## 5 Experiments
### YOLO Experiments  
The clipping experiment was mainly to validate the influence of clipping operation on the model accuracy and obtain the parameter values with the smallest influence for post-quantization. Thus, to minimize the effect of the clipping operation, we needed to make the value of the clipped values approximate to the real values in the original models.  
The weight value is static and can be obtained by training. We obtained the range of model weight from the original models, as shown in Figure 7. It can be found that the weights of the convolution layer are distributed between [-1, 1], mainly concentrated in [-0.0625, 0.0625]. The total number of network parameters is 62,944,352, of which 99.2% of the parameters are located between [-0.03125, 0.03125], and 0.67% of the parameters are between [-0.0625, -0.03125] and [0.03125, 0.625].  
The values of input data flow are dynamic and difficult to collect. We used the following steps to determine its value range. First, the weights were clipped to [-1, 1]. Since the weight was within this range, as shown in Figure 7, the weights were not changed at this time. Then, according to the experience, the clip strategies of three data streams [-8, 8], [-4, 4], [-2, 2] were selected for experiments. The experimental results are shown in Table 1. Table 1 compares these three clip strategies, and it can be found that the accuracy decreases the least when the input interval is [-8, 8] compared to baseline, there is a small loss of accuracy when it is [-4, 4], and there is a significant decrease of 5% when the input interval is [-2, 2]. The smaller the interval is, the more missing parameters there are and the greater the decrease in accuracy. This indicates that the inputs are mainly distributed in the interval [-8, 8].  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Input Clip** & **AP(IOU)** & **AP(IOU)** & **AP(IOU)** & **AR(IOU)** & **AR(IOU)** & **AR(IOU)** \\
**Strategies** & **0.5:0.95** & **0.5** & **0.75** & **0.5:0.95** & **0.5:0.95** & **0.5:0.95** \\ \hline
[-8, 8] & 0.5853 & 0.7990 & 0.6417 & 0.4700 & 0.6812 & 0.6971 \\
[-4, 4] & 0.5703 & 0.7911 & 0.6345 & 0.4636 & 0.6728 & 0.6861 \\
[-2, 2] & 0.5302 & 0.7453 & 0.5868 & 0.4400 & 0.6377 & 0.6491 \\ Baseline & 0.5858 & 0.8010 & 0.6421 & 0.4702 & 0.6831 & 0.6976 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Results of three input clip strategies in float type during training.  
Figure 7: Histogram of weight distribution.  
According to the distribution of weights reflected in the figure, five clipping strategies were adopted for the clipping experiment of weights to observe the change of accuracy, including \([-1,\,1]\), \([-0.5,\,0.5]\), \([-0.25,\,0.25]\), \([-0.125,\,0.125]\), and \([-0.0625,\,0.0625]\). We first clipped the data stream to \([-8,\,8]\), and then compared these five weights clipping strategies. The results are in Table 2. Table 2 shows that the accuracy loss becomes smaller step by step as the weighting interval narrows from \([-1,\,1]\) to \([-0.0625,\,0.0625]\). However, it is worth mentioning that the accuracy loss is very small when the weight interval is from \([-1,\,1]\) to \([-0.125,\,0.125]\), and the accuracy difference with the baseline is kept within \(0.1\%\). This indicates that the weights are mainly distributed between \([-0.125,\,0.125]\), and the small number of parameters in other parts hardly affects the accuracy. However, at \([-0.0625,\,0.0625]\), the maximum accuracy is only \(0.78\), with a significant accuracy drop of \(2\%\), indicating that the number of parameters between \(10.0625,\,0.125\,|\) has increased and their absence has affected the accuracy. Therefore, we selected the first four strategies for the subsequent experiments.