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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.24672 |
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| _version_ | 1866913065951297536 |
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| author | Park, Sun Woo Choi, Yun Young Choi, U Jin Woo, Youngho |
| author_facet | Park, Sun Woo Choi, Yun Young Choi, U Jin Woo, Youngho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24672 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Functorial Formulation of Neighborhood Aggregating Deep Learning Park, Sun Woo Choi, Yun Young Choi, U Jin Woo, Youngho Machine Learning Algebraic Topology 68T07, 18F20, 55N30 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. |
| title | A Functorial Formulation of Neighborhood Aggregating Deep Learning |
| topic | Machine Learning Algebraic Topology 68T07, 18F20, 55N30 |
| url | https://arxiv.org/abs/2604.24672 |