  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 .
