# Vocabulary In-Context Learning in Transformers: Benefits of Positional Encoding

arXiv: https://arxiv.org/abs/2511.06376 · HTML: https://mlsanity.com/paper/2511.06376/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 45 of its 60 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## Builds on (most cited first, 30 of 45)

- [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)
- [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)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Retrieval-Augmented Generation for Large Language Models: A Survey](https://mlsanity.com/paper/2312.10997/) (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)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Training Large Language Models to Reason in a Continuous Latent Space](https://mlsanity.com/paper/2412.06769/) (2024)
- [In-Context Retrieval-Augmented Language Models](https://mlsanity.com/paper/2302.00083/) (2023)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Are Transformers universal approximators of sequence-to-sequence functions?](https://mlsanity.com/paper/1912.10077/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Transformers learn to implement preconditioned gradient descent for in-context learning](https://mlsanity.com/paper/2306.00297/) (2023)
- [Is GPT-3 a Good Data Annotator?](https://mlsanity.com/paper/2212.10450/) (2022)
- [Rethinking Positional Encoding in Language Pre-training](https://mlsanity.com/paper/2006.15595/) (2020)
- [Want To Reduce Labeling Cost? GPT-3 Can Help](https://mlsanity.com/paper/2108.13487/) (2021)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Large Language Models Are Latent Variable Models: Explaining and Finding Good Demonstrations for In-Context Learning](https://mlsanity.com/paper/2301.11916/) (2023)

## Abstract (arXiv)

Numerous studies have demonstrated that the Transformer architecture possesses the capability for in-context learning (ICL). In scenarios involving function approximation, context can serve as a control parameter for the model, endowing it with the universal approximation property (UAP). In practice, context is represented by tokens from a finite set, referred to as a vocabulary, which is the case considered in this paper, i.e., vocabulary in-context learning (VICL). We demonstrate that VICL in single-layer Transformers, without positional encoding, does not possess the UAP; however, it is possible to achieve the UAP when positional encoding is included. Several sufficient conditions for the positional encoding are provided. Our findings reveal the benefits of positional encoding from an approximation theory perspective in the context of ICL.