# The Locality and Symmetry of Positional Encodings

arXiv: https://arxiv.org/abs/2310.12864 · HTML: https://mlsanity.com/paper/2310.12864/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 72 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [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)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Efficient Streaming Language Models with Attention Sinks](https://mlsanity.com/paper/2309.17453/) (2023)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [SentEval: An Evaluation Toolkit for Universal Sentence Representations](https://mlsanity.com/paper/1803.05449/) (2018)
- [Fine-grained Analysis of Sentence Embeddings Using Auxiliary Prediction Tasks](https://mlsanity.com/paper/1608.04207/) (2016)
- [Rethinking Positional Encoding in Language Pre-training](https://mlsanity.com/paper/2006.15595/) (2020)
- [Masked Language Modeling and the Distributional Hypothesis: Order Word Matters Pre-training for Little](https://mlsanity.com/paper/2104.06644/) (2021)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [Multilingual Constituency Parsing with Self-Attention and Pre-Training](https://mlsanity.com/paper/1812.11760/) (2018)
- [Sharp Nearby, Fuzzy Far Away: How Neural Language Models Use Context](https://mlsanity.com/paper/1805.04623/) (2018)

## Built on by (most cited first, 1 of 1)

- [Query-Level Uncertainty in Large Language Models](https://mlsanity.com/paper/2506.09669/) (2025)

## Abstract (arXiv)

Positional Encodings (PEs) are used to inject word-order information into transformer-based language models. While they can significantly enhance the quality of sentence representations, their specific contribution to language models is not fully understood, especially given recent findings that various positional encodings are insensitive to word order. In this work, we conduct a systematic study of positional encodings in Bidirectional Masked Language Models (BERT-style) , which complements existing work in three aspects: (1) We uncover the core function of PEs by identifying two common properties, Locality and Symmetry; (2) We show that the two properties are closely correlated with the performances of downstream tasks; (3) We quantify the weakness of current PEs by introducing two new probing tasks, on which current PEs perform poorly. We believe that these results are the basis for developing better PEs for transformer-based language models. The code is available at faGithub~ urlhttps://github.com/tigerchen52/localitysymmetry