No Soundness in the Real World: On the Challenges of the Verification of Deployed Neural Networks
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Abstract (arXiv)
The ultimate goal of verification is to guarantee the safety of deployed neural networks. Here, we claim that all the state-of-the-art verifiers we are aware of fail to reach this goal. Our key insight is that theoretical soundness (bounding the full-precision output while computing with floating point) does not imply practical soundness (bounding the floating point output in a potentially stochastic environment). We prove this observation for the approaches that are currently used to achieve provable theoretical soundness, such as interval analysis and its variants. We also argue that achieving practical soundness is significantly harder computationally. We support our claims empirically as well by evaluating several well-known verification methods. To mislead the verifiers, we create adversarial networks that detect and exploit features of the deployment environment, such as the order and precision of floating point operations. We demonstrate that all the tested verifiers are vulnerable to our new deployment-specific attacks, which proves that they are not practically sound.
Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Builds on 19 of its 38 references that are in the map. First posted on arXiv 1 Jun 2025.
Builds on
19 of 38 references.
References · 19
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7 more
- 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 103
- 2022Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Boundcited by 92
- 2021Introduction to Neural Network Verificationcited by 63
- 2020Exploiting Verified Neural Networks via Floating Point Numerical Errorcited by 35
- 2024Impacts of floating-point non-associativity on reproducibility for HPC and deep learning applicationscited by 24
- 2025Neural Network Verification is a Programming Language Challengecited by 12
- 2025Robustness of deep learning classification to adversarial input on GPUs: asynchronous parallel accumulation is a source of vulnerabilitycited by 1
Built on by
Citing papers per year: 2025: 3; 2026: 3.
6 papers.
- 2026TorchLean: Formalizing Neural Networks in Leancited by 4
- 2025Floating-Point Neural Network Verification at the Software Levelcited by 2
- 2025TAO: Tolerance-Aware Optimistic Verification for Floating-Point Neural Networkscited by 1
- 2025Of Good Demons and Bad Angels: Guaranteeing Safe Control under Finite Precisioncited by 0
- 2026Lipschitz-Based Robustness Certification Under Floating-Point Executioncited by 0
- 2026From Mathematical to Executable Certificates for Machine Unlearningcited by 0
- 2026From Mathematical to Executable Certificates for Machine Unlearning1 Oct 2026
- 2026Lipschitz-Based Robustness Certification Under Floating-Point Execution6 Mar 2026
- 2026TorchLean: Formalizing Neural Networks in Lean26 Feb 2026
- 2025Floating-Point Neural Network Verification at the Software Level27 Oct 2025
- 2025TAO: Tolerance-Aware Optimistic Verification for Floating-Point Neural Networks15 Oct 2025
- 2025Of Good Demons and Bad Angels: Guaranteeing Safe Control under Finite Precision30 Jul 2025