发表机构
Idaho State University（爱达荷州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出神经网络对拓扑向量空间间连续映射的通用逼近定理，覆盖局部凸及非局部凸情形，并推广至有限维紧凸集上的映射。
AI 中文摘要
我们研究了神经网络对拓扑向量空间之间连续映射的通用逼近问题。我们给出了在具有和不具有仿紧性假设的局部凸拓扑向量空间之间映射的通用逼近定理。我们将此结果推广到在有限拓扑维数假设下，紧凸集上的非局部凸拓扑向量空间之间的连续映射。
英文摘要
We study the problem of universal approximation of continuous maps between topological vector spaces by neural networks. We provide a universal approximation theorem for maps between locally convex topological vector spaces with and without paracompactness assumptions. We extend this result to continuous maps between non-locally convex topological vector spaces on compact sets under the assumption of finite topological dimension.
Comments8 pages. Comments are welcome! v2: various typos have been corrected, and Theorem 4.2 has been improved by removing two unnecessary hypotheses
