Year: 2018
Type: preprint
Abstract: 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. This makes the construction more practical for applications. We present both theoretical analysis and numerical examples to demonstrate its properties.
Source: arXiv (Cornell University)
Authors: Wu, Kailiang, Xiu, Dongbin
Institution: The Ohio State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2888635693