# HexaConv

arXiv: https://arxiv.org/abs/1803.02108 · HTML: https://mlsanity.com/paper/1803.02108/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2018.

## Built on by (most cited first, 27 of 27)

- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Commutative Lie Group VAE for Disentanglement Learning](https://mlsanity.com/paper/2106.03375/) (2021)
- [Fourier Series Expansion Based Filter Parametrization for Equivariant Convolutions](https://mlsanity.com/paper/2107.14519/) (2021)
- [Continual Learning for Instruction Following from Realtime Feedback](https://mlsanity.com/paper/2212.09710/) (2022)
- [Continual Learning for Grounded Instruction Generation by Observing Human Following Behavior](https://mlsanity.com/paper/2108.04812/) (2021)
- [E2PN: Efficient SE(3)-Equivariant Point Network](https://mlsanity.com/paper/2206.05398/) (2022)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Group Equivariant Subsampling](https://mlsanity.com/paper/2106.05886/) (2021)
- [A Convolutional Neural Network based Cascade Reconstruction for the IceCube Neutrino Observatory](https://mlsanity.com/paper/2101.11589/) (2021)
- [Rule-Based Reinforcement Learning for Efficient Robot Navigation with Space Reduction](https://mlsanity.com/paper/2104.07282/) (2021)
- [Deformation Robust Roto-Scale-Translation Equivariant CNNs](https://mlsanity.com/paper/2111.10978/) (2021)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [Rotation-Equivariant Self-Supervised Method in Image Denoising](https://mlsanity.com/paper/2505.19618/) (2025)
- [RSF-Conv: Rotation-and-Scale Equivariant Fourier Parameterized Convolution for Retinal Vessel Segmentation](https://mlsanity.com/paper/2309.15638/) (2023)
- [Rotation Equivariant Arbitrary-scale Image Super-Resolution](https://mlsanity.com/paper/2508.05160/) (2025)
- [The Preliminary Results on Analysis of TAIGA-IACT Images Using Convolutional Neural Networks](https://mlsanity.com/paper/2112.10168/) (2021)
- [Learning Invariant Representations for Equivariant Neural Networks Using Orthogonal Moments](https://mlsanity.com/paper/2209.10944/) (2022)
- [Energy Reconstruction in Analysis of Cherenkov Telescopes Images in TAIGA Experiment Using Deep Learning Methods](https://mlsanity.com/paper/2211.08971/) (2022)
- [Deep Neural Networks with Efficient Guaranteed Invariances](https://mlsanity.com/paper/2303.01567/) (2023)
- [H-NeXt: The next step towards roto-translation invariant networks](https://mlsanity.com/paper/2311.01111/) (2023)
- [CB2: Collaborative Natural Language Interaction Research Platform](https://mlsanity.com/paper/2303.08127/) (2023)
- [Resampling and super-resolution of hexagonally sampled images using deep learning](https://mlsanity.com/paper/2111.02520/) (2021)
- [Domain-informed neural networks for interaction localization within astroparticle experiments](https://mlsanity.com/paper/2112.07995/) (2021)
- [DUN-SRE: Deep Unrolling Network with Spatiotemporal Rotation Equivariance for Dynamic MRI Reconstruction](https://mlsanity.com/paper/2506.10309/) (2025)
- [A multi-view contrastive learning framework for spatial embeddings in risk modelling](https://mlsanity.com/paper/2511.17954/) (2025)
- [Accelerated Rotation-Invariant Convolution for UAV Image Segmentation](https://mlsanity.com/paper/2512.08888/) (2025)
- [Embedding Rotation Invariance for Provable Multi-Oriented Scene Text Recognition](https://mlsanity.com/paper/2608.10684/) (2026)

## Abstract (arXiv)

The effectiveness of Convolutional Neural Networks stems in large part from their ability to exploit the translation invariance that is inherent in many learning problems. Recently, it was shown that CNNs can exploit other invariances, such as rotation invariance, by using group convolutions instead of planar convolutions. However, for reasons of performance and ease of implementation, it has been necessary to limit the group convolution to transformations that can be applied to the filters without interpolation. Thus, for images with square pixels, only integer translations, rotations by multiples of 90 degrees, and reflections are admissible. Whereas the square tiling provides a 4-fold rotational symmetry, a hexagonal tiling of the plane has a 6-fold rotational symmetry. In this paper we show how one can efficiently implement planar convolution and group convolution over hexagonal lattices, by re-using existing highly optimized convolution routines. We find that, due to the reduced anisotropy of hexagonal filters, planar HexaConv provides better accuracy than planar convolution with square filters, given a fixed parameter budget. Furthermore, we find that the increased degree of symmetry of the hexagonal grid increases the effectiveness of group convolutions, by allowing for more parameter sharing. We show that our method significantly outperforms conventional CNNs on the AID aerial scene classification dataset, even outperforming ImageNet pre-trained models.