mlsanityData to 7 Oct 2026

On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks

arXiv 2209.11740 ↗First posted 19 Sep 2022cs.CV cs.AI eess.SPcited by 2

Not on the map. Why?

Abstract (arXiv)

This paper focuses on improving the mathematical interpretability of convolutional neural networks (CNNs) in the context of image classification. Specifically, we tackle the instability issue arising in their first layer, which tends to learn parameters that closely resemble oriented band-pass filters when trained on datasets like ImageNet. Subsampled convolutions with such Gabor-like filters are prone to aliasing, causing sensitivity to small input shifts. In this context, we establish conditions under which the max pooling operator approximates a complex modulus, which is nearly shift invariant. We then derive a measure of shift invariance for subsampled convolutions followed by max pooling. In particular, we highlight the crucial role played by the filter's frequency and orientation in achieving stability. We experimentally validate our theory by considering a deterministic feature extractor based on the dual-tree complex wavelet packet transform, a particular case of discrete Gabor-like decomposition.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 42 of its 82 references that are in the map. First posted on arXiv 19 Sep 2022.

Builds on

42 of 82 references.

References · 42

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020An Image is Worth 16x16 Words: Transformers for Image Recognition at Scalecited by 29,915
  3. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  4. 2014ImageNet Large Scale Visual Recognition Challengecited by 8,441
  5. 2015Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shiftcited by 6,979
  6. 2013Intriguing properties of neural networkscited by 5,114
  7. 2014How transferable are features in deep neural networks?cited by 1,216
  8. 2021CvT: Introducing Convolutions to Vision Transformerscited by 946
  9. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  10. 2019Making Convolutional Networks Shift-Invariant Againcited by 390
  11. 2021Escaping the Big Data Paradigm with Compact Transformerscited by 261
  12. 2021Incorporating Convolution Designs into Visual Transformerscited by 248
30 more
  1. 2022UniFormer: Unifying Convolution and Self-attention for Visual Recognitioncited by 206
  2. 2018Why do deep convolutional networks generalize so poorly to small image transformations?cited by 198
  3. 2019On the Inductive Bias of Neural Tangent Kernelscited by 177
  4. 2016Understanding Deep Convolutional Networkscited by 76
  5. 2020Delving Deeper into Anti-aliasing in ConvNetscited by 60
  6. 2019Multi-level Wavelet Convolutional Neural Networkscited by 59
  7. 2017Gabor Convolutional Networkscited by 55
  8. 2020Truly shift-invariant convolutional neural networkscited by 53
  9. 2014Deep Roto-Translation Scattering for Object Classificationcited by 49
  10. 2015A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extractioncited by 46
  11. 2018Graph Convolutional Neural Networks via Scatteringcited by 46
  12. 2017Scaling the Scattering Transform: Deep Hybrid Networkscited by 35
  13. 2019Stability of Graph Scattering Transformscited by 34
  14. 2021Approximation and Learning with Deep Convolutional Models: a Kernel Perspectivecited by 31
  15. 2018On Lipschitz Bounds of General Convolutional Neural Networkscited by 29
  16. 2020Separation and Concentration in Deep Networkscited by 28
  17. 2020An Effective Anti-Aliasing Approach for Residual Networkscited by 23
  18. 2017Wavelet Convolutional Neural Networks for Texture Classificationcited by 21
  19. 2022Group-invariant max filteringcited by 18
  20. 2019Deep Network Classification by Scattering and Homotopy Dictionary Learningcited by 17
  21. 2021Parametric Scattering Networkscited by 15
  22. 2015A mathematical motivation for complex-valued convolutional networkscited by 13
  23. 2018Compressing the Input for CNNs with the First-Order Scattering Transformcited by 11
  24. 2019A Learnable ScatterNet: Locally Invariant Convolutional Layerscited by 10
  25. 2017Lipschitz Properties for Deep Convolutional Networkscited by 9
  26. 2019Gabor Layers Enhance Network Robustnesscited by 9
  27. 2017Gabor Filter Assisted Energy Efficient Fast Learning Convolutional Neural Networkscited by 8
  28. 2019Geometric Wavelet Scattering Networks on Compact Riemannian Manifoldscited by 7
  29. 2020Harmonic Decompositions of Convolutional Networkscited by 6
  30. 2017Dual-Tree Wavelet Scattering Network with Parametric Log Transformation for Object Classificationcited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 0; 2024: 0; 2025: 0; 2026: 1.

2 papers.

  1. 2022From CNNs to Shift-Invariant Twin Models Based on Complex Waveletscited by 0
  2. 2026Transversal Pooling Neural Networkscited by 0