## 1 Introduction  
In the field of image recognition, various types of deep learning models based on CNN have been proposed and achieved excellent results [1; 2; 3; 4; 5]. A typical CNN model consists of several convolution layers that extract features of input data and fully-connected layers that perform classification from feature maps. Through such a structure, CNN records superior performance exceeding human classifying ability, but there is trade-off. CNN consists of very deep layers to extract the features of input data, and the number of weights used in each layer is very large. In other words, despite its excellent performance, the deep learning model has high computational costs. For example, AlexNet has about 60 million parameters with 8 layers and VGGNet-16 consists of about 138 million parameters with 16 layers. As there is a lot of computation from input to output in these deep learning models, for a mobile or embedded device with insufficient memory space or power, it is difficult to distribute the deep learning model for various applications. In order to efficiently train CNN architectures, which are composed of multiple layers, a graphics processing device capable of performing operations with a lot of weights and gradients is indispensably required. In contrast, when only the forward propagation is performed to apply the pre-trained CNN, the hardware restriction is relatively free. Nevertheless, forward propagation of CNN is also problematic for applications in mobile and embedded hardware devices because it requires a large amount of computation between input data and numerous weights. First, the manufacturing of high-performance embedded hardware capable of performing large-scale tasks requires relatively high production cost. Second, the high computational costs of the deep learning model make it difficult to apply the model in the real-time environment, and increase the energy consumption of the device. Therefore, it is important to reduce the computational costs in order to apply the CNN model with high performance in such an environment. Weights quantization is one of the potential solutions to this situation. In the past, various neural network quantization methodologies have been studied to make digital hardware implementation easier [6]. The recently proposed quantization studies of deep learning model are not only focused on simplifying the hardware implementation but further reducing the computational costs while maintaining the performance of the original model. For example, in FPGA based hardware, it is possible to develop a more efficient deep learning model application device by reducing the number of multipliers required for the operation [7]. By reducing the bit size of the weights from the neurons to the neurons, the number of FPGA based hardware multipliers that actually perform calculations can be reduced. As a result, the power efficiency of the hardware can be increased, and the computational efficiency of real-time applications of the object recognition model in the embedded environment can be increased. Figure 1 shows the general weights quantization process for the CNN model. In this process, clustering for the pre-trained weights of CNN is performed first and then a codebook of weights is created. The size of the codebook is determined by the target bit-width of quantization. When a codebook is generated through a quantizer, the original weights are mapped to an index of the codebook having the closest value to the original weights. Through this process, we can obtain quantized weights that have smaller bandwidth compared to that of 32-bit float type weights. This process is referred to as weights quantization, and it enables more efficient application of various deep learning models. Recent studies related to weights quantization attempt to restore the performance of the deep learning model in the quantization process, including the retraining process as well as the quantization [8; 9]. General weights quantization methodologies with retrain have some disadvantages.