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arXiv · 2604.24672

A Functorial Formulation of Neighborhood Aggregating Deep Learning

Sun Woo Park·Yun Young Choi·U Jin Choi·Youngho Woo
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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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Sun Woo Park, Yun Young Choi, U Jin Choi, Youngho Woo. 2026-04-27. A Functorial Formulation of Neighborhood Aggregating Deep Learning. https://arxiv.org/abs/2604.24672

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