## Center for Applied Mathematics Colloquium

Abstract: "Science is the quest for understanding the natural world through observation and reasoning. The abstraction of the behavior of a system or a phenomenon into a consistent mathematical model is instrumental for a variety of applications in science and engineering. In the context of scientific discovery, a fundamental problem is to explain natural phenomena in a manner consistent with both (noisy) experimental data, and a body of (possibly inexact and incomplete) background knowledge about the laws of the universe. Historically, models were manually derived in a first-principles deductive fashion. The first-principles approach often offers the derivation of interpretable symbolic models of remarkable levels of universality while being substantiated by little data. Nonetheless, derivation of such models is time-consuming and relies heavily upon domain expertise. Conversely, with the rising pervasiveness of statistical AI and data-driven approaches, automated, rapid construction and deployment of models has become a reality. Many data-driven modeling techniques demonstrate remarkable scalability due to their reliance upon predetermined, exploitable model form (functional form) structures. Such structures, entail non-interpretable models, demand Big Data for training, and provide limited predictive power for out-of-set instances.

In this talk, we will review some of the recent transformations in the field, and the ongoing attempts to bridge the divide between statistical AI and symbolic AI. We will begin by discussing algorithms that can search for free-form symbolic models, where neither the structure nor the set of operator primitives is predetermined. We will proceed in reviewing innovations in the field of automated theorem proving (ATP) machinery, and discuss how ATPs can be harnessed to certify whether a candidate hypothesis model is conforming with background theory. Lastly, we shall discuss efforts to consistently unify the two approaches. These endeavors will promote the conceptualization of AI algorithms capable of making the discovery of principled, universal, and meaningful symbolic models, using small data and incomplete background theory. With some optimism, such approaches, can unveil to us the secrets of the universe."

Bio: Dr. Lior Horesh is a Principal Research Scientist and a Senior Manager of the Mathematics and Theoretical Computer Science group the MIT-IBM Research Lab. His group’s mission is to approach some of the big challenges the field of AI is facing, from a principled mathematical angle. This involves conceiving and bringing in state-of-the-art mathematical theories, algorithms and analysis tools, in hope of advancing fundamentally generalizability, scalability and interpretability of AI.

Additionally, Dr. Horesh holds an adjunct Associate Professor position at the Computer Science department of Columbia University where he teaches graduate level Advanced Machine Learning and Quantum Computing courses. Dr. Horesh Received his Ph.D. in 2006 from UCL and joined IBM in 2009.

Dr. Horesh's research work focuses on algorithmic and theoretical aspects of tensor algebra, numerical analysis, simulation of complex systems, inverse problems, non-linear optimization, experimental design, machine learning, quantum computing and the interplay between first principles models and AI in the context of symbolic scientific discovery.