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

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