# MGIC: Multigrid-in-Channels Neural Network Architectures

arXiv: https://arxiv.org/abs/2011.09128 · HTML: https://mlsanity.com/paper/2011.09128/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

## Built on by (most cited first, 8 of 8)

- [Gauge-equivariant neural networks as preconditioners in lattice QCD](https://mlsanity.com/paper/2302.05419/) (2023)
- [Gauge-equivariant pooling layers for preconditioners in lattice QCD](https://mlsanity.com/paper/2304.10438/) (2023)
- [Multiscale Training of Convolutional Neural Networks](https://mlsanity.com/paper/2501.12739/) (2025)
- [MGiaD: Multigrid in all dimensions. Efficiency and robustness by coarsening in resolution and channel dimensions](https://mlsanity.com/paper/2211.05525/) (2022)
- [A Neural-preconditioned Poisson Solver for Mixed Dirichlet and Neumann Boundary Conditions](https://mlsanity.com/paper/2310.00177/) (2023)
- [Poly-MgNet: Polynomial Building Blocks in Multigrid-Inspired ResNets](https://mlsanity.com/paper/2503.10594/) (2025)
- [Multilevel Training for Kolmogorov Arnold Networks](https://mlsanity.com/paper/2603.04827/) (2026)
- [LFA applied to CNNs: Efficient Singular Value Decomposition of Convolutional Mappings by Local Fourier Analysis](https://mlsanity.com/paper/2506.05617/) (2025)

## Abstract (arXiv)

We present a multigrid-in-channels (MGIC) approach that tackles the quadratic growth of the number of parameters with respect to the number of channels in standard convolutional neural networks (CNNs). Thereby our approach addresses the redundancy in CNNs that is also exposed by the recent success of lightweight CNNs. Lightweight CNNs can achieve comparable accuracy to standard CNNs with fewer parameters; however, the number of weights still scales quadratically with the CNN's width. Our MGIC architectures replace each CNN block with an MGIC counterpart that utilizes a hierarchy of nested grouped convolutions of small group size to address this. Hence, our proposed architectures scale linearly with respect to the network's width while retaining full coupling of the channels as in standard CNNs. Our extensive experiments on image classification, segmentation, and point cloud classification show that applying this strategy to different architectures like ResNet and MobileNetV3 reduces the number of parameters while obtaining similar or better accuracy.