External seminar - James Sethna & Jason Kim (Cornell University)

Abstract: Despite the complex and high-dimensional spaces occupied by biological systems, we can make progress in understanding and modeling their behavior. This is because their behavior space is essentially low dimensional: it is only sensitive (wide) to a few parameter combinations, thereby forming 'hyperribbons' with a hierarchy of widths. In recent years, we have shown that multiparameter models in many fields including systems biology possess this hyperribbons structure, allowing us to reduce their complexity in a principled and interpretable way. In this talk, we will first develop theories in physics and information geometry to explain why low-dimensional manifolds arise in high-dimensional spaces and discuss how to capture simple and mechanistic understanding from complex models of physics and systems biology. Then we will extend these ideas to deep neural networks by capturing these low-dimensional model manifolds from high-dimensional data through curvature-regularized variational autoencoders. We apply our methods to data from the gene expression of cancer and cell differentiation, and from neural activity of hippocampal representations of space and time. By imbuing dimensionality reduction with the modeling power of physics, we demonstrate how to build model manifolds that are biologically interpretable, predictive on new (out-of-distribution) data, and capture the relevant low-dimensional biology that globally organize low-dimensional behavior in high-dimensional spaces.