# Sequence and Circle: Exploring the Relationship Between Patches

arXiv: https://arxiv.org/abs/2210.09871 · HTML: https://mlsanity.com/paper/2210.09871/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 18 Oct 2022.

## Builds on (most cited first, 20 of 20)

- [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)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Tokens-to-Token ViT: Training Vision Transformers from Scratch on ImageNet](https://mlsanity.com/paper/2101.11986/) (2021)
- [Transformers in Vision: A Survey](https://mlsanity.com/paper/2101.01169/) (2021)
- [CvT: Introducing Convolutions to Vision Transformers](https://mlsanity.com/paper/2103.15808/) (2021)
- [Exploring Plain Vision Transformer Backbones for Object Detection](https://mlsanity.com/paper/2203.16527/) (2022)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [PETR: Position Embedding Transformation for Multi-View 3D Object Detection](https://mlsanity.com/paper/2203.05625/) (2022)
- [Conditional Positional Encodings for Vision Transformers](https://mlsanity.com/paper/2102.10882/) (2021)
- [Attention Mechanisms in Computer Vision: A Survey](https://mlsanity.com/paper/2111.07624/) (2021)
- [Rethinking and Improving Relative Position Encoding for Vision Transformer](https://mlsanity.com/paper/2107.14222/) (2021)
- [Learning to Encode Position for Transformer with Continuous Dynamical Model](https://mlsanity.com/paper/2003.09229/) (2020)
- [Recent Advances in Vision Transformer: A Survey and Outlook of Recent Work](https://mlsanity.com/paper/2203.01536/) (2022)

## Abstract (arXiv)

The vision transformer (ViT) has achieved state-of-the-art results in various vision tasks. It utilizes a learnable position embedding (PE) mechanism to encode the location of each image patch. However, it is presently unclear if this learnable PE is really necessary and what its benefits are. This paper explores two alternative ways of encoding the location of individual patches that exploit prior knowledge about their spatial arrangement. One is called the sequence relationship embedding (SRE), and the other is called the circle relationship embedding (CRE). Among them, the SRE considers all patches to be in order, and adjacent patches have the same interval distance. The CRE considers the central patch as the center of the circle and measures the distance of the remaining patches from the center based on the four neighborhoods principle. Multiple concentric circles with different radii combine different patches. Finally, we implemented these two relations on three classic ViTs and tested them on four popular datasets. Experiments show that SRE and CRE can replace PE to reduce the random learnable parameters while achieving the same performance. Combining SRE or CRE with PE gets better performance than only using PE.