# MGiaD: Multigrid in all dimensions. Efficiency and robustness by coarsening in resolution and channel dimensions

arXiv: https://arxiv.org/abs/2211.05525 · HTML: https://mlsanity.com/paper/2211.05525/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 10 Nov 2022.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [MorphNet: Fast & Simple Resource-Constrained Structure Learning of Deep Networks](https://mlsanity.com/paper/1711.06798/) (2017)
- [Learning the Number of Neurons in Deep Networks](https://mlsanity.com/paper/1611.06321/) (2016)
- [Pruning Convolutional Neural Networks for Resource Efficient Inference](https://mlsanity.com/paper/1611.06440/) (2016)
- [MGIC: Multigrid-in-Channels Neural Network Architectures](https://mlsanity.com/paper/2011.09128/) (2020)
- [An Interpretive Constrained Linear Model for ResNet and MgNet](https://mlsanity.com/paper/2112.07441/) (2021)

## Built on by (most cited first, 2 of 2)

- [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)

## Abstract (arXiv)

Current state-of-the-art deep neural networks for image classification are made up of 10 - 100 million learnable weights and are therefore inherently prone to overfitting. The complexity of the weight count can be seen as a function of the number of channels, the spatial extent of the input and the number of layers of the network. Due to the use of convolutional layers the scaling of weight complexity is usually linear with regards to the resolution dimensions, but remains quadratic with respect to the number of channels. Active research in recent years in terms of using multigrid inspired ideas in deep neural networks have shown that on one hand a significant number of weights can be saved by appropriate weight sharing and on the other that a hierarchical structure in the channel dimension can improve the weight complexity to linear. In this work, we combine these multigrid ideas to introduce a joint framework of multigrid inspired architectures, that exploit multigrid structures in all relevant dimensions to achieve linear weight complexity scaling and drastically reduced weight counts. Our experiments show that this structured reduction in weight count is able to reduce overfitting and thus shows improved performance over state-of-the-art ResNet architectures on typical image classification benchmarks at lower network complexity.