# Attentive Group Equivariant Convolutional Networks

arXiv: https://arxiv.org/abs/2002.03830 · HTML: https://mlsanity.com/paper/2002.03830/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 30 of 63)

- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformers](https://mlsanity.com/paper/2310.10375/) (2023)
- [Is Attention Better Than Matrix Decomposition?](https://mlsanity.com/paper/2109.04553/) (2021)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [Geometric Algebra Transformer](https://mlsanity.com/paper/2305.18415/) (2023)
- [Learning Partial Equivariances from Data](https://mlsanity.com/paper/2110.10211/) (2021)
- [Unsupervised Learning of Group Invariant and Equivariant Representations](https://mlsanity.com/paper/2202.07559/) (2022)
- [Attention Mechanism in Neural Networks: Where it Comes and Where it Goes](https://mlsanity.com/paper/2204.13154/) (2022)
- [E(2)-Equivariant Vision Transformer](https://mlsanity.com/paper/2306.06722/) (2023)
- [Enabling equivariance for arbitrary Lie groups](https://mlsanity.com/paper/2111.08251/) (2021)
- [Learnable Polyphase Sampling for Shift Invariant and Equivariant Convolutional Networks](https://mlsanity.com/paper/2210.08001/) (2022)
- [Equivariant Networks for Pixelized Spheres](https://mlsanity.com/paper/2106.06662/) (2021)
- [Making Vision Transformers Truly Shift-Equivariant](https://mlsanity.com/paper/2305.16316/) (2023)
- [Truly Scale-Equivariant Deep Nets with Fourier Layers](https://mlsanity.com/paper/2311.02922/) (2023)
- [Group Equivariant Subsampling](https://mlsanity.com/paper/2106.05886/) (2021)
- [Addressing the Topological Defects of Disentanglement via Distributed Operators](https://mlsanity.com/paper/2102.05623/) (2021)
- [Alias-Free Convnets: Fractional Shift Invariance via Polynomial Activations](https://mlsanity.com/paper/2303.08085/) (2023)
- [Learning with Capsules: A Survey](https://mlsanity.com/paper/2206.02664/) (2022)
- [VTAE: Variational Transformer Autoencoder with Manifolds Learning](https://mlsanity.com/paper/2304.00948/) (2023)
- [Investigating how ReLU-networks encode symmetries](https://mlsanity.com/paper/2305.17017/) (2023)
- [Steerable Transformers for Volumetric Data](https://mlsanity.com/paper/2405.15932/) (2024)
- [Diffusion Generative Modeling on Lie Group Representations](https://mlsanity.com/paper/2502.02513/) (2025)
- [Flopping for FLOPs: Leveraging equivariance for computational efficiency](https://mlsanity.com/paper/2502.05169/) (2025)
- [Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration](https://mlsanity.com/paper/2202.03967/) (2022)
- [FRED: Towards a Full Rotation-Equivariance in Aerial Image Object Detection](https://mlsanity.com/paper/2401.06159/) (2023)
- [Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks](https://mlsanity.com/paper/2409.11772/) (2024)
- [GradMetaNet: An Equivariant Architecture for Learning on Gradients](https://mlsanity.com/paper/2507.01649/) (2025)
- [Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms](https://mlsanity.com/paper/2104.11244/) (2021)
- [SE(3) Equivariant Ray Embeddings for Implicit Multi-View Depth Estimation](https://mlsanity.com/paper/2411.07326/) (2024)

## Abstract (arXiv)

Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we present attentive group equivariant convolutions, a generalization of the group convolution, in which attention is applied during the course of convolution to accentuate meaningful symmetry combinations and suppress non-plausible, misleading ones. We indicate that prior work on visual attention can be described as special cases of our proposed framework and show empirically that our attentive group equivariant convolutional networks consistently outperform conventional group convolutional networks on benchmark image datasets. Simultaneously, we provide interpretability to the learned concepts through the visualization of equivariant attention maps.