Colloquium Series: Dr. Nina Miolane, University of California, Santa Barbara

Dr. Nina Miolane, Assistant Professor, University of California, Santa Barbara

Department of electrical & Computer Engineering

Tuesday November 28, 2023 4pm Chapman Hall Rm. 125

Title: The Geometry of Neural Manifolds

Abstract: 

In machine learning, the manifold hypothesis states that many real-world high-dimensional data sets actually lie along low-dimensional latent manifolds inside the high-dimensional space. In neurosciences, the neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In this work, we combine topological deep generative models and extrinsic Riemannian geometry to quantify the structure of (neural) manifolds. This approach (i) computes an explicit parameterization of the manifolds and (ii) estimates their local extrinsic curvature–hence quantifying their shape within the high-dimensional neural state space. Importantly, our methodology is invariant with respect to transformations that do not bear meaningful neuroscience information, such as permutation of the order in which neurons are recorded. We show empirically that we correctly estimate the geometry of synthetic manifolds generated from smooth deformations of circles, spheres, and tori, using realistic noise levels. We additionally validate our methodology on simulated and real neural recordings, and show that we recover geometric structure known to exist in hippocampal place cells. We expect this approach to open new avenues of inquiry into geometric neural correlates of perception and behavior, and quantify manifolds’ geometry in natural and artificial neural networks.

Bio:

Nina Miolane is an Assistant Professor of Geometric Learning at UC Santa Barbara. Her lab’s research explores the geometric foundations of natural and artificial intelligence, and co-develops the open-source python packages: Geomstats and TopoX.

Dr. Miolane received her M.S. in Mathematics from Ecole Polytechnique (France) & Imperial College (UK), and her Ph.D. in Computer Science from INRIA (France) in collaboration with Stanford University. She was an instructor in the French Army for a year and was decorated for succeeding in a commando training program. After her studies, Nina spent two years at Stanford University in Statistics as a postdoctoral fellow and worked as a deep learning software engineer in the Silicon Valley.

At UCSB, Nina directs the BioShape Lab, whose goal is to explore the “geometries of life”. Her research investigates how the shapes of proteins, cells, and organs relate to their biological functions, how abnormal shape changes correlate with pathologies, and how these findings can help design new automatic diagnosis tools. Her team also co-develops the open-source Geomstats library, a software that provides methods at the intersection of geometry and machine learning, to compute with geometric data such as biological shape data.

Dr. Miolane is a co-author of the book “Riemannian Geometric Statistics For Medical Imaging” and a co-inventor on patents in computational medicine. Research fundings include a NIH R01 grant on Biological and Mathematical Science, a NSF SCALE MoDL grant on Mathematical and Scientific Foundations of Deep Learning, Google Season of Code and Noyce Initiative UC Partnerships in Computational Transformation Program grant for “The University of California Women’s Brain Initiative – Leveraging AI to Advance Women’s Health. Dr. Miolane was the recipient of the L’Oréal-Unesco for Women in Science Award, the Hellman Fellow Award, a UCSB Academic Senate Award, UCSB Prowess Fellowship, and a UC Regent’s Junior Faculty Award.

In her free time, Dr. Miolane adventures in the golden state’s outdoors, hiking in the mountains, riding motorcycles along the coast, or piloting single-engine airplanes in the Californian skies.