A Functorial Formulation of Neighborhood Aggregating Deep Learning
For theorists and practitioners of geometric deep learning, this offers a foundational mathematical perspective on limitations of message-passing networks, but is purely theoretical without empirical validation.
The paper provides a mathematical interpretation of convolutional neural networks using presheaves and copresheaves, and formulates a theoretical heuristic explaining empirical limitations via obstructions to sheaf conditions. No concrete numbers are given.
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.