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 studies have indicated that the amplitude spectrum is susceptible to the disturbance caused by distribution shifts. On the other hand, the phase spectrum preserves highly-structured spatial information, which is crucial for robust visual representation learning. However, the spatial relationships of phase spectrum remain unexplored in previous research. In this paper, we aim to clarify the relationships between Domain Generalization (DG) and the frequency components, and explore the spatial relationships of the phase spectrum. Specifically, we first introduce a Fourier-based structural causal model which interprets the phase spectrum as semi-causal factors and the amplitude spectrum as non-causal factors. Then, we propose Phase Matching (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.

翻译：傅里叶变换作为视觉信号的显式分解方法，已被用于解释卷积神经网络（CNN）的分布外泛化行为。先前研究表明，幅度谱易受分布偏移引起的扰动影响，而相位谱则保留了高度结构化的空间信息，这对鲁棒视觉表示学习至关重要。然而，已有研究尚未探讨相位谱的空间关系。本文旨在阐明域泛化（DG）与频率分量之间的关系，并探索相位谱的空间特性。具体而言，我们首先提出基于傅里叶的结构因果模型，将相位谱解释为半因果因子，将幅度谱解释为非因果因子；随后，我们提出相位匹配（PhaMa）方法以解决域泛化问题。该方法通过引入幅度谱扰动并建立空间关系来实现相位分量的匹配。在多个基准数据集上的实验表明，所提方法在域泛化与分布外鲁棒性任务中均取得了最先进的性能。