A Functorial Formulation of Neighborhood Aggregating Deep Learning

• URL: http://arxiv.org/abs/2604.24672v1
• Date: Mon, 27 Apr 2026 16:31:22 GMT
• Title: A Functorial Formulation of Neighborhood Aggregating Deep Learning
• Abstract summary: We provide a mathematical interpretation of convolutional (or message passing) neural networks by using presheaves and copresheaves.<n>We formulate a theoretical which elaborates a number of empirical limitations of these neural networks by using obstructions to be sheaves or copresheaves.
• Score: 3.2756362729975517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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