mlsanityData to 14 Oct 2026

Geometric robustness of deep networks: analysis and improvement

arXiv 1711.09115 ↗First posted 24 Nov 2017cs.CV cs.LGcited by 45

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Abstract (arXiv)

Deep convolutional neural networks have been shown to be vulnerable to arbitrary geometric transformations. However, there is no systematic method to measure the invariance properties of deep networks to such transformations. We propose ManiFool as a simple yet scalable algorithm to measure the invariance of deep networks. In particular, our algorithm measures the robustness of deep networks to geometric transformations in a worst-case regime as they can be problematic for sensitive applications. Our extensive experimental results show that ManiFool can be used to measure the invariance of fairly complex networks on high dimensional datasets and these values can be used for analyzing the reasons for it. Furthermore, we build on Manifool to propose a new adversarial training scheme and we show its effectiveness on improving the invariance properties of deep neural networks.

Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Nov 2017.

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Citing papers per year: 2021: 12; 2022: 14; 2023: 11; 2024: 3; 2025: 3; 2026: 2.

45 papers.

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  1. 2022ViewFool: Evaluating the Robustness of Visual Recognition to Adversarial Viewpointscited by 48
  2. 20213DB: A Framework for Debugging Computer Vision Modelscited by 31
  3. 2022On the Strong Correlation Between Model Invariance and Generalizationcited by 23
  4. 2021Enhancing MR Image Segmentation with Realistic Adversarial Data Augmentationcited by 20
  5. 2022Just Rotate it: Deploying Backdoor Attacks via Rotation Transformationcited by 20
  6. 2023Attacks in Adversarial Machine Learning: A Systematic Survey from the Life-cycle Perspectivecited by 20
  7. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 19
  8. 2023Towards Viewpoint-Invariant Visual Recognition via Adversarial Trainingcited by 19
  9. 2023A Survey of Robustness and Safety of 2D and 3D Deep Learning Models Against Adversarial Attackscited by 19
  10. 2021DeformRS: Certifying Input Deformations with Randomized Smoothingcited by 17
  11. 2022Automatic Data Augmentation via Invariance-Constrained Learningcited by 17
  12. 2023Making Vision Transformers Truly Shift-Equivariantcited by 16
33 more
  1. 2022Towards Good Practices in Evaluating Transfer Adversarial Attackscited by 15
  2. 2022Provable Defense Against Geometric Transformationscited by 14
  3. 2021Relative stability toward diffeomorphisms indicates performance in deep netscited by 12
  4. 2021Anti-aliasing Deep Image Classifiers using Novel Depth Adaptive Blurring and Activation Functioncited by 11
  5. 2022ALA: Naturalness-aware Adversarial Lightness Attackcited by 11
  6. 2021Deep Learning Generalization and the Convex Hull of Training Setscited by 10
  7. 2021AGKD-BML: Defense Against Adversarial Attack by Attention Guided Knowledge Distillation and Bi-directional Metric Learningcited by 10
  8. 2022LinSyn: Synthesizing Tight Linear Bounds for Arbitrary Neural Network Activation Functionscited by 10
  9. 2022Adversarially Robust Learning with Tolerancecited by 9
  10. 2023Defense against Adversarial Cloud Attack on Remote Sensing Salient Object Detectioncited by 8
  11. 2023Improving Viewpoint Robustness for Visual Recognition via Adversarial Trainingcited by 7
  12. 2024How Deep Networks Learn Sparse and Hierarchical Data: the Sparse Random Hierarchy Modelcited by 7
  13. 2024Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisationcited by 7
  14. 2021Generating Unrestricted Adversarial Examples via Three Parameterscited by 5
  15. 2022How deep convolutional neural networks lose spatial information with trainingcited by 5
  16. 2023Exploring Robust Features for Improving Adversarial Robustnesscited by 4
  17. 2024Single Character Perturbations Break LLM Alignmentcited by 4
  18. 2022Generalization to translation shifts: a study in architectures and augmentationscited by 3
  19. 2023Generating Less Certain Adversarial Examples Improves Robust Generalizationcited by 3
  20. 2021Natural Perturbed Training for General Robustness of Neural Network Classifierscited by 2
  21. 2021Robust Training Using Natural Transformationcited by 2
  22. 2022Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimizationcited by 2
  23. 2022A Closer Look at Robustness to L-infinity and Spatial Perturbations and their Compositioncited by 2
  24. 2023Pixel-wise Smoothing for Certified Robustness against Camera Motion Perturbationscited by 2
  25. 2022Verifying Attention Robustness of Deep Neural Networks against Semantic Perturbationscited by 1
  26. 2023Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbitscited by 1
  27. 2021Wiggling Weights to Improve the Robustness of Classifierscited by 0
  28. 2023RetouchUAA: Unconstrained Adversarial Attack via Image Retouchingcited by 0
  29. 2025Disentangling Safe and Unsafe Corruptions via Anisotropy and Localitycited by 0
  30. 2025The Power of Many: Synergistic Unification of Diverse Augmentations for Efficient Adversarial Robustnesscited by 0
  31. 2025NAPPure: Adversarial Purification for Robust Image Classification under Non-Additive Perturbationscited by 0
  32. 2026Lipschitz Optimization for Formal Verification of Homographiescited by 0
  33. 2026Generating Multi-view Adversarial Examples for Visual Geometry Grounded Transformercited by 0