18 citations · 47 across the 9 of their papers we have counts for
10 papers
A Mathematical Framework for Citation Disruption
Thomas Gebhart, Russell Funk
Many theories of scientific and technological progress imagine science as an iterative, developmental process periodically interrupted by innovations which disrupt and restructure…
Graph Convolutional Networks from the Perspective of Sheaves and the Neural Tangent Kernel
Thomas Gebhart
Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph c…
Go with the Flow? A Large-Scale Analysis of Health Care Delivery Networks in the United States Using Hodge Theory
Thomas Gebhart, Xiaojun Fu, Russell Funk
Health care delivery is a collaborative process, requiring close coordination among networks of providers with specialized expertise. Yet in the United States, care is often spread…
Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding
Thomas Gebhart, Jakob Hansen, Paul Schrater
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting represent…
A Unified Paths Perspective for Pruning at Initialization
Thomas Gebhart, Udit Saxena, Paul Schrater
A number of recent approaches have been proposed for pruning neural network parameters at initialization with the goal of reducing the size and computational burden of models while…
Sheaf Neural Networks
Jakob Hansen, Thomas Gebhart
We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are…
The Emergence of Higher-Order Structure in Scientific and Technological Knowledge Networks
Thomas Gebhart, Russell J. Funk
The growth of science and technology is a recombinative process, wherein new discoveries and inventions are built from prior knowledge. Yet relatively little is known about the man…
Path homologies of deep feedforward networks
Samir Chowdhury, Thomas Gebhart, Steve Huntsman +1
We provide a characterization of two types of directed homology for fully-connected, feedforward neural network architectures. These exact characterizations of the directed homolog…
Characterizing the Shape of Activation Space in Deep Neural Networks
Thomas Gebhart, Paul Schrater, Alan Hylton
The representations learned by deep neural networks are difficult to interpret in part due to their large parameter space and the complexities introduced by their multi-layer struc…
Adversary Detection in Neural Networks via Persistent Homology
Thomas Gebhart, Paul Schrater
We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out-…