The Extrapolation Power of Implicit Models

Abstract

Faced with out-of-distribution data, deep neural networks may break down, even on simple tasks. In this paper, we consider the extrapolation ability of implicit deep learning models, which allow layer depth flexibility and feedback in their computational graph. We compare the out-of-sample performance of implicit and non-implicit deep learning models on both mathematical extrapolation tasks and real-world use cases in time series forecasting and earthquake location prediction. Throughout our experiments, we demonstrate a marked performance increase with implicit models. In addition, we observe that to achieve acceptable performance, the architectures of the non-implicit models must be carefully tailored to the task at hand. In contrast, implicit models do not require such task-specific architectural design, as they learn the model structure during training.