A Functorial Formulation of Neighborhood Aggregating Deep Learning
Sun Woo Park, Yun Young Choi, U Jin Choi, Youngho Woo
cs.LG math.AT
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.
Topics
Classified with taxonomy v2 on Wed, 2 Sept 2026.