1 citations · 1 across the 8 of their papers we have counts for
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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…
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…
Obstructions to Reality: Torsors & Visual Paradox
Robert Ghrist, Zoe Cooperband
Visual paradoxes like the Penrose staircase present a fundamental tension: locally coherent geometric relationships that cannot be realized globally. Inspired by Penrose's observat…
Unified Origami Kinematics via Cosheaf Homology
Zoe Cooperband, Robert Ghrist
We establish a novel local-global framework for analyzing rigid origami mechanics through cosheaf homology, proving the equivalence of truss and hinge constraint systems via an ind…