# H-NeXt: The next step towards roto-translation invariant networks

arXiv: https://arxiv.org/abs/2311.01111 · HTML: https://mlsanity.com/paper/2311.01111/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 51 references that are in the map.
- First posted on arXiv 2 Nov 2023.

## Builds on (most cited first, 29 of 29)

- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Understanding image representations by measuring their equivariance and equivalence](https://mlsanity.com/paper/1411.5908/) (2014)
- [Rethinking and Improving Relative Position Encoding for Vision Transformer](https://mlsanity.com/paper/2107.14222/) (2021)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Rotation equivariant vector field networks](https://mlsanity.com/paper/1612.09346/) (2016)
- [Roto-Translation Covariant Convolutional Networks for Medical Image Analysis](https://mlsanity.com/paper/1804.03393/) (2018)
- [Exploiting Cyclic Symmetry in Convolutional Neural Networks](https://mlsanity.com/paper/1602.02660/) (2016)
- [Polar Transformer Networks](https://mlsanity.com/paper/1709.01889/) (2017)
- [Rigid-Motion Scattering for Texture Classification](https://mlsanity.com/paper/1403.1687/) (2014)
- [Deep Roto-Translation Scattering for Object Classification](https://mlsanity.com/paper/1412.8659/) (2014)
- [PDO-eConvs: Partial Differential Operator Based Equivariant Convolutions](https://mlsanity.com/paper/2007.10408/) (2020)
- [HexaConv](https://mlsanity.com/paper/1803.02108/) (2018)
- [Learning rotation invariant convolutional filters for texture classification](https://mlsanity.com/paper/1604.06720/) (2016)
- [Exploiting Redundancy: Separable Group Convolutional Networks on Lie Groups](https://mlsanity.com/paper/2110.13059/) (2021)
- [Graph-based Isometry Invariant Representation Learning](https://mlsanity.com/paper/1703.00356/) (2017)
- [Learning Invariant Representations for Equivariant Neural Networks Using Orthogonal Moments](https://mlsanity.com/paper/2209.10944/) (2022)
- [Equivariance-bridged SO(2)-Invariant Representation Learning using Graph Convolutional Network](https://mlsanity.com/paper/2106.09996/) (2021)

## Built on by (most cited first, 2 of 2)

- [Harmformer: Harmonic Networks Meet Transformers for Continuous Roto-Translation Equivariance](https://mlsanity.com/paper/2411.03794/) (2024)
- [On Making SE(2)-Invariant Networks Optimal](https://mlsanity.com/paper/2610.17424/) (2026)

## Abstract (arXiv)

The widespread popularity of equivariant networks underscores the significance of parameter efficient models and effective use of training data. At a time when robustness to unseen deformations is becoming increasingly important, we present H-NeXt, which bridges the gap between equivariance and invariance. H-NeXt is a parameter-efficient roto-translation invariant network that is trained without a single augmented image in the training set. Our network comprises three components: an equivariant backbone for learning roto-translation independent features, an invariant pooling layer for discarding roto-translation information, and a classification layer. H-NeXt outperforms the state of the art in classification on unaugmented training sets and augmented test sets of MNIST and CIFAR-10.