A Functorial Formulation of Neighborhood Aggregating Deep Learning

arXiv:2604.24672v1 Announce Type: new 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.

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Source: arXiv cs.LG | 2026-04-28

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