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

2025-03-13

Proceedings of the 14th International Conference on Pattern Recognition Applications and Methods

AI Summary

This paper addresses the longstanding trade-off between accuracy and parameter efficiency in deep neural networks. Inspired by polynomial smoothers from multigrid (MG) theory, we propose a lightweight yet high-accuracy ResNet building block. Our core innovation is the first integration of a quadratic polynomial module into the residual path, coupled with a novel real/complex-root complex initialization strategy that optimizes coefficient distribution in the complex domain—thereby enhancing representational capacity while minimizing parameter count. Replacing standard convolutional layers, this module enables multi-scale feature co-smoothing. On image classification benchmarks, our approach matches or exceeds the accuracy of standard ResNet and MgNet variants while reducing model parameters by 30–50%, achieving a superior accuracy–parameter trade-off.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Develops Poly-MgNet with polynomial building blocks inspired by Multigrid methods.
• Reduces weights in MgNet while enhancing model accuracy.
• Explores polynomial degree and activation placement for improved performance.

Innovation

• Polynomial blocks inspired by MG smoothers
• Reduces weights while enhancing accuracy
• Integrates MG schemes into ResNet design