153 citations · 253 across the 21 of their papers we have counts for
6 papers · 1 filter
Finsler Geometry, Graph Neural Networks, and You
T. Mitchell Roddenberry, Richard G. Baraniuk
Graph neural network architectures based on the graph Laplacian approximate the Laplace-Beltrami operator, thus limiting their application to isotropic operators. As a nonlinear al…
The Geometric Structure of Models Learning Sparse Data
Thomas Walker, T. Mitchell Roddenberry, Ahmed Imtiaz Humayun +2
The manifold hypothesis (MH) is often used to explain how machine learning can overcome the curse of dimensionality. However, the MH is only applicable in regimes where the trainin…
Rates and architectures for learning geometrically non-trivial operators
T. Mitchell Roddenberry, Leo Tzou, Ivan Dokmanić +2
Deep learning methods have proven capable of recovering operators between high-dimensional spaces, such as solution maps of PDEs and similar objects in mathematical physics, from v…
Signal Processing on Cell Complexes
T. Mitchell Roddenberry, Michael T. Schaub, Mustafa Hajij
The processing of signals supported on non-Euclidean domains has attracted large interest recently. Thus far, such non-Euclidean domains have been abstracted primarily as graphs wi…
An Impossibility Theorem for Node Embedding
T. Mitchell Roddenberry, Yu Zhu, Santiago Segarra
With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in t…
Principled Simplicial Neural Networks for Trajectory Prediction
T. Mitchell Roddenberry, Nicholas Glaze, Santiago Segarra
We consider the construction of neural network architectures for data on simplicial complexes. In studying maps on the chain complex of a simplicial complex, we define three desira…