# Pruning Deep Neural Network Models via Minimax Concave Penalty Regression
## 4 Comparison of Scenarios Applicable to the MCP Regression and MCP-L1 Methods
### Time Dimension  
Efficiency in model pruning is a crucial area of interest. This subsection evaluates the pruning efficiency of the two methods based on their time consumption during the pruning of convolutional layers. For comparative purposes, Table 7 presents data on the time needed to crop a single convolutional kernel layer. This measurement excludes data preparation and other time-consuming factors, with the unit standardized in seconds (s).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Ratio** & **Flop** & **Flop Ratio** & **Param** & **Param Ratio** \\ \hline \multirow{4}{*}{Prune Strategy A} & 0.1 & \(1.07\times 10^{9}\) & 33.46\% & \(2.05\times 10^{7}\) & 3.56\% \\  & 0.2 & \(9.77\times 10^{8}\) & 39.31\% & \(1.97\times 10^{7}\) & 7.42\% \\  & 0.3 & \(8.81\times 10^{8}\) & 45.27\% & \(1.89\times 10^{7}\) & 11.17\% \\  & 0.4 & \(7.87\times 10^{8}\) & 51.11\% & \(1.81\times 10^{7}\) & 15.04\% \\ \cline{2-6}  & 0.5 & \(6.89\times 10^{8}\) & 57.19\% & \(1.73\times 10^{7}\) & 18.92\% \\ \hline \multirow{4}{*}{Prune Strategy B} & 0.1 & \(1.09\times 10^{9}\) & 32.18\% & \(2.04\times 10^{7}\) & 4.06\% \\  & 0.2 & \(1.02\times 10^{9}\) & 36.76\% & \(1.95\times 10^{7}\) & 8.44\% \\ \cline{1-1}  & 0.3 & \(9.46\times 10^{9}\) & 41.23\% & \(1.86\times 10^{7}\) & 12.68\% \\ \cline{1-1}  & 0.4 & \(8.73\times 10^{8}\) & 45.80\% & \(1.77\times 10^{7}\) & 17.06\% \\ \cline{1-1}  & 0.5 & \(7.99\times 10^{8}\) & 50.37\% & \(1.67\times 10^{7}\) & 21.43\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameter count and floating-point computation of ResNet34 model with different pruning ratios.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Layer**} & \multirow{2}{*}{**MCP-L1**} & \
\begin{tabular}{c} **MCP** \\ **Regression** \\ \end{tabular} & **Layer** & **MCP-L1** &
\begin{tabular}{c} **MCP** \\ **Regression** \\ \end{tabular} \\ \hline Conv\_1 & 0.029 & — & Conv\_9 & 0.705 & 25.276 \\ Conv\_2 & 0.077 & 2.315 & Conv\_10 & 0.813 & 43.445 \\ Conv\_3 & 0.068 & 2.674 & Conv\_11 & 0.798 & 88.056 \\ Conv\_4 & 0.189 & 2.2  
Within the MCP regression method, convolutional layer filters are pruned considering both inputs and outputs. Consequently, for the initial layer of the model, which receives raw data as inputs, pruning is unsuitable. Therefore, there are no available data on the time consumption of the MCP regression compression method under Conv_1.  
When considering time consumption, the VGG19 model's increasing depth correlates with an extended duration for MCP regression pruning. This elongation can be attributed to rising dimensions, requiring fitting through the coordinate descent method, thus increasing the fitting time for a single layer. Dichotomous parameter selection during fitting necessitates continuous adjustments to maintain the retained channel count within the pruning range, amplifying the number of iterations. The time required is more pronounced with larger sample sizes. In contrast, the MCP-L1 method performs fewer operations when pruning a single convolutional layer, resulting in relatively minor time consumption. Even in deeper layers of the convolutional structure, its time consumption remains below 1 s.