An Explicit Neural Network Construction for Piecewise Constant Function Approximation

Understand

We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions.

• The proposed FNN has two hidden layers, where the weights and thresholds are explicitly defined and do not require numerical optimization for training.
• Unlike most of the existing work on explicit FNN construction, the proposed FNN does not rely on tensor structure in multiple dimensions.
• Instead, it automatically creates Voronoi tessellation of the domain, based on the given data of the target function, and piecewise constant approximation of the function.