3 papers
cs.LG2025
Topological Signatures of ReLU Neural Network Activation Patterns
Vicente Bosca, Tatum Rask, Sunia Tanweer +2
This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the po…
cs.CG2022
Learning on Persistence Diagrams as Radon Measures
Alex Elchesen, Iryna Hartsock, Jose A. Perea +1
Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures…
math.AT2022
Poincaré Duality for Generalized Persistence Diagrams of (co)Filtrations
Amit Patel, Tatum Rask
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincaré dualit…