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$\times$).

本文提出一种名为频率正则化的方法，在频域约束网络参数的非零元素，进而可以极大程度上压缩神经网络的参数，保证网络训练的同时提高计算效率和节约存储空间。通过在多种现有神经网络架构上的实证，验证了此方法在装备有 GPU 执行引擎的嵌入式设备场景下的优越性。

频率规则化：约束卷积神经网络的信息冗余

Frequency Regularization: Restricting Information Redundancy of  Convolutional Neural Networks

Convolutional neural networks require significant memory bandwidth and
storage for intermediate computations, apart from substantial computing
resources. Neural network quantization has significant benefits in reducing the
amount of intermediate results, but it often requires the full datasets and
time-consuming fine tuning to recover the accuracy lost after quantization.
This paper introduces the first practical 4-bit post training quantization
approach: it does not involve training the quantized model (fine-tuning), nor
it requires the availability of the full dataset. We target the quantization of
both activations and weights and suggest three complementary methods for
minimizing quantization error at the tensor level, two of whom obtain a
closed-form analytical solution. Combining these methods, our approach achieves
accuracy that is just a few percents less the state-of-the-art baseline across
a wide range of convolutional models. The source code to replicate all
experiments is available on GitHub:
https://github.com/submission2019/cnn-quantization.

本研究提出了第一种实用的 4 位后训练量化方法，不涉及训练经过量化模型（微调），也不需要完整数据集的可用性。我们针对激活和权重的量化提出了三种互补方法，以在张量层面上最小化量化误差，并取得了几个百分点少于各种卷积模型现有技术水平基准值的准确性。