A General Constructive Upper Bound on Shallow Neural Nets Complexity
This work addresses a foundational problem in neural network theory for researchers and practitioners, offering a general theoretical bound, though it appears incremental as it builds on existing proof techniques.
The paper tackles the problem of approximating continuous functions on compact sets with shallow neural networks by providing a constructive upper bound on the number of neurons needed for a given accuracy, which is more general than previous bounds as it applies to any continuous function on any compact set.
We provide an upper bound on the number of neurons required in a shallow neural network to approximate a continuous function on a compact set with a given accuracy. This method, inspired by a specific proof of the Stone-Weierstrass theorem, is constructive and more general than previous bounds of this character, as it applies to any continuous function on any compact set.