Convolutional Model Trees
Abstract
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small distortions of training images, and creating forests of model trees to increase accuracy and achieve a smooth fit. A 1-to-1 correspondence among pixels of images, coefficients of hyperplanes and coefficients of leaf functions offers the possibility of dealing with larger distortions such as arbitrary rotations or changes of perspective. A theoretical method for smoothing forest outputs to produce a continuously differentiable approximation is described. Within that framework, a training procedure is proved to converge.
Cite
@article{arxiv.2511.12725,
title = {Convolutional Model Trees},
author = {William Ward Armstrong and Hongyi Li and Jun Xu},
journal= {arXiv preprint arXiv:2511.12725},
year = {2026}
}
Comments
11 pages. 2 figures. This article was extensively revised. Drawings were added. Co-authors were added responsible for cited experimental results and their description: Hongyi Li and Jun Xu. Attention is on distilling a deep net into a model tree with convolutions done on hyperplane and leaf-function coefficients. Distortions of images are treated by similar changes to coefficient locations