# Multiscale Deep Equilibrium Models

We propose a new class of implicit networks, the multiscale deep equilibrium model (MDEQ), suited to large-scale and highly hierarchical pattern recognition domains. An MDEQ directly solves for and backpropagates through the equilibrium points of multiple feature resolutions simultaneously, using implicit differentiation to avoid storing intermediate states (and thus requiring only $O(1)$ memory consumption). These simultaneously-learned multi-resolution features allow us to train a single model on a diverse set of tasks and loss functions, such as using a single MDEQ to perform both image classification and semantic segmentation. We illustrate the effectiveness of this approach on two large-scale vision tasks: ImageNet classification and semantic segmentation on high-resolution images from the Cityscapes dataset. In both settings, MDEQs are able to match or exceed the performance of recent competitive computer vision models: the first time such performance and scale have been achieved by an implicit deep learning approach. The code and pre-trained models are at https://github.com/locuslab/mdeq .

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## Results from the Paper Add Remove

Task Dataset Model Metric Name Metric Value Global Rank Benchmark
Semantic Segmentation Cityscapes val Multiscale DEQ (MDEQ-large) mIoU 77.8% # 33
Semantic Segmentation Cityscapes val Multiscale DEQ (MDEQ-XL) mIoU 80.3% # 26
Image Classification ImageNet Multiscale DEQ (MDEQ-XL) Top 1 Accuracy 79.2% # 404
Hardware Burden None # 1
Operations per network pass None # 1