Algorithm 1. The neural network algorithm with convolution module and residual structure

Input: Training samples $\left\{x_i\right\}$. Initialized parameters ${\theta }_c$ in convolution kernel. Weight matrix $W$. The $j\mathrm{th}$ class center $c_j$ of features. Hyper-parameter $s$, $\mu$ in $L_{AMS}$. Learning rate $\alpha$ for feature center in $L_C$. Weight $\lambda$ and learning rate $lr$ in network. The number of iteration $t\leftarrow 0$.

Output: The parameters ${\theta }_c$.

Step 1: while not converge do

Step 2: $t\leftarrow t+1$.

Step 3: compute the joint loss by $L_{AMSC}^t=L_{AMS}^t+\lambda L_C^t$.

Step 4: compute the backpropagation error $\frac{\partial L_{AMSC}^t}{\partial x_i^t}$ for each $i$ by $\frac{\partial L_{AMSC}^t}{\partial x_i^t}=\frac{\partial L_{AMS}^t}{\partial x_i^t}+\lambda \cdot \frac{\partial L_C^t}{\partial x_i^t}$.

Step 5: update the parameters $W$ by $W^{t+1}=W^t-lr\cdot \frac{\partial L_{AMSC}^t}{\partial W^t}=W^t-lr\cdot \frac{\partial L_{AMS}^t}{\partial W^t}$.

Step 6: update the parameters $c_j$ by $c_j^{t+1}=c_j^t-\alpha \cdot \mathsf{\Delta }{c}_j^t$.

Step 7: update the parameters ${\theta }_c$ by ${\theta }_c^{t+1}={\theta }_c^t-lr{\displaystyle \sum _i^m\frac{\partial L_{AMSC}^t}{\partial x_i^t}\cdot }\frac{\partial x_i^t}{\partial {\theta }_c^t}$.

Step 8: end while