Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence to a solution and lack guarantees that a solution exists. On the other hand, Neural ODEs, another class of implicit-depth models, do guarantee existence of a unique solution but perform poorly compared with traditional networks. In this paper, we develop a new class of implicit-depth model based on the theory of monotone operators, the Monotone Operator Equilibrium Network (MON). We show the close connection between finding the equilibrium point of an implicit network and solving a form of monotone operator splitting problem, which admits efficient solvers with guaranteed, stable convergence. We then develop a parameterization of the network which ensures that all operators remain monotone, which guarantees the existence of a unique equilibrium point. Finally, we show how to instantiate several versions of these models, and implement the resulting iterative solvers, for structured linear operators such as multi-scale convolutions. The resulting models vastly outperform the Neural ODE-based models while also being more computationally efficient. Code is available at http://github.com/locuslab/monotone_op_net.Preprint. Under review.
Domain adaptation addresses the common problem when the target distribution generating our test data drifts from the source (training) distribution. While absent assumptions, domain adaptation is impossible, strict conditions, e.g. covariate or label shift, enable principled algorithms. Recently-proposed domain-adversarial approaches consist of aligning source and target encodings, often motivating this approach as minimizing two (of three) terms in a theoretical bound on target error. Unfortunately, this minimization can cause arbitrary increases in the third term, e.g. they can break down under shifting label distributions. We propose asymmetrically-relaxed distribution alignment, a new approach that overcomes some limitations of standard domain-adversarial algorithms. Moreover, we characterize precise assumptions under which our algorithm is theoretically principled and demonstrate empirical benefits on both synthetic and real datasets.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.