Representations of Physical Objects with Application to Certifying Correct Packing Configurations](https://mlsanity.com/paper/2312.06791/) (2023)
- [VeRecycle: Reclaiming Guarantees from Probabilistic Certificates for Stochastic Dynamical Systems after Change](https://mlsanity.com/paper/2505.14001/) (2025)
- [A Model-Driven Approach for Developing Families of Reinforcement Learning Environments](https://mlsanity.com/paper/2606.20324/) (2026)

## Abstract (arXiv)

Artificial intelligence (AI) has been advancing at a fast pace and it is now poised for deployment in a wide range of applications, such as autonomous systems, medical diagnosis and natural language processing. Early adoption of AI technology for real-world applications has not been without problems, particularly for neural networks, which may be unstable and susceptible to adversarial examples. In the longer term, appropriate safety assurance techniques need to be developed to reduce potential harm due to avoidable system failures and ensure trustworthiness. Focusing on certification and explainability, this paper provides an overview of techniques that have been developed to ensure safety of AI decisions and discusses future challenges.