On shallow feedforward neural networks with inputs from a topological space
This work addresses theoretical foundations for neural networks in topological spaces, which is incremental as it extends existing approximation results to more general input domains.
The paper tackled the problem of approximating continuous functions on topological spaces using shallow feedforward neural networks, proving a universal approximation theorem and deriving an approximative version of Kolmogorov's superposition theorem for compact metric spaces.
We study feedforward neural networks with inputs from a topological space (TFNNs). We prove a universal approximation theorem for shallow TFNNs, which demonstrates their capacity to approximate any continuous function defined on this topological space. As an application, we obtain an approximative version of Kolmogorov's superposition theorem for compact metric spaces.