When: Tuesday, March 25, 2025 from 12pm – 1pm
Where: Amy Gutmann Hall, Room 414
Title: “Learning as Manifold Packing”
Abstract: Contrastive self-supervised learning based on point-wise comparisons has been widely studied for vision tasks. In the neural cortex, neuronal responses to distinct stimulus classes are organized into geometric structures known as neural manifolds. Accurate classification of stimuli can be achieved by effectively separating these manifolds, akin to solving a packing problem. Despite its intuitive appeal, neurobiological relevance, and potential for enhancing interpretability, the perspective of neural manifold packing in contrastive learning remains largely unexplored. In this talk, Stefano Martiniani will discuss how concepts from statistical and soft matter physics can be leveraged to analyze neural manifold packing dynamics under stochastic gradient descent and related optimization algorithms. This perspective not only informs the development of highly interpretable self-supervised learning methods but also reveals striking parallels between the energy landscapes of sphere packings and the loss landscapes of neural networks. Stefano will present a combination of numerical experiments and analytical theory demonstrating the depth of these analogies.
Bio: Stefano Martiniani is an Assistant Professor of Physics, Chemistry, and Mathematics. He is a core member of NYU’s Center for Soft Matter Research and the Simons Center for Computational Physical Chemistry, and an affiliate of the Center for Data Science. Prof. Martiniani’s research focuses on the computational and statistical physics of complex systems. He directs an interdisciplinary research group that explores neural circuit theories of brain function, the statistical mechanics of systems far from equilibrium (such as the statistical physics of learning and living systems), high-dimensional energy landscapes, disordered metamaterials, and AI for science. In the context of AI research, he leads prominent open science initiatives related to data standards, data repositories, and machine learning frameworks. He has pioneered techniques to accurately determine the volume of high-dimensional basins of attraction in generic dynamical systems, elucidating their complex geometric structures and resolving decades-old questions in the statistical physics of disordered systems, most notably the Edwards hypothesis, which posits that all jammed packings occur with equal probability. He introduced information-theoretic approaches to quantify order and irreversibility in systems far from equilibrium, significantly advanced the understanding of the transport and energetics of bacterial rectification, and developed innovative methods for engineering and characterizing function in disordered systems (such as the state-of-the-art algorithm for generating point patterns with desired spectral properties, with applications including the design of optical metamaterials and sampling). His research is supported by the NSF, NIH, Chan Zuckerberg Initiative (CZI), and the Simons Foundation.
