# What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systems

arXiv: https://arxiv.org/abs/2307.11784 · HTML: https://mlsanity.com/paper/2307.11784/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 76 references that are in the map.
- First posted on arXiv 20 Jul 2023.

## Builds on (most cited first, 30 of 42)

- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Unmasking Clever Hans Predictors and Assessing What Machines Really Learn](https://mlsanity.com/paper/1902.10178/) (2019)
- [DeepXplore: Automated Whitebox Testing of Deep Learning Systems](https://mlsanity.com/paper/1705.06640/) (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)
- [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 the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [A Dual Approach to Scalable Verification of Deep Networks](https://mlsanity.com/paper/1803.06567/) (2018)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validation](https://mlsanity.com/paper/2305.11391/) (2023)
- [Verifying Properties of Binarized Deep Neural Networks](https://mlsanity.com/paper/1709.06662/) (2017)
- [A Statistical Approach to Assessing Neural Network Robustness](https://mlsanity.com/paper/1811.07209/) (2018)
- [Towards Verified Artificial Intelligence](https://mlsanity.com/paper/1606.08514/) (2016)
- [Outside the Box: Abstraction-Based Monitoring of Neural Networks](https://mlsanity.com/paper/1911.09032/) (2019)
- [Runtime Monitoring Neuron Activation Patterns](https://mlsanity.com/paper/1809.06573/) (2018)
- [A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1807.03571/) (2018)
- [Analyzing Deep Neural Networks with Symbolic Propagation: Towards Higher Precision and Faster Verification](https://mlsanity.com/paper/1902.09866/) (2019)
- [SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretability](https://mlsanity.com/paper/2208.09418/) (2022)
- [Sources of Uncertainty in Supervised Machine Learning -- A Statisticians' View](https://mlsanity.com/paper/2305.16703/) (2023)
- [Distribution-Aware Testing of Neural Networks Using Generative Models](https://mlsanity.com/paper/2102.13602/) (2021)
- [A Safety Framework for Critical Systems Utilising Deep Neural Networks](https://mlsanity.com/paper/2003.05311/) (2020)
- [Into the Unknown: Active Monitoring of Neural Networks](https://mlsanity.com/paper/2009.06429/) (2020)

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

- [Stop Reducing Responsibility in LLM-Powered Multi-Agent Systems to Local Alignment](https://mlsanity.com/paper/2510.14008/) (2025)
- [Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guide](https://mlsanity.com/paper/2502.14833/) (2025)
- [Ensuring Reliability via Hyperparameter Selection: Review and Advances](https://mlsanity.com/paper/2502.04206/) (2025)
- [Runtime Monitoring and Fault Detection for Neural Network-Controlled Systems](https://mlsanity.com/paper/2403.16132/) (2024)
- [Enhancing Performance of Explainable AI Models with Constrained Concept Refinement](https://mlsanity.com/paper/2502.06775/) (2025)
- [Towards provable probabilistic safety for scalable embodied AI systems](https://mlsanity.com/paper/2506.05171/) (2025)

## Abstract (arXiv)

Machine learning has made remarkable advancements, but confidently utilising learning-enabled components in safety-critical domains still poses challenges. Among the challenges, it is known that a rigorous, yet practical, way of achieving safety guarantees is one of the most prominent. In this paper, we first discuss the engineering and research challenges associated with the design and verification of such systems. Then, based on the observation that existing works cannot actually achieve provable guarantees, we promote a two-step verification method for the ultimate achievement of provable statistical guarantees.