Universal approximation theorem for neural networks with inputs from a topological vector space
This work provides a theoretical foundation for applying neural networks to a broader range of data types, such as sequences and functions, which is incremental as it extends existing approximation theorems.
The authors tackled the problem of extending neural networks to handle inputs from topological vector spaces, proving a universal approximation theorem that shows these networks can approximate any continuous function on such spaces.
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.