A. Neuman

activity

20192023

most citedTransferability of Graph Neural Networks using Graphon and Sampling Theories

1 citations · 3 across the 8 of their papers we have counts for

collaborators

8 papers

cs.LG2023★ 1 cited

Transferability of Graph Neural Networks using Graphon and Sampling Theories

A. Martina Neuman, Jason J. Bramburger

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained…

stat.ML2023★ 1 cited

Graph Laplacians on Shared Nearest Neighbor graphs and graph Laplacians on $k$ -Nearest Neighbor graphs having the same limit

A. Martina Neuman

A Shared Nearest Neighbor (SNN) graph is a type of graph construction using shared nearest neighbor information, which is a secondary similarity measure based on the rankings induc…

cs.LG2022

Theoretical guarantees for the advantage of GNNs over NNs in generalizing bandlimited functions on Euclidean cubes

A. Martina Neuman, Rongrong Wang, Yuying Xie

Graph Neural Networks (GNNs) have emerged as formidable resources for processing graph-based information across diverse applications. While the expressive power of GNNs has traditi…

math.DG2021

Restricted Riemannian geometry for positive semidefinite matrices

A. Martina Neuman, Yuying Xie, Qiang Sun

We introduce the manifold of {\it restricted} $n \times n$ positive semidefinite matrices of fixed rank $p$ , denoted $S (n, p)^{*}$ . The manifold itself is an open and dense submanifo…

math.CA2020

The pyramid operator

A. Martina Neuman

This paper gives a concept of an integral operator defined on a manifold $M$ consisting of triple of points in $R^{d}$ making up a regular $3$ -simplex with the origin. The…

math.CA2020★ 1 cited

$L^{2} \times L^{2} \times L^{2} \to L^{2/3}$ boundedness for trilinear multiplier operator

A. Martina Neuman

This paper discusses the boundedness of the trilinear multiplier operator $T_{m} (f_{1}, f_{2}, f_{3})$ , when the multiplier satisfies a certain degree of smoothness but with no decaying co…

math.CA2019

Anti-uniformity norms, anti-uniformity functions and their algebras on Euclidean spaces

A. Martina Neuman

Let $k \geq 2$ be an integer. Given a uniform function $f$ - one that satisfies $∥ f ∥_{U (k)} < \infty$ , there is an associated anti-uniform function $g$ - one that satisfied $\|g\|_{…

math.CA2019

Sparse bounds on variational norms along monomial curves

A. Martina Neuman

Consider a monomial curve $γ : R \to R^{d}$ and a family of truncated Hilbert transforms along $γ$ , $H^{γ}$ . This paper addresses the possibility of the point…

Transferability of Graph Neural Networks using Graphon and Sampling Theories

Graph Laplacians on Shared Nearest Neighbor graphs and graph Laplacians on k-Nearest Neighbor graphs having the same limit

Theoretical guarantees for the advantage of GNNs over NNs in generalizing bandlimited functions on Euclidean cubes

Restricted Riemannian geometry for positive semidefinite matrices

The pyramid operator

L2×L2×L2→L2/3 boundedness for trilinear multiplier operator

Anti-uniformity norms, anti-uniformity functions and their algebras on Euclidean spaces

Sparse bounds on variational norms along monomial curves

Graph Laplacians on Shared Nearest Neighbor graphs and graph Laplacians on $k$ -Nearest Neighbor graphs having the same limit

$L^{2} \times L^{2} \times L^{2} \to L^{2/3}$ boundedness for trilinear multiplier operator