Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training.

本研究旨在通过应用离散傅立叶变换和频谱表示提供有效的计算卷积方法，并且展示频谱域应用于卷积神经网络设计的创新，如频谱池化、随机修改分辨率的新形式随机正则化、卷积过滤器的复系数频谱参数化等。在不使用任何dropout或max-pooling的情况下，这些方法在分类和逼近任务中取得了有竞争力的结果，并且观察到这些方法可以显著加快训练的收敛速度。

卷积神经网络的频谱表示