Deep equilibrium networks (DEQs) are a new class of models that eschews
traditional depth in favor of finding the fixed point of a single nonlinear
layer. These models have been shown to achieve performance competitive with the
state-of-the-art deep networks while using significantly less memory. Yet they
are also slower, brittle to architectural choices, and introduce potential
instability to the model. In this paper, we propose a regularization scheme for
DEQ models that explicitly regularizes the Jacobian of the fixed-point update
equations to stabilize the learning of equilibrium models. We show that this
regularization adds only minimal computational cost, significantly stabilizes
the fixed-point convergence in both forward and backward passes, and scales
well to high-dimensional, realistic domains (e.g., WikiText-103 language
modeling and ImageNet classification). Using this method, we demonstrate, for
the first time, an implicit-depth model that runs with approximately the same
speed and level of performance as popular conventional deep networks such as
ResNet-101, while still maintaining the constant memory footprint and
architectural simplicity of DEQs. Code is available at
this https URL .

本文提出一种正则化方案来加强深度均衡网络（DEQ）模型的学习稳定性，该正则化方案显著提高了 DEQ 模型的收敛速度和性能，使得 DEQ 模型与传统深度网络在速度和性能上保持相当，并且具有恒定的内存占用和简单的架构。