Phase Match for Out-of-Distribution Generalization

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.