# Alias-Free Convnets: Fractional Shift Invariance via Polynomial Activations

arXiv: https://arxiv.org/abs/2303.08085 · HTML: https://mlsanity.com/paper/2303.08085/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 36 references that are in the map.
- First posted on arXiv 14 Mar 2023.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Alias-Free Generative Adversarial Networks](https://mlsanity.com/paper/2106.12423/) (2021)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Attentive Group Equivariant Convolutional Networks](https://mlsanity.com/paper/2002.03830/) (2020)
- [Delving Deeper into Anti-aliasing in ConvNets](https://mlsanity.com/paper/2008.09604/) (2020)
- [Truly shift-invariant convolutional neural networks](https://mlsanity.com/paper/2011.14214/) (2020)
- [An Effective Anti-Aliasing Approach for Residual Networks](https://mlsanity.com/paper/2011.10675/) (2020)
- [Equivariance Discovery by Learned Parameter-Sharing](https://mlsanity.com/paper/2204.03640/) (2022)
- [Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networks](https://mlsanity.com/paper/2210.08001/) (2022)
- [Shift Invariance Can Reduce Adversarial Robustness](https://mlsanity.com/paper/2103.02695/) (2021)
- [Group Equivariant Subsampling](https://mlsanity.com/paper/2106.05886/) (2021)
- [Shift Equivariance in Object Detection](https://mlsanity.com/paper/2008.05787/) (2020)
- [Anti-aliasing Deep Image Classifiers using Novel Depth Adaptive Blurring and Activation Function](https://mlsanity.com/paper/2110.00899/) (2021)
- [Generalization to translation shifts: a study in architectures and augmentations](https://mlsanity.com/paper/2207.02349/) (2022)

## Built on by (most cited first, 11 of 11)

- [Making Vision Transformers Truly Shift-Equivariant](https://mlsanity.com/paper/2305.16316/) (2023)
- [Alias-Free Latent Diffusion Models: Improving Fractional Shift Equivariance of Diffusion Latent Space](https://mlsanity.com/paper/2503.09419/) (2025)
- [Optimizing PatchCore for Few/many-shot Anomaly Detection](https://mlsanity.com/paper/2307.10792/) (2023)
- [Shifting the Paradigm: A Diffeomorphism Between Time Series Data Manifolds for Achieving Shift-Invariancy in Deep Learning](https://mlsanity.com/paper/2502.19921/) (2025)
- [CoNO: Complex Neural Operator for Continuous Dynamical Systems](https://mlsanity.com/paper/2310.02094/) (2023)
- [Exponential Quantum Communication Advantage in Distributed Inference and Learning](https://mlsanity.com/paper/2310.07136/) (2023)
- [Alias-Free ViT: Fractional Shift Invariance via Linear Attention](https://mlsanity.com/paper/2510.22673/) (2025)
- [Translation-Equivariance of Normalization Layers and Aliasing in Convolutional Neural Networks](https://mlsanity.com/paper/2505.19805/) (2025)
- [Equivariant Splitting: Self-supervised learning from incomplete data](https://mlsanity.com/paper/2510.00929/) (2025)
- [UNet-AF: Alias-free UNet architectures](https://mlsanity.com/paper/2603.11323/) (2026)
- [A Theory of Contrastive Learning with Natural Images](https://mlsanity.com/paper/2607.07470/) (2026)

## Abstract (arXiv)

Although CNNs are believed to be invariant to translations, recent works have shown this is not the case, due to aliasing effects that stem from downsampling layers. The existing architectural solutions to prevent aliasing are partial since they do not solve these effects, that originate in non-linearities. We propose an extended anti-aliasing method that tackles both downsampling and non-linear layers, thus creating truly alias-free, shift-invariant CNNs. We show that the presented model is invariant to integer as well as fractional (i.e., sub-pixel) translations, thus outperforming other shift-invariant methods in terms of robustness to adversarial translations.