# Optimization of Linear Quantization for General and Effective Low Bit-Width Network Compression
## 5 Conclusions  
This paper presents an optimized linear quantization method with a two-stage strategy including clustering and mapping. It improves low bit-width quantization without model retraining and can be easily applied to a common framework such as Distiller and Tensorflow-Lite. An interesting fact appears when evaluating how model pruning affects the model's accuracy. Experimental results show that the accuracy of the model after pruning will be even higher than that of the original model when the quantization bit-width is less than 5 bits. Through unstructured pruning and quantization, the size of a DNN model can be reduced by at least \(16\times\), which can effectively address the current extensive demands of edge applications for neural networks.  
Different from the outlier clipping method proposed by previous quantization research works, this paper introduces a new thought by splitting the quantification process into two stages, clustering, and mapping. From the experiment results, it can be found that the accuracy loss is usually generated in the clustering stage. This paper adopts PSO-K-means to minimize the loss of accuracy. Compared with previous research clipping-based quantization methods, our two-stage quantization method achieves superior precision performance when using 4-bit precision. Thus, the proposed proposal of adding a clustering stage before the mapping stage can effectively maintain the distribution of weights, thereby reducing the loss of accuracy in the quantization process.  
Future work can include more complex models such as RNNs (recurrent neural networks) and BERT for more in-depth research, as the current work is mainly focused on convolutional neural networks. Another effort for the future is to use other weight-sharing algorithms. In this article, we propose PSO-K-means as an algorithm for the clustering stage. In addition, there are many other weight-sharing algorithms that can be used.  
Conceptualization, W.Y.; Software, W.Y.; Formal analysis, W.Y.; Writing--original draft, W.Y.; Writing--review and editing, X.Z.; Supervision, X.Z. and W.T.; Project administration, X.Z. and W.T. All authors have read and agreed to the published version of the manuscript.  
This work was funded in part by the Chinese Universities Industry-University-Research Innovation Food under Grant No. 2020 HYA02011, and in part by the Natural Science Foundation of Shandong Province under Grant No. ZR2019 LZH002.  
Not applicable.  
The authors gratefully appreciate the anonymous reviewers for their valuable comments.  
All authors disclosed no relevant relationship.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Approach**} & \multicolumn{2}{c}{**Bit-Width**} & \multirow{2}{*}{**Top-1 (\%)**} \\  & & **(Weight/Activation)** & \\ \hline Baseline & - & W32/A32 & 69.538 \\ none & Linear & W4/A4 & 0.1 \\ MSE [38] & Clip-Linear & W4/A4 & 0.2 \\ ACIQ [22] & Clip-Linear & W4/A4 & 0.1 \\ KL [15] & Clip-Linear & W4/A8 & 1.6 \\ OCS [23] & OCS-Linear & W4/A8 & 2.3 \\ PSO-K-means & Cluster-Map & W4/A4 & 33.076 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparisons with existing quantization work based on clipping methods for Inception-v3 on ImageNet, using the 4-bit precision. The quantization methods include linear, clip-linear, OCS-linear, and our two-stage quantization with PSO-K-means and mapping.