Time: Friday, January 9, 2:30-3:30PM      Location: Walters M307

Geometry-aware generative models for scientific data generation

Abstract:

Biological and biochemical data are increasingly high-dimensional, noisy, but we can take advantage of the fact that they are constrained to low-dimensional manifolds that encode meaningful state spaces, dynamics, and regulatory structure. In this talk, I will present a unifying view of generative modeling for manifold-structured scientific data, focusing on methods that explicitly learn and exploit geometry rather than density alone. I will begin with SUGAR (synthesis using geometrically-aligned random walks), a graph-based diffusion framework for geometry-aware data generation that samples evenly along learned manifolds, enabling exploration of rare or undersampled biological states. Building on this foundation, I will show how neural networks yield more generalizable and expressive models of manifold geometry. I will first discuss our PHATE manifold learning and dimensionality reduction method, and how its diffusion geometry allows regularized autoencoders that faithfully capture global and local structure. I will then introduce our Neural FIM (Fisher Information Metric) framework, which leverages the autoencoder pullback to learn a continuous Riemannian metric from data, enabling principled measurement of volume and sampling along geodesics. Next, I will present GAGA (geometry-aware generative autoencoders), which generalizes this framework to arbitrary metrics and multiple generative modes, allowing interpolation, transport, and geodesic generation on complex biological manifolds. Finally, I will show how our new method RiTINI (Regulatory interaction network inference) complements these generative approaches by inferring dynamic regulatory networks from manifold-respecting trajectories, including those produced by GAGA or MIOFlow. Together, these methods provide a geometry-first framework for generative modeling, dynamics, and mechanism discovery in biology.

Bio:

Dr. Smita Krishnaswamy is an Associate Professor of Genetics and Computer Science at the Yale School of Medicine. She holds affiliations with the Applied Mathematics program, the Computational Biology and Bioinformatics program, the Yale Center for Biomedical Data Science, and the Yale Cancer Center. Her research is centered on the development of novel machine learning techniques to interpret high-dimensional biomedical data. Dr. Krishnaswamy’s lab specializes in creating unsupervised methods, particularly using manifold learning and deep learning, to visualize, denoise, and reveal hidden structures within complex datasets. These powerful algorithms have been applied across a wide range of biological data, including single-cell RNA-sequencing and cytometry, to advance our understanding of immunology, cancer, neuroscience, and developmental biology. She earned her Ph.D. in Computer Science and Engineering from the University of Michigan.