6 citations · 11 across the 8 of their papers we have counts for
9 papers
Embedding Dimension Lower Bounds for Universality of Deep Sets and Janossy Pooling
Ali Syed, Aditya Nambiar, Jonathan W. Siegel
In many practical applications it is important to build symmetries into neural network architectures. Consider the important case of permutation symmetry on point clouds consisting…
Quantitative Approximation Rates for Group Equivariant Learning
Jonathan W. Siegel, Snir Hordan, Hannah Lawrence +2
The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitat…
In-Context Multi-Operator Learning with DeepOSets
Shao-Ting Chiu, Aditya Nambiar, Ali Syed +2
An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linea…
Acceleration via silver step-size on Riemannian manifolds with applications to Wasserstein space
Jiyoung Park, Abhishek Roy, Jonathan W. Siegel +1
There is extensive literature on accelerating first-order optimization methods in a Euclidean setting. Under which conditions such acceleration is feasible in Riemannian optimizati…
Optimal Recovery Meets Minimax Estimation
Ronald DeVore, Robert D. Nowak, Rahul Parhi +2
A fundamental problem in statistics and machine learning is to estimate a function from possibly noisy observations of its point samples. The goal is to design a numerical algo…
On the expressiveness and spectral bias of KANs
Yixuan Wang, Jonathan W. Siegel, Ziming Liu +1
Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the…
Convergence and error control of consistent PINNs for elliptic PDEs
Andrea Bonito, Ronald DeVore, Guergana Petrova +1
We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize…
Efficient Structure-Informed Featurization and Property Prediction of Ordered, Dilute, and Random Atomic Structures
Adam M. Krajewski, Jonathan W. Siegel, Zi-Kui Liu
Structure-informed materials informatics is a rapidly evolving discipline of materials science relying on the featurization of atomic structures or configurations to construct vect…
Equivariant Frames and the Impossibility of Continuous Canonicalization
Nadav Dym, Hannah Lawrence, Jonathan W. Siegel
Canonicalization provides an architecture-agnostic method for enforcing equivariance, with generalizations such as frame-averaging recently gaining prominence as a lightweight and…