Convolutional neural networks have demonstrated impressive results in many computer vision tasks. However, the increasing size of these networks raises concerns about the information overload resulting from the large number of network parameters. In this paper, we propose Frequency Regularization to restrict the non-zero elements of the network parameters in frequency domain. The proposed approach operates at the tensor level, and can be applied to almost all network architectures. Specifically, the tensors of parameters are maintained in the frequency domain, where high frequency components can be eliminated by zigzag setting tensor elements to zero. Then, the inverse discrete cosine transform (IDCT) is used to reconstruct the spatial tensors for matrix operations during network training. Since high frequency components of images are known to be less critical, a large proportion of these parameters can be set to zero when networks are trained with the proposed frequency regularization. Comprehensive evaluations on various state-of-the-art network architectures, including LeNet, Alexnet, VGG, Resnet, ViT, UNet, GAN, and VAE, demonstrate the effectiveness of the proposed frequency regularization. Under the condition of a very small accuracy decrease (less than 2\%), a LeNet5 with 0.4M parameters can be represented by only 776 float16 numbers(over 1100$\times$), and a UNet with 34M parameters can be represented by only 759 float16 numbers (over 80000$\times$).

翻译：卷积神经网络在许多计算机视觉任务中展现了令人瞩目的成果。然而，这些网络规模的日益增大引发了对大量网络参数导致信息过载的担忧。本文提出频率正则化方法，用于限制网络参数在频域中的非零元素。该方法在张量级别运作，可适用于几乎所有网络架构。具体而言，参数张量被保持在频域中，通过锯齿形设置张量元素为零来消除高频分量。随后，利用离散余弦逆变换重建空域张量，用于网络训练过程中的矩阵运算。由于已知图像的高频分量重要性较低，当网络采用所提出的频率正则化训练时，这些参数中的大部分可被设为零。针对多种最先进网络架构（包括LeNet、AlexNet、VGG、ResNet、ViT、UNet、GAN和VAE）的综合评估表明，所提出的频率正则化方法具有有效性。在精度下降极小（低于2%）的条件下，一个含0.4M参数的LeNet5可仅用776个float16数字表示（压缩超过1100倍），而一个含34M参数的UNet可仅用759个float16数字表示（压缩超过80000倍）。