# Cascading Robustness Verification: Toward Efficient Model-Agnostic Certification

arXiv: https://arxiv.org/abs/2602.04236 · HTML: https://mlsanity.com/paper/2602.04236/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 29 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 17 of 17)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (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)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [SoK: Certified Robustness for Deep Neural Networks](https://mlsanity.com/paper/2009.04131/) (2020)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Invisible for both Camera and LiDAR: Security of Multi-Sensor Fusion based Perception in Autonomous Driving Under Physical-World Attacks](https://mlsanity.com/paper/2106.09249/) (2021)
- [Measuring Neural Net Robustness with Constraints](https://mlsanity.com/paper/1605.07262/) (2016)
- [Enabling certification of verification-agnostic networks via memory-efficient semidefinite programming](https://mlsanity.com/paper/2010.11645/) (2020)
- [First Three Years of the International Verification of Neural Networks Competition (VNN-COMP)](https://mlsanity.com/paper/2301.05815/) (2023)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)
- [Scalable Semidefinite Programming](https://mlsanity.com/paper/1912.02949/) (2019)
- [SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programming](https://mlsanity.com/paper/2506.06665/) (2025)

## Built on by (most cited first, 1 of 1)

- [Certified Robustness via Sparse Second-Order Cone Relaxations](https://mlsanity.com/paper/2610.16016/) (2026)

## Abstract (arXiv)

Certifying neural network robustness against adversarial examples is challenging, as formal guarantees often require solving non-convex problems. Hence, incomplete verifiers are widely used because they scale efficiently and substantially reduce the cost of robustness verification compared to complete methods. However, relying on a single verifier can underestimate robustness because of loose approximations or misalignment with training methods. In this work, we propose Cascading Robustness Verification (CRV), which goes beyond an engineering improvement by exposing fundamental limitations of existing robustness metric and introducing a framework that enhances both reliability and efficiency. CRV is a model-agnostic verifier, meaning that its robustness guarantees are independent of the model's training process. The key insight behind the CRV framework is that, when using multiple verification methods, an input is certifiably robust if at least one method certifies it as robust. Rather than relying solely on a single verifier with a fixed constraint set, CRV progressively applies multiple verifiers to balance the tightness of the bound and computational cost. Starting with the least expensive method, CRV halts as soon as an input is certified as robust; otherwise, it proceeds to more expensive methods. For computationally expensive methods, we introduce a Stepwise Relaxation Algorithm (SR) that incrementally adds constraints and checks for certification at each step, thereby avoiding unnecessary computation. Our theoretical analysis demonstrates that CRV achieves equal or higher verified accuracy compared to powerful but computationally expensive incomplete verifiers in the cascade, while significantly reducing verification overhead. Empirical results confirm that CRV certifies at least as many inputs as benchmark approaches, while improving runtime efficiency by up to ~90%.