[WTI-trainee] Fw: Course announcement for CPSC 6440-- Geometric and Topological Methods in ML

[Remole, Kelley]

See below for a new course in the fall taught by Smita Krishnaswamy.


Kelley Remole, PhD, MS
Managing Director
Wu Tsai Institute, Yale University
kelley.remole at yale.edu
c: 917-254-2992

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From: Krishnaswamy, Smita
Sent: Wednesday, April 30, 2025 7:59 AM
Subject: Course announcement for CPSC 6440-- Geometric and Topological Methods in ML


Hello All,
I’m teaching a new course in fall 2025 in Computer Science/Math for students interested in the intersection between machine learning and computational methods: CPSC 6440: Geometric and Topological Methods in Machine Learning<https://courses.yale.edu/?details&srcdb=202503&crn=10645> (CPSC 6440 01 / MATH 5220 01).
This class will explore the idea that data has shape at multiple levels, and accounting for the shape leads to improvements in machine learning based inference from data. First we will model the shape of data using data geometry, which involves modeling data as graphs and higher order objects such as simplicial complexes. We will show that such models help derive meaningful embeddings of the data (Laplacian eigenmaps, diffusion maps, tSNE, UMAP, PHATE), clustering (community detection, spectral clustering), trajectories (diffusion components, pseudotime). We will then delve into the underpinnings of these graphs as discretization of Riemannian manifolds, and introduce ideas from Riemannian manifolds such as the metric tensor, geodesics, volume, Levi-Civita connection, curvature, volume. We then go back to data to show how neural networks can help translate these concepts directly to data via implicit continuous models they make of discrete data. Here we discuss recent deep learning techniques such as Riemannian flow matching, Neural FIM, GAGA that incorporate core ideas from Riemannian geometry, particularly in generative modeling. We will also cover applications in computational biology and neuroscience.  The class will also involve a final research project.

Smita
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