Michel Fabrice Serret

Michel Fabrice Serret, Alice Cortinovis, Yijun Dong et al.

The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale inference. This has motivated a rapidly growing body of work aimed at accelerating attention through approximation and reformulation. In this survey, we revisit attention mechanisms through the lens of numerical analysis, with a particular emphasis on tools and perspectives from numerical linear algebra. Our goal is twofold: first, we aim to systematically review and classify fast approximation methods according to the numerical principles they exploit. These include sparsity and clustering approaches, low-rank and subspace projection techniques, randomized sketching methods, and tensor-based decompositions. We also discuss kernel-inspired reformulations of attention and recent architectural variants, such as Latent Attention, that modify the standard softmax formulation to improve efficiency. Second, by presenting these developments within a unified mathematical framework, we aim to bridge the gap between disciplines and highlight opportunities for further contributions from computational mathematics, particularly numerical linear algebra, to the design of scalable attention mechanisms.

Michel Fabrice Serret

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".