Algorithm 1: Training Procedure of the RC-SEI method.

Require: K: Number of training iterations; N: Number of training samples; C: Number of batches; B: Number of Batchsize; $w,w_{SF}$: Parameters of neural network and sparse parameters; $z,z_{SF}$: Original features and sparse features; $\eta$: Learning rate; $\mu$: Coefficient of momentum; ${\lambda }_{SF}$: Sparse factor; $\mathbf{Training}\mathbf{on}{\{x_i,y_i\}}_{i=1}^N$ for $k=1$ to K do    for $c=1$ to C do      [Forward propagation]:      Sampling a batch of training samples ${\{x_i,y_i\}}_{i=1}^B$      Initialize ${\mathit{w}}_{SF}=\{1,1,\dots ,1\}$      Extracting the Original features: $\mathit{z}$      Pruning the Original features: ${\mathit{z}}_{SF}={\mathit{w}}_{SF}\odot \mathit{z}$      Obtaining the artificial labels:      for $b=1$ to B do         $\widehat{y}=arg{max}_{y\in \mathcal{Y}}f\left(y_i\right|x_i;{\mathit{z}}_{SF})$      end for      Calculating the loss: $\mathcal{L}={\mathcal{L}}_{CE}+\mathcal{R}\left({\mathit{w}}_{SF}\right)$      [Backward propagation]:      Updating $\mathit{w}$ by Adam algorithm:      $\begin{array}{c}{\mathit{w}}^k={\mathit{w}}^{k-1}-\eta ·{\displaystyle \frac{{\widehat{m}}_{k-1}}{\sqrt{{\widehat{v}}_{k-1}}+ϵ}}\hfill \end{array}$      Updating ${\mathit{w}}_{SF}$ by APGD-NAG algorithm:      $\begin{array}{c}\left\{\begin{array}{c}{\mathit{J}}^k={\mathit{w}}_{SF}^{\prime k-1}-\eta \nabla {\mathcal{L}}_{CE}\left({\mathit{w}}_{SF}^{\prime k-1}\right)\hfill \\ {\mathit{v}}^k=S_{\eta {\lambda }_{SF}}\left({\mathit{J}}^k\right)-{\mathit{w}}_{SF}^{\prime k-1}+\mu ·{\mathit{v}}^{k-1}\hfill \\ {\mathit{w}}_{SF}^{\prime k-1}=S_{\eta {\lambda }_{SF}}\left({\mathit{J}}^k\right)+\mu ·{\mathit{v}}^{k-1}\hfill \\ k=1,2,3,\dots ,K\hfill \end{array}\right.\hfill \end{array}$    end for end for