7 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…