Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets

Antonia van Betteray, Matthias Rottmann, Karsten Kahl

2025

Abstract

The structural analogies of ResNets and Multigrid (MG) methods such as common building blocks like convolutions and poolings where already pointed out by He et al. in 2016. Multigrid methods are used in the context of scientific computing for solving large sparse linear systems arising from partial differential equations. MG methods particularly rely on two main concepts: smoothing and residual restriction / coarsening. Exploiting these analogies, He and Xu developed the MgNet framework, which integrates MG schemes into the design of ResNets. In this work, we introduce a novel neural network building block inspired by polynomial smoothers from MG theory. Our polynomial block from an MG perspective naturally extends the MgNet framework to Poly-Mgnet and at the same time reduces the number of weights in MgNet. We present a comprehensive study of our polynomial block, analyzing the choice of initial coefficients, the polynomial degree, the placement of activation functions, as well as of batch normalizations. Our results demonstrate that constructing (quadratic) polynomial building blocks based on real and imaginary polynomial roots enhances Poly-MgNet’s capacity in terms of accuracy. Furthermore, our approach achieves an improved trade-off of model accuracy and number of weights compared to ResNet as well as compared to specific configurations of MgNet.

Paper Citation

in Harvard Style

van Betteray A., Rottmann M. and Kahl K. (2025). Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets. In Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM; ISBN 978-989-758-730-6, SciTePress, pages 181-191. DOI: 10.5220/0013382800003905

in Bibtex Style

@conference{icpram25,
author={Antonia van Betteray and Matthias Rottmann and Karsten Kahl},
title={Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets},
booktitle={Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM},
year={2025},
pages={181-191},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013382800003905},
isbn={978-989-758-730-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM
TI - Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets
SN - 978-989-758-730-6
AU - van Betteray A.
AU - Rottmann M.
AU - Kahl K.
PY - 2025
SP - 181
EP - 191
DO - 10.5220/0013382800003905
PB - SciTePress