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