The Fourier transform, serving as an explicit decomposition method for visual
signals, has been employed to explain the out-of-distribution generalization
behaviors of Convolutional Neural Networks (CNNs). Previous research and
empirical studies have indicated that the amplitude spectrum plays a decisive
role in CNN recognition, but it is susceptible to disturbance caused by
distribution shifts. On the other hand, the phase spectrum preserves
highly-structured spatial information, which is crucial for visual
representation learning. In this paper, we aim to clarify the relationships
between Domain Generalization (DG) and the frequency components by introducing
a Fourier-based structural causal model. Specifically, we interpret the phase
spectrum as semi-causal factors and the amplitude spectrum as non-causal
factors. Building upon these observations, we propose Phase Match (PhaMa) to
address DG problems. Our method introduces perturbations on the amplitude
spectrum and establishes spatial relationships to match the phase components.
Through experiments on multiple benchmarks, we demonstrate that our proposed
method achieves state-of-the-art performance in domain generalization and
out-of-distribution robustness tasks.

通过引入基于 Fourier 变换的结构性因果模型，本文旨在阐明领域泛化和频率组分之间的关系，将相位谱解释为半因果因素，将幅度谱解释为非因果因素。在多个基准测试中，通过对幅度谱进行扰动并建立空间关系来匹配相位组分，我们的方法在领域泛化和超出分布鲁棒性任务中取得了最先进的性能。