Emergence and Generalization in Machine Learning --- Nigel Goldenfeld

Seminar by Nigel Goldenfeld, Department of Physics and Halıcıoğlu Data Science Institute, University of California San Diego. https://guava.physics.ucsd.edu/~nigel/ This talk is given at the level of a Colloquium, mostly accessible to first year graduate students, and no prior detailed knowledge of machine learning or advanced statistical mechanics is expected of the audience.  Delivered at Rutgers University Mathematical Physics online seminar on Wednesday Sept. 30 2026. Part of series at https://cmsr.rutgers.edu/newsevents-c... TITLE: Emergence and Generalization in Machine Learning ABSTRACT: I present some brief remarks about emergence from a physicist's perspective, emphasizing the often overlooked feature of generalized rigidity.  Then, I discuss the role of emergence in understanding the remarkable ability of modern neural networks to generalize.  The performance on generalization improves with increasing network capacity, even when the number of model parameters or effective degrees of freedom exceeds the number of training data points.  I show how this phenomenon is an example of emergent behavior, and specifically calculate the phase transition behavior, emergent rigidity, universal scaling theory and the specific features that give rise to the good generalization performance of modern neural networks. Our results are distinct from earlier work, because we calculate the time-dependence specifically, not just the least norm equilibrium solutions. This is what enables us to identify the origin of the emergent behavior. Our work provides a specific framework with which to understand emergent behavior in artificial neural networks, and I outline some future directions. Work performed in collaboration with Chan Li. Preprint at: https://arxiv.org/pdf/2607.04135