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Continuum Limits of Ollivier’s Ricci Curvature on data clouds: pointwise consistency and global lower bounds
Let M in R^d denote a low-dimensional manifold and let X={x1, …, xn} be a collection of points uniformly sampled from M. We …
N. García Trillos, M. Weber
PDF Project
Disciplined Geodesically Convex Programming: A Symbolic Framework for Verifying Geodesic Convexity
Convex programming plays a fundamental role in machine learning, data science, and engineering. Disciplined Programming tests and …
A. Cheng*, V. Dixit*, M. Weber
Preprint Project
Neural Algorithmic Reasoning for Approximate k-Coloring with Recursive Warm Starts
This paper studies neural algorithmic reasoning for approximate k-coloring, a relaxed graph-coloring problem that seeks to minimize …
K. Vanderbush, M. Weber
Preprint PDF Project
Structured Regularization for Constrained Optimization on the SPD Manifold
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of …
A. Cheng*, M. Weber
Preprint Project
Curvature-based Clustering on Graphs
Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which …
Y. Tian, Z. Lubberts, M. Weber
PDF Project
Geometric Machine Learning
This article surveys geometric machine learning as an approach to identifying and exploiting structure in high-dimensional data. It …
M. Weber
Project
Structured Regularization for SPD Optimization with Side Information
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of …
A. Cheng*, M. Weber
PDF Project
Graph Pooling via Ricci Flow
Graph Machine Learning often involves the clustering of nodes based on similarity structure encoded in the graph’s topology and …
A. Feng, M. Weber
PDF Project
Controlling Unknown Linear Dynamics with Bounded Multiplicative Regret
We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We …
J. Carruth, M. F. Eggl, C. Fefferman, C. W. Rowley, M. Weber
Preprint PDF Project
Riemannian Optimization via Frank-Wolfe Methods
We study projection-free methods for constrained Riemannian optimization. We propose a Riemannian Frank-Wolfe (RFW) method that handles …
M. Weber, S. Sra
PDF Code Project Video