arXiv:2604.24672cs.LGmath.AT2026-04
用拓扑数学解释卷积网络局限性，揭示其理论瓶颈。
A Functorial Formulation of Neighborhood Aggregating Deep Learning
- 用预层与余预层构建卷积网络的数学框架
- 发现连续函数集无法形成层结构是性能瓶颈
- 适合研究深度学习理论的数学背景读者
我们通过拓扑空间上连续函数集的预层与余预层，为卷积神经网络（或消息传递网络）提供了一种数学解释。基于此，提出一个理论启发式方法，利用拓扑空间上连续函数集无法成为层或余预层的障碍，阐明了这些神经网络的一系列经验性局限性。
原文摘要 · Abstract (English)
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.
深度学习拓扑理论分析
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。