# An Explicit Neural Network Construction for Piecewise Constant Function Approximation

arXiv: https://arxiv.org/abs/1808.07390 · HTML: https://mlsanity.com/paper/1808.07390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Approximation of relation functions and attention mechanisms](https://mlsanity.com/paper/2402.08856/) (2024)

## Abstract (arXiv)

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.