12 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…
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…
The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)
Andrew Ferguson, Marisa LaFleur, Lars Ruthotto +97
This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 w…
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…
Categorical Diffusion of Weighted Lattices
Robert Ghrist, Miguel Lopez, Paige Randall North +1
We introduce a categorical formalization of diffusion processes for network-structured data, motivated by applications in data science and information dynamics. At the heart of our…