Steven Smith: Say It With Matrices?

Join us for ASE-60, where we celebrate the life and the career of Professor Alan Stuart Edelman, on the occasion of his 60th birthday: https://math.mit.edu/events/ase60celebration/

My career and contributions have been greatly influenced by Alan Edelman’s work on random matrices, optimization, scientific computing, along with his cherished collaboration and advice. This talk starts with a brief survey of how Alan and his ideas provide a strong foundation for applied research in important areas: random matrices and optimization are applied extensively in diverse fields from sensor arrays to social media networks. The recent, interwoven developments of networked multimedia content sharing and neural-network-based large language and diffusion models would appear to provide a natural home for this theory, which has a great deal to say about the underlying matrices and algorithms that describe both the data and nonlinear optimization methods used in AI. Yet progress in these AI fields has evolved rapidly and spectacularly almost wholly without explicit insights from matrix theory, in spite of their deep reliance on random matrices. The second part of the talk uses related experience from recent work on MCMC- and LLM-based causal inference of real-world network influence to describe the challenges and potential opportunities of applying matrix theory to these recent developments.