We are pleased to announce the publication of Deep learning, transformers, and graph neural networks: a linear algebra perspective in Numerical Algorithms.

Authors: Abdelkader Baggag and Yousef Saad (SIAM von Neumann Award winner).

Abstract (brief): As AI permeates nearly every field of science and engineering, this article invites the numerical linear algebra (NLA) community to engage directly with the foundations of deep learning. It argues that modern AI rests on four pillars –data, optimization, statistical reasoning, and linear algebra– and shows how, from the first step of mapping words to token embeddings, large language models operate on vectors, matrices, and tensors. The paper offers a linear-algebraic tour of core deep learning components, including multilayer perceptrons and attention mechanisms central to LLMs, and highlights graph-based methods such as Graph Convolutional Networks and Graph Attention Networks. It concludes with perspectives on how NLA can continue to shape the future of AI.

Read the paper (DOI) https://doi.org/10.1007/s11075-025-02218-2