Understanding Transformers and Attention Mechanisms: An Introduction for Applied Mathematicians

TL;DR

This paper introduces the attention mechanism in Transformer models, explaining how it encodes semantic information, describes variants like Multi-Headed Attention, and discusses methods to optimize computational efficiency, targeting applied mathematicians.

Contribution

It provides an accessible introduction to Transformer attention mechanisms, including variants and efficiency techniques, tailored for the applied mathematics community.

Findings

Explains how text is encoded as vectors for attention processing.

Describes Multi-Headed Attention and Transformer architecture variants.

Discusses methods like KV caching and Latent Attention to reduce costs.

Abstract

This document provides a brief introduction to the attention mechanism used in modern language models based on the Transformer architecture. We first illustrate how text is encoded as vectors and how the attention mechanism processes these vectors to encode semantic information. We then describe Multi-Headed Attention, examine how the Transformer architecture is built and look at some of its variants. Finally, we provide a glimpse at modern methods to reduce the computational and memory cost of attention, namely KV caching, Grouped Query attention and Latent Attention. This material is aimed at the applied mathematics community and was written as introductory presentation in the context of the IPAM Research Collaboration Workshop entitled "Randomized Numerical Linear Algebra" (RNLA), for the project: "Randomization in Transformer models".