A Functorial Formulation of Neighborhood Aggregating Deep Learning
Machine Learning
2026-04-28 v1 Algebraic Topology
Abstract
We provide a mathematical interpretation of convolutional (or message passing) neural networks by using presheaves and copresheaves of the set of continuous functions over a topological space. Based on this interpretation, we formulate a theoretical heuristic which elaborates a number of empirical limitations of these neural networks by using obstructions on such sets of continuous functions over a topological space to be sheaves or copresheaves.
Cite
@article{arxiv.2604.24672,
title = {A Functorial Formulation of Neighborhood Aggregating Deep Learning},
author = {Sun Woo Park and Yun Young Choi and U Jin Choi and Youngho Woo},
journal= {arXiv preprint arXiv:2604.24672},
year = {2026}
}
Comments
32 pages, 11 figures. Comments welcome