Frequency analysis is useful for understanding the mechanisms of representation learning in neural networks (NNs). Most research in this area focuses on the learning dynamics of NNs for regression tasks, while little for classification. This study empirically investigates the latter and expands the understanding of frequency shortcuts. First, we perform experiments on synthetic datasets, designed to have a bias in different frequency bands. Our results demonstrate that NNs tend to find simple solutions for classification, and what they learn first during training depends on the most distinctive frequency characteristics, which can be either low- or high-frequencies. Second, we confirm this phenomenon on natural images. We propose a metric to measure class-wise frequency characteristics and a method to identify frequency shortcuts. The results show that frequency shortcuts can be texture-based or shape-based, depending on what best simplifies the objective. Third, we validate the transferability of frequency shortcuts on out-of-distribution (OOD) test sets. Our results suggest that frequency shortcuts can be transferred across datasets and cannot be fully avoided by larger model capacity and data augmentation. We recommend that future research should focus on effective training schemes mitigating frequency shortcut learning.

频率分析这一研究领域在理解神经网络中的表示学习机制方面具有重要作用。本研究通过实证调查，扩展了对频率快捷方式的理解，并验证了其在分类任务中的应用，结果显示频率快捷方式是可转移的，且无法完全避免，建议未来的研究应该专注于有效的训练方案以减轻频率快捷方式的学习。

神经网络在图像分类中学习了什么？一个频率捷径的视角