# Confidence Composition for Monitors of Verification Assumptions

arXiv: https://arxiv.org/abs/2111.03782 · HTML: https://mlsanity.com/paper/2111.03782/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 54 references that are in the map.
- First posted on arXiv 3 Nov 2021.

## Builds on (most cited first, 14 of 14)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Probabilistically Safe Robot Planning with Confidence-Based Human Predictions](https://mlsanity.com/paper/1806.00109/) (2018)
- [SOTER: A Runtime Assurance Framework for Programming Safe Robotics Systems](https://mlsanity.com/paper/1808.07921/) (2018)
- [PAC Confidence Predictions for Deep Neural Network Classifiers](https://mlsanity.com/paper/2011.00716/) (2020)
- [ReSonAte: A Runtime Risk Assessment Framework for Autonomous Systems](https://mlsanity.com/paper/2102.09419/) (2021)
- [Quantifying Assurance in Learning-enabled Systems](https://mlsanity.com/paper/2006.10345/) (2020)
- [Verified Runtime Validation for Partially Observable Hybrid Systems](https://mlsanity.com/paper/1811.06502/) (2018)
- [Assurance Monitoring of Learning Enabled Cyber-Physical Systems Using Inductive Conformal Prediction based on Distance Learning](https://mlsanity.com/paper/2110.03120/) (2021)
- [Monitoring Assumptions in Assume-Guarantee Contracts](https://mlsanity.com/paper/1606.00505/) (2016)
- [ModelGuard: Runtime Validation of Lipschitz-continuous Models](https://mlsanity.com/paper/2104.15006/) (2021)
- [Improving Prediction Confidence in Learning-Enabled Autonomous Systems](https://mlsanity.com/paper/2110.03123/) (2021)

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

- [How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2308.12252/) (2023)
- [Bridging Dimensions: Confident Reachability for High-Dimensional Controllers](https://mlsanity.com/paper/2311.04843/) (2023)
- [Language-Enhanced Latent Representations for Out-of-Distribution Detection in Autonomous Driving](https://mlsanity.com/paper/2405.01691/) (2024)
- [Physically Interpretable World Models via Weakly Supervised Representation Learning](https://mlsanity.com/paper/2412.12870/) (2024)
- [How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2508.09346/) (2025)
- [Causal Repair of Learning-enabled Cyber-physical Systems](https://mlsanity.com/paper/2304.02813/) (2023)

## Abstract (arXiv)

Closed-loop verification of cyber-physical systems with neural network controllers offers strong safety guarantees under certain assumptions. It is, however, difficult to determine whether these guarantees apply at run time because verification assumptions may be violated. To predict safety violations in a verified system, we propose a three-step confidence composition (CoCo) framework for monitoring verification assumptions. First, we represent the sufficient condition for verified safety with a propositional logical formula over assumptions. Second, we build calibrated confidence monitors that evaluate the probability that each assumption holds. Third, we obtain the confidence in the verification guarantees by composing the assumption monitors using a composition function suitable for the logical formula. Our CoCo framework provides theoretical bounds on the calibration and conservatism of compositional monitors. Two case studies show that compositional monitors are calibrated better than their constituents and successfully predict safety violations.