# Pruning Deep Neural Network Models via Minimax Concave Penalty Regression
## 4 Comparison of Scenarios Applicable to the MCP Regression and MCP-L1 Methods
### The Space Dimension  
Concerns regarding resource consumption arise during model pruning. This subsection gauges the necessary memory resources by evaluating the volume of data processed during the pruning of convolutional layers for both methods. For comparative analysis, the data in Table 8 represent the dimensions of data that require processing when pruning a single convolutional kernel layer. The outcomes presented in Table 8 reveal that, within the MCP regression method, regression fitting is applied to the current output feature channel. The channel is censored based on whether the coefficient is zero or not to facilitate the pruning of the corresponding filter. Consequently, the data in this method need to be transformed into a two-dimensional format. In contrast, MCP-L1 directly prunes the filter in terms of parameters, utilizing it directly within the filter's four-dimensional data structure. When considering the spatial dimension, the MCP regression method faces an escalating challenge as the VGG19 model deepens. The pruning of a single convolutional layer involves an increasing number of samples and higher data dimensions. The solution process incorporates matrix operations, leading to significant memory occupancy during pruning. With the growing number of selected samples for pruning, the dimensionality of the data becomes more demanding on hardware resources. In contrast, MCP-L1 solely prunes in the original parameters, resulting in a modest change in the data processing volume and smaller memory occupancy for the model. The data delineated in Tables 7 and 8 unequivocally demonstrate the augmented time and memory requirements of the MCP regression method compared with the MCP-L1 method, particularly when processing deeper network structures. As evidenced in Table 7, the MCP regression approach exhibits a notable increase in the time needed for single-layer pruning as the model depth intensifies. This is especially pronounced in deeper convolutional layers, where the time consumption for MCP regression substantially exceeds that of the MCP-L1 method. For instance, at the Conv_16 layer, the time required \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Layer** & **MCP-L1** & \
\begin{tabular}{c} **MCP** \\ **Regression** \\ \end{tabular} & **Layer** & **MCP-L1** &
\begin{tabular}{c} **MCP** \\ **Regression** \\ \end{tabular} \\ \hline Conv\_1 & (3,64,3,3) & \(\longrightarrow\) & Conv\_9 & (256,512,3,3) & (1376256,256) \\ Conv\_2 & (64,64,3,3) & (172032,64) & Conv\_10 & (512,512,3,3) & (1376256,512) \\ Conv\_3 & (64,128,3,3) & (344064,64) & Conv\_11 & (512,512,3,3) & (1376256,512) \\ Conv\_4 & (128,128,3,3) & (344064,128) & Conv\_12 & (512,512,3,3) & (1376256,512) \\ Conv\_5 & (128,256,3,3) & (688128,128) & Conv\_13 & (512,512,3,3) & (1376256,512) \\ Conv\_6 & (256,256,3,3) & (688128,256) & Conv\_14 & (512,512,3,3) & (1376256,512) \\ Conv\_7 & (256,256,3,3) & (688128,256) & Conv\_15 & (512,512,3,3) & (1376256,512) \\ Conv\_8 & (256,256,3,3) & (688128,256) & Conv\_16 & (512,512,3,3) & (1376256,512) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Table of dimensions of data cropped by the two methods. by MCP regression amounts to 270.149 s, in stark contrast to the mere 0.779 s necessitated by the MCP-L1 method. This significant difference primarily stems from the necessity of more complex fitting computations via the coordinate descent method at each layer within the MCP regression framework. Regarding spatial resource consumption, the data from Table 8 indicate that the MCP regression method entails transforming the data into a two-dimensional format for each layer processed, resulting in increased memory usage. Notably, at the Conv_16 layer, the data dimension handled by the MCP regression method reaches 1,376,256,512, far surpassing the 51,251,233 managed by the MCP-L1 method. This illustrates that the memory requirements for filter pruning in MCP regression are significantly higher than those for the MCP-L1 method.