# Advances in the Neural Network Quantization: A Comprehensive Review
## 4 Experimental Results
### Results  
First, we compare the PTQ methods [41; 42; 43] on image classification models, the small target detection model, and the segment model. The results of the PTQ methods are shown in Table 1. Higher accuracy can be achieved due to the use of hybrid asymmetric quantization [43]. Upon implementing the hybrid asymmetric quantization approach [43] within the GoogleNet classification model, the resultant accuracy loss is minimal, amounting to a mere 0.39% when compared to the traditional symmetric quantization method [41; 42]. Similarly, when applied to the VGG16 classification model, this method achieves an accuracy loss of only 0.52%. In the context of object detection, the application of the hybrid asymmetric quantization method [43] to the YOLO v1 model yields an accuracy loss of just 0.72%. Furthermore, when utilized in the U-net segmentation model, the method results in an accuracy loss of a mere 0.64%. The hybrid asymmetric quantization technique effectively reconciles the trade-off between the precision of quantized neural networks and the simplicity of their implementation, striking a balance between clipping range and quantization precision. Therefore, for the PTQ quantization method, using hybrid quantization with symmetric weights and asymmetric activation can improve the accuracy of the quantized model as much as possible while ensuring that it is hardware-friendly. Then, we compare the QAT methods with the mixed bit-widths on the image classification model. The results of the QAT methods are shown in Table 2. We compare three methods for mixed-precision allocation and QAT: PACT [44], HAWQv2 [55], and LIMPQ [56]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Task** & **Model** & \begin{tabular}{c} **PC Accuracy** \\ **(FP32)** \\ \end{tabular} & \begin{tabular}{c} **Method** \\ **[**42**]** \\ \end{tabular} & \
\begin{tabular}{c} **Method** \\ **[**41**]** \\ \end{tabular} &
\begin{tabular}{c} **Method** \\ **[**43**]** \\ \end{tabular} \\ \hline Image Classification & GoogleNet & 67.04 & 65.22 & 65.91 & 66.65 \\ Image Classification & VGG16 & 66.13 & 64.72 & 62.53 & 65.61 \\ Object Detection & YOLOv1 & 61.99 & 59.41 & 60.94 & 61.27 \\ Image Segmentation & U-net & 82.78 & 82.13 & 81.71 & 82.14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of the PTQ methods. It is evident that LIMPQ, due to its ability to assign different precision levels to different layers based on their sensitivity, achieves the best results with minimal loss. The LIMPQ technique intelligently discerns the significance of each neural network layer and dynamically assigns appropriate levels of precision. This sophisticated, adaptive strategy ensures that pivotal layers receive the requisite high precision to preserve functionality, while allowing less crucial layers to operate with reduced precision. This nuanced approach not only maintains the integrity of the model's performance but also enhances overall efficiency. By precisely gauging and applying the necessary level of precision to each layer, LIMPQ lays the groundwork for the development of more potent and streamlined neural network architectures. The method's scalability is evident in its applicability across a spectrum of neural network configurations, including but not limited to convolutional neural networks (CNNs), recurrent neural networks (RNNs), and transformer models. This versatility positions LIMPQ as a multifaceted asset within the realm of deep learning, capable of addressing diverse computational needs and optimizing performance across a wide range of applications. This advantage allows LIMPQ to create a more balanced trade-off between model size reduction and accuracy retention, leading to it being the most effective model among the three methods. In conclusion, when quantizing neural network models, it can be divided into two technical routes according to different application requirements. When a large amount of training data is not available, neural network models can be quickly quantized using the PTQ method, as in [43].