Academic

Exact and Asymptotically Complete Robust Verifications of Neural Networks via Quantum Optimization

arXiv:2603.00408v1 Announce Type: new Abstract: Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust verification that reduce the combinatorial burden of certification under bounded input perturbations. For piecewise-linear activations (e.g., ReLU and hardtanh), our first model yields an exact formulation that is sound and complete, enabling precise identification of adversarial examples. For general activations (including sigmoid and tanh), our second model constructs scalable over-approximations via piecewise-constant bounds and is asymptotically complete, with approximation error vanishing as the segmentation is refined. We further integrate Quantum Benders Decomposition with interval arithmetic to accelerate solving, and propose certificate-transfer bounds that relate robustness guarantees of pruned ne

W
Wenxin Li, Wenchao Liu, Chuan Wang, Qi Gao, Yin Ma, Hai Wei, Kai Wen · · 1 min read · 16 views
#cs.LG #cs.AI #physics.optics #quant-ph

arXiv:2603.00408v1 Announce Type: new Abstract: Deep neural networks (DNNs) enable high performance across domains but remain vulnerable to adversarial perturbations, limiting their use in safety-critical settings. Here, we introduce two quantum-optimization-based models for robust verification that reduce the combinatorial burden of certification under bounded input perturbations. For piecewise-linear activations (e.g., ReLU and hardtanh), our first model yields an exact formulation that is sound and complete, enabling precise identification of adversarial examples. For general activations (including sigmoid and tanh), our second model constructs scalable over-approximations via piecewise-constant bounds and is asymptotically complete, with approximation error vanishing as the segmentation is refined. We further integrate Quantum Benders Decomposition with interval arithmetic to accelerate solving, and propose certificate-transfer bounds that relate robustness guarantees of pruned networks to those of the original model. Finally, a layerwise partitioning strategy supports a quantum--classical hybrid workflow by coupling subproblems across depth. Experiments on robustness benchmarks show high certification accuracy, indicating that quantum optimization can serve as a principled primitive for robustness guarantees in neural networks with complex activations.

Executive Summary

This article introduces two quantum-optimization-based models for robust verification of deep neural networks (DNNs) that reduce the combinatorial burden of certification under bounded input perturbations. The first model yields an exact formulation for piecewise-linear activations, while the second model constructs scalable over-approximations for general activations. The authors also propose certificate-transfer bounds and a layerwise partitioning strategy to accelerate solving and support a quantum-classical hybrid workflow. Experiments on robustness benchmarks show high certification accuracy, indicating that quantum optimization can serve as a principled primitive for robustness guarantees in neural networks with complex activations. The article contributes to the development of reliable and trustworthy AI systems by providing a robust verification framework for DNNs.

Key Points

  • ▸ Two quantum-optimization-based models are proposed for robust verification of DNNs.
  • ▸ The first model yields an exact formulation for piecewise-linear activations.
  • ▸ The second model constructs scalable over-approximations for general activations.
  • ▸ Certificate-transfer bounds and a layerwise partitioning strategy are proposed to accelerate solving and support a quantum-classical hybrid workflow.

Merits

Strength

The article presents a novel and robust verification framework for DNNs that can handle complex activations and bounded input perturbations.

Methodological Advancement

The authors leverage quantum optimization and interval arithmetic to develop scalable and accurate over-approximations for general activations.

Practical Impact

The proposed framework has the potential to improve the reliability and trustworthiness of AI systems in safety-critical settings.

Demerits

Limitation

The article assumes a fixed segmentation of the activation function, which may not be optimal for all cases.

Scalability

The proposed framework may not scale well to large and complex neural networks due to the computational overhead of quantum optimization.

Practical Implementation

The article does not provide a detailed discussion on the practical implementation and deployment of the proposed framework.

Expert Commentary

The article presents a novel and robust verification framework for DNNs that leverages quantum optimization and interval arithmetic to develop scalable and accurate over-approximations for general activations. The proposed framework has the potential to improve the reliability and trustworthiness of AI systems in safety-critical settings. However, the article assumes a fixed segmentation of the activation function, which may not be optimal for all cases, and the proposed framework may not scale well to large and complex neural networks due to the computational overhead of quantum optimization. Nevertheless, the article contributes to the development of reliable and trustworthy AI systems by providing a robust verification framework for DNNs.

Recommendations

  • ✓ Further research is needed to investigate the scalability of the proposed framework to large and complex neural networks.
  • ✓ Practical implementation and deployment of the proposed framework should be discussed in future work.

Sources

Related Articles