# Improving Shift Invariance in Convolutional Neural Networks with Translation Invariant Polyphase Sampling

arXiv: https://arxiv.org/abs/2404.07410 · HTML: https://mlsanity.com/paper/2404.07410/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 52 of its 74 references that are in the map.
- First posted on arXiv 11 Apr 2024.

## Builds on (most cited first, 30 of 52)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)

## Built on by (most cited first, 6 of 6)

- [Alias-Free Latent Diffusion Models: Improving Fractional Shift Equivariance of Diffusion Latent Space](https://mlsanity.com/paper/2503.09419/) (2025)
- [To Erase, or Not to Erase: Robust Training-Free Concept Erasure with Preservation aware Adaptive Ranked Subspace Expansion](https://mlsanity.com/paper/2607.23492/) (2026)
- [Translation-Equivariance of Normalization Layers and Aliasing in Convolutional Neural Networks](https://mlsanity.com/paper/2505.19805/) (2025)
- [OracleZoom: On-Policy Self-Distillation Inspired Reference-Constrained Recursive Image Super Resolution](https://mlsanity.com/paper/2609.06490/) (2026)
- [BEFORE THE FLIP: Measuring Hidden Score Shifts In Quantized Vision Language Models Before The Answer Changes for Visual Question Answering](https://mlsanity.com/paper/2609.06922/) (2026)
- [New Evidence, Same Choice: Testing Physical Experiment Selection in Vision Language Models](https://mlsanity.com/paper/2609.11022/) (2026)

## Abstract (arXiv)

Downsampling operators break the shift invariance of convolutional neural networks (CNNs) and this affects the robustness of features learned by CNNs when dealing with even small pixel-level shift. Through a large-scale correlation analysis framework, we study shift invariance of CNNs by inspecting existing downsampling operators in terms of their maximum-sampling bias (MSB), and find that MSB is negatively correlated with shift invariance. Based on this crucial insight, we propose a learnable pooling operator called Translation Invariant Polyphase Sampling (TIPS) and two regularizations on the intermediate feature maps of TIPS to reduce MSB and learn translation-invariant representations. TIPS can be integrated into any CNN and can be trained end-to-end with marginal computational overhead. Our experiments demonstrate that TIPS results in consistent performance gains in terms of accuracy, shift consistency, and shift fidelity on multiple benchmarks for image classification and semantic segmentation compared to previous methods and also leads to improvements in adversarial and distributional robustness. TIPS results in the lowest MSB compared to all previous methods, thus explaining our strong empirical results.