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.

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。先前研究与实证表明，振幅谱在CNN识别中起决定性作用，但其易受分布偏移扰动。另一方面，相位谱保留了高度结构化的空间信息，这对视觉表征学习至关重要。本文通过引入基于傅里叶的结构因果模型，旨在阐明域泛化（DG）与频率成分之间的关系。具体而言，我们将相位谱解释为半因果因子，振幅谱解释为非因果因子。基于上述发现，我们提出相位匹配（PhaMa）方法以解决DG问题。该方法通过引入振幅谱扰动并建立空间关系，实现对相位成分的匹配。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达到了当前最优性能。