# An Introduction to Transformers

arXiv: https://arxiv.org/abs/2304.10557 · HTML: https://mlsanity.com/paper/2304.10557/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 16 references that are in the map.
- First posted on arXiv 20 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Rethinking and Improving Relative Position Encoding for Vision Transformer](https://mlsanity.com/paper/2107.14222/) (2021)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Formal Algorithms for Transformers](https://mlsanity.com/paper/2207.09238/) (2022)

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

- [Mathematics of Data Science](https://mlsanity.com/paper/2607.11938/) (2026)

## Abstract (arXiv)

The transformer is a neural network component that can be used to learn useful representations of sequences or sets of data-points. The transformer has driven recent advances in natural language processing, computer vision, and spatio-temporal modelling. There are many introductions to transformers, but most do not contain precise mathematical descriptions of the architecture and the intuitions behind the design choices are often also missing. Moreover, as research takes a winding path, the explanations for the components of the transformer can be idiosyncratic. In this note we aim for a mathematically precise, intuitive, and clean description of the transformer architecture. We will not discuss training as this is rather standard. We assume that the reader is familiar with fundamental topics in machine learning including multi-layer perceptrons, linear transformations, softmax functions and basic probability.