We study feedforward neural networks with inputs from a topological vector space (TVS-FNNs). Unlike traditional feedforward neural networks, TVS-FNNs can process a broader range of inputs, including sequences, matrices, functions and more. We prove a universal approximation theorem for TVS-FNNs, which demonstrates their capacity to approximate any continuous function defined on this expanded input space.

翻译：我们研究输入来自拓扑向量空间的前馈神经网络（TVS-FNN）。与传统前馈神经网络不同，TVS-FNN能够处理更广泛的输入类型，包括序列、矩阵、函数等。我们证明了TVS-FNN的通用逼近定理，该定理表明此类网络具备逼近定义在此扩展输入空间上任意连续函数的能力。