## 3 Proposed Methods
### Supervisory Losses  
As shown in Figure 5, our total supervised loss is divided into two parts, \(\mathrm{L_{C}}\) and \(\mathrm{L_{IC}}\). We feed the artificial images generated on the fly into the student model for training, along with the actual training samples (note that here the fake images are passed into the student model in real-time, so there is no need to save them). The predicted values obtained are then compared with the actual values, as shown below.  
We map the sample labels (actual samples vs. artificial samples) as vectors that serve as \"benchmarks\" to compare with the intrinsic information of the samples in the network as our loss \(\mathrm{L_{IC}}\). Specifically, given a small batch of input samples containing B samples, we define the sample intrinsic information map of the L-layer as \(\mathrm{F^{L}}\in\mathrm{R^{B_{C}\mathrm{s}\mathrm{r}\mathrm{H}\mathrm{z} \mathrm{W}}}\), where H and W are the spatial dimensions of the feature map and C is the number of channels, and the matrix obtained by normalizing the intrinsic information of this small batch of input samples is as Equation (8).  
\[\mathrm{F_{C}}=\left(\frac{\mathrm{F(x)_{1}^{L}}}{\parallel\mathrm{F(x)_{1}^{ L}}},\cdots,\frac{\mathrm{F(x)_{B}^{L}}}{\parallel\mathrm{F(x)_{B}^{L}} \parallel}\right) \tag{8}\]  
\(\mathrm{F_{C}}\) denotes the sample feature information of B samples within the network. Similarly, the label information is mapped to a vector with the same number of feature image elements as the layer, and the mapping vector of label information for this small set of input samples is normalized to obtain the following matrix:  
\[\mathrm{V_{L}}=\left(\frac{\mathrm{f(y)_{1}^{L}}}{\parallel\mathrm{f(y)_{1}^{ L}}\parallel},\cdots,\frac{\mathrm{f(y)_{B}^{L}}}{\parallel\mathrm{f(y)_{B}^{L}} \parallel}\right) \tag{9}\]  
\(\mathrm{V_{L}}\) represents the \"benchmark\" of B sample feature information within the network. Here, x represents the samples inputted into the student model, and y represents the labels of these samples. \(\mathrm{F(x)_{1}^{L}}\) means the intrinsic information of each sample inside the network, and \(\mathrm{f(y)_{1}^{L}}\) represents the vector units that map the label information of the sample to the L-layer, i.e., the \"benchmark\" information. Because the inherent feature maps from deeper layers contain more semantic information, the intrinsic information of the samples after the last pooling layer is chosen [38; 39] to compare with the label information, defined as Equation (10).  
\[L_{IC}=\sum_{x}\frac{1}{B}\parallel F_{C}-V_{L}\parallel_{2}^{2} \tag{10}\]  
As shown in Figure 6, we improved the original loss of supervision. The sample features are thoroughly learned by determining whether the predicted labels obtained by the student model are consistent with the labels to enable the model to be filtered sample by sample during the training process. For correctly classified samples, the sample loss is assigned a smaller weight \(\mathrm{L\_w}=(1-\mathrm{p_{t}(max)})^{2}\); otherwise, the weight given is \(\mathrm{H\_w}=1\). The final loss \(\mathrm{L_{C}}\) is defined as Equation (11).  
\[\mathrm{L_{C}}=\left