[CS] TODAY: Ryan Robinett Dissertation Defense/Dec 10, 2025

[via cs]

This is an announcement of Ryan Robinett's Dissertation Defense.
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Candidate: Ryan Robinett

Date: Wednesday, December 10, 2025

Time: 12 pm CST

Remote Location: https://uchicago.zoom.us/j/99036933620?pwd=tExOI1TZe7JIKgYkEyaPuDP9UglM0a.1

Location: JCL 298

Title: Novel computational and geometric frameworks for manifold learning, Riemannian optimization, and feature selection

Abstract: In machine learning, Riemannian manifolds offer a useful abstraction for approximating commonly encountered, non-Euclidean empirical data distributions and optimization state spaces. Further, the “manifold hypothesis”, which states that the support of an empirical data distribution can be modeled as a low-dimensional submanifold of the ambient space, is increasingly accepted as integral part of data analysis across domains. This is particularly true in the biological sciences, where unifying a framework across orders of magnitude of spatial resolution (e.g., from cells to organoids to organisms) requires intelligible simplification and abstraction at each scale. While researchers assume the manifold hypothesis in various domains, techniques that infer manifold approximations forfeit geometric and topological ground truth in simple test cases. Generalizing machine learning techniques to manifolds is a major challenge, even when an underlying manifold structure is known, as is the case in several machine learning tasks. This is largely due to the difficulty of computing exponential maps and parallel transports, the natural differential-geometric forms of first-order updates. Here, we present simple, novel approaches for representing and learning submanifolds embedded in Euclidean space or in the space of positive measures on a compact metric space. These approaches are theoretically motivated, interpretable, and amenable to downstream applications of Riemannian machine learning. Concretely, first, we present algorithms for learning manifolds from point cloud data and efficiently approximating differential-geometric primitives on them via construction of an atlas object. We then give an approach to learn representations of low-dimensional submanifolds in an optimal transport geometry, which we use to study morphological variation in Drosophila melanogaster wings. Lastly, we describe a hybrid quantum-classical feature selection method, inspired by the phenomenon of parameter transfer in the recursive quantum approximate optimization algorithm (RQAOA); parameter transfer provides a mapping between RQAOA subproblems, which, by extending the support to the unit hypercube, induces a manifold alignment.

Advisors: Lorenzo Orecchia and Samantha Riesenfeld

Committee Members: Lorenzo Orecchia, Fred Chong, Shmuel Weinberger , and Samantha Riesenfeld