mlsanityData to 14 Oct 2026

Towards Verifying the Geometric Robustness of Large-scale Neural Networks

arXiv 2301.12456 ↗First posted 29 Jan 2023cs.LG cs.AI cs.CVcited by 11

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Abstract (arXiv)

Deep neural networks (DNNs) are known to be vulnerable to adversarial geometric transformation. This paper aims to verify the robustness of large-scale DNNs against the combination of multiple geometric transformations with a provable guarantee. Given a set of transformations (e.g., rotation, scaling, etc.), we develop GeoRobust, a black-box robustness analyser built upon a novel global optimisation strategy, for locating the worst-case combination of transformations that affect and even alter a network's output. GeoRobust can provide provable guarantees on finding the worst-case combination based on recent advances in Lipschitzian theory. Due to its black-box nature, GeoRobust can be deployed on large-scale DNNs regardless of their architectures, activation functions, and the number of neurons. In practice, GeoRobust can locate the worst-case geometric transformation with high precision for the ResNet50 model on ImageNet in a few seconds on average. We examined 18 ImageNet classifiers, including the ResNet family and vision transformers, and found a positive correlation between the geometric robustness of the networks and the parameter numbers. We also observe that increasing the depth of DNN is more beneficial than increasing its width in terms of improving its geometric robustness. Our tool GeoRobust is available at https://github.com/TrustAI/GeoRobust.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 29 of its 49 references that are in the map. First posted on arXiv 29 Jan 2023.

Builds on

29 of 49 references.

References · 29

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2020Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attackscited by 1,451
  4. 2015Spatial Transformer Networkscited by 1,429
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,340
  6. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  7. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 255
  8. 2019Algorithms for Verifying Deep Neural Networkscited by 221
  9. 2018Spatially Transformed Adversarial Examplescited by 195
  10. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
  11. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  12. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
17 more
  1. 2020Certified Defense to Image Transformations via Randomized Smoothingcited by 51
  2. 2020TSS: Transformation-Specific Smoothing for Robustness Certificationcited by 49
  3. 2018ADef: an Iterative Algorithm to Construct Adversarial Deformationscited by 38
  4. 2018A Game-Based Approximate Verification of Deep Neural Networks with Provable Guaranteescited by 33
  5. 2022GSmooth: Certified Robustness against Semantic Transformations via Generalized Randomized Smoothingcited by 23
  6. 2017Reachable Set Computation and Safety Verification for Neural Networks with ReLU Activationscited by 22
  7. 2017Towards Practical Verification of Machine Learning: The Case of Computer Vision Systemscited by 19
  8. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  9. 2020Generalizing Universal Adversarial Attacks Beyond Additive Perturbationscited by 17
  10. 2021On the Regularity of Attentioncited by 11
  11. 2021Sparse Adversarial Video Attacks with Spatial Transformationscited by 11
  12. 2022DIMBA: Discretely Masked Black-Box Attack in Single Object Trackingcited by 11
  13. 2023Reachability Analysis of Neural Network Control Systemscited by 8
  14. 2021Adversarial Robustness of Deep Learning: Theory, Algorithms, and Applicationscited by 5
  15. 20223DVerifier: Efficient Robustness Verification for 3D Point Cloud Modelscited by 5
  16. 2022Understanding Adversarial Robustness of Vision Transformers via Cauchy Problemcited by 4
  17. 2015Digging Deep into the layers of CNNs: In Search of How CNNs Achieve View Invariancecited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 2; 2025: 1; 2026: 5.

11 papers.

  1. 2023A Survey of Safety and Trustworthiness of Large Language Models through the Lens of Verification and Validationcited by 93
  2. 2024Building Guardrails for Large Language Modelscited by 65
  3. 2023Reward Certification for Policy Smoothed Reinforcement Learningcited by 7
  4. 2026Revisiting Robustness for LLM Safety Alignment via Selective Geometry Controlcited by 4
  5. 2024A Black-Box Evaluation Framework for Semantic Robustness in Bird's Eye View Detectioncited by 3
  6. 2023Model-Agnostic Reachability Analysis on Deep Neural Networkscited by 1
  7. 2025Mini-Batch Robustness Verification of Deep Neural Networkscited by 1
  8. 2026Semantic Robustness Certification for Vision-Language Modelscited by 1
  9. 2026Lipschitz Optimization for Formal Verification of Homographiescited by 0
  10. 2026Hybrid Robustness Verification for Spatio-Temporal Neural Networkscited by 0
  11. 2026Robust Validation to Geometric Perturbations for Autonomous Pose Estimationcited by 0