70 citations · 316 across the 56 of their papers we have counts for
59 papers
Clearing in Liability Networks via Sheaves on Directed Hypergraphs
Robert Ghrist
We associate to a decorated liability network a liability sheaf on a directed hypergraph whose hyperedges separate the distribution of payments from the collection of receipts. Cle…
Neural Networks as Local-to-Global Computations
Vicente Bosca, Robert Ghrist
We construct a cellular sheaf from any feedforward ReLU neural network by placing one vertex for each intermediate quantity in the forward pass and encoding each computational step…
Impossible by Degrees: Cohomology & Bistable Visual Paradox
Lewis Ghrist, Robert Ghrist
The Penrose triangle, staircase, and related ``impossible objects'' have long been understood as related to first cohomology : the obstruction to extending locally consistent…
Selective Adaptation of Beliefs and Communication on Cellular Sheaves
Vicente Bosca, Robert Ghrist
We extend opinion dynamics on discourse sheaves to incorporate "directional stubbornness": agents may hold fixed positions in specified directions of their opinion stalk while rema…
Precision-Graded Cohomology and Arithmetic Persistence for Network Sheaves
Robert Ghrist, Cassie Ding
Persistent homology tracks topological features across geometric scales, encoding birth and death of cycles as barcodes. We develop a complementary theory where the filtration para…
Learning from Frustration: Torsor CNNs on Graphs
Daiyuan Li, Shreya Arya, Robert Ghrist
Most equivariant neural networks rely on a single global symmetry, limiting their use in domains where symmetries are instead local. We introduce Torsor CNNs, a framework for learn…