Voronoi Convolutional Neural Networks

TL;DR

This paper introduces Voronoi CNNs that extend traditional CNNs to irregularly sampled functions using convex geometry, enabling exact inference on non-grid data.

Contribution

It presents a novel approach to adapt CNN layers for functions sampled in Voronoi cells, with an algorithm for exact inference using convex geometry.

Findings

Effective extension of CNNs to non-grid data

Exact inference algorithm based on convex geometry

Potential applications in irregular data domains

Abstract

In this technical report, we investigate extending convolutional neural networks to the setting where functions are not sampled in a grid pattern. We show that by treating the samples as the average of a function within a cell, we can find a natural equivalent of most layers used in CNN. We also present an algorithm for running inference for these models exactly using standard convex geometry algorithms.