A Numerical Investigation of the Minimum Width of a Neural Network
This work addresses a theoretical gap in neural network design for researchers, but it appears incremental as it tests existing bounds without new methods.
The authors tackled the problem of determining the minimum width required for neural networks to approximate functions well in practice, testing established theoretical lower bounds through numerical experiments, but no concrete results or numbers were reported.
Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These theorems assume requirements, such as infinite data, that must be discretized in practice. Through numerical experiments, we seek to test the lower bounds established by Hanin in 2017.