# Equivariant Transformer Networks

arXiv: https://arxiv.org/abs/1901.11399 · HTML: https://mlsanity.com/paper/1901.11399/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2019.

## Built on by (most cited first, 30 of 35)

- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Deep Learning for UAV-based Object Detection and Tracking: A Survey](https://mlsanity.com/paper/2110.12638/) (2021)
- [PUG: Photorealistic and Semantically Controllable Synthetic Data for Representation Learning](https://mlsanity.com/paper/2308.03977/) (2023)
- [RoI Tanh-polar Transformer Network for Face Parsing in the Wild](https://mlsanity.com/paper/2102.02717/) (2021)
- [Self-Interpretable Model with TransformationEquivariant Interpretation](https://mlsanity.com/paper/2111.04927/) (2021)
- [Maximum Class Separation as Inductive Bias in One Matrix](https://mlsanity.com/paper/2206.08704/) (2022)
- [Learning the RoPEs: Better 2D and 3D Position Encodings with STRING](https://mlsanity.com/paper/2502.02562/) (2025)
- [Equivariance Discovery by Learned Parameter-Sharing](https://mlsanity.com/paper/2204.03640/) (2022)
- [LieRE: Lie Rotational Positional Encodings](https://mlsanity.com/paper/2406.10322/) (2024)
- [Addressing the Topological Defects of Disentanglement via Distributed Operators](https://mlsanity.com/paper/2102.05623/) (2021)
- [Spatially Covariant Lesion Segmentation](https://mlsanity.com/paper/2301.07895/) (2023)
- [Training or Architecture? How to Incorporate Invariance in Neural Networks](https://mlsanity.com/paper/2106.10044/) (2021)
- [Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration](https://mlsanity.com/paper/2202.03967/) (2022)
- [Tilt your Head: Activating the Hidden Spatial-Invariance of Classifiers](https://mlsanity.com/paper/2405.03730/) (2024)
- [Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks](https://mlsanity.com/paper/2408.05496/) (2024)
- [Robust Self-Supervised Learning with Lie Groups](https://mlsanity.com/paper/2210.13356/) (2022)
- [Using and Abusing Equivariance](https://mlsanity.com/paper/2308.11316/) (2023)
- [Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictors](https://mlsanity.com/paper/2309.16646/) (2023)
- [Group Downsampling with Equivariant Anti-aliasing](https://mlsanity.com/paper/2504.17258/) (2025)
- [Geometrically Constrained and Token-Based Probabilistic Spatial Transformers](https://mlsanity.com/paper/2509.11218/) (2025)
- [Emergent Riemannian geometry over learning discrete computations on continuous manifolds](https://mlsanity.com/paper/2512.00196/) (2025)
- [A Simple Strategy to Provable Invariance via Orbit Mapping](https://mlsanity.com/paper/2209.11916/) (2022)
- [Efficient Rotation Invariance in Deep Neural Networks through Artificial Mental Rotation](https://mlsanity.com/paper/2311.08525/) (2023)
- [Artificial Intelligence for Direct Prediction of Molecular Dynamics Across Chemical Space](https://mlsanity.com/paper/2505.16301/) (2025)
- [FILTRA: Rethinking Steerable CNN by Filter Transform](https://mlsanity.com/paper/2105.11636/) (2021)
- [Invariance-based Multi-Clustering of Latent Space Embeddings for Equivariant Learning](https://mlsanity.com/paper/2107.11717/) (2021)
- [Augmenting Imitation Experience via Equivariant Representations](https://mlsanity.com/paper/2110.07668/) (2021)
- [Perspective Transformation Layer](https://mlsanity.com/paper/2201.05706/) (2022)
- [Hierarchical Self-Attention: Generalizing Neural Attention Mechanics to Multi-Scale Problems](https://mlsanity.com/paper/2509.15448/) (2025)

## Abstract (arXiv)

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the robustness of models towards pre-defined continuous transformation groups. Through the use of specially-derived canonical coordinate systems, ETs incorporate functions that are equivariant by construction with respect to these transformations. We show empirically that ETs can be flexibly composed to improve model robustness towards more complicated transformation groups in several parameters. On a real-world image classification task, ETs improve the sample efficiency of ResNet classifiers, achieving relative improvements in error rate of up to 15% in the limited data regime while increasing model parameter count by less than 1%.