# Translational Equivariance in Kernelizable Attention

arXiv: https://arxiv.org/abs/2102.07680 · HTML: https://mlsanity.com/paper/2102.07680/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 23 references that are in the map.
- First posted on arXiv 15 Feb 2021.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Efficient Transformers: A Survey](https://mlsanity.com/paper/2009.06732/) (2020)
- [Efficient Content-Based Sparse Attention with Routing Transformers](https://mlsanity.com/paper/2003.05997/) (2020)
- [Convolutional Conditional Neural Processes](https://mlsanity.com/paper/1910.13556/) (2019)
- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [A Data and Compute Efficient Design for Limited-Resources Deep Learning](https://mlsanity.com/paper/2004.09691/) (2020)

## Built on by (most cited first, 5 of 5)

- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [ComRoPE: Scalable and Robust Rotary Position Embedding Parameterized by Trainable Commuting Angle Matrices](https://mlsanity.com/paper/2506.03737/) (2025)
- [Linearized Relative Positional Encoding](https://mlsanity.com/paper/2307.09270/) (2023)
- [Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers](https://mlsanity.com/paper/2302.01925/) (2023)
- [Simplex Random Features](https://mlsanity.com/paper/2301.13856/) (2023)

## Abstract (arXiv)

While Transformer architectures have show remarkable success, they are bound to the computation of all pairwise interactions of input element and thus suffer from limited scalability. Recent work has been successful by avoiding the computation of the complete attention matrix, yet leads to problems down the line. The absence of an explicit attention matrix makes the inclusion of inductive biases relying on relative interactions between elements more challenging. An extremely powerful inductive bias is translational equivariance, which has been conjectured to be responsible for much of the success of Convolutional Neural Networks on image recognition tasks. In this work we show how translational equivariance can be implemented in efficient Transformers based on kernelizable attention - Performers. Our experiments highlight that the devised approach significantly improves robustness of Performers to shifts of input images compared to their naive application. This represents an important step on the path of replacing Convolutional Neural Networks with more expressive Transformer architectures and will help to improve sample efficiency and robustness in this realm.