Regularizing Energy among Training Samples for Out-of-Distribution Generalization

The energy-based model provides a unified framework for various learning models where an energy value is assigned to each configuration of random variables based on probability. Recently, different methods have been proposed to derive an energy value out of the logits of a classifier for out-of-distribution (OOD) detection or OOD generalization. However, these methods mainly focus on the energy difference between in-distribution and OOD data samples, neglecting the energy difference among in-distribution data samples. In this paper, we show that the energy among in-distribution data also requires attention. We propose to investigate the energy difference between in-distribution data samples. Both empirically and theoretically, we show that previous methods for subpopulation shift (\emph{e.g.}, long-tail classification) such as data re-weighting and margin control apply implicit energy regularization and we provide a unified framework from the energy perspective. With the influence function, we further extend the energy regularization framework to OOD generalization scenarios where the distribution shift is more implicit compared to the long-tail recognition scenario. We conduct experiments on long-tail datasets, subpopulation shift benchmarks, and OOD generalization benchmarks to show the effectiveness of the proposed energy regularization.