## 3 Method
### Self-Training-Based Confident Pseudo-Sample Generation Network  
To filter and refine \(P_{P}\) generated by STPPGN and generate high-quality pseudo-samples, we proposed STCPSGN. During the fine-tuning phase, there are two sets of proposals to deal with: \(P_{O}\) and \(P_{P}\). Therefore, we have two networks to handle the proposals: one is the original BBH, located in Branch 1, as shown in Figure 0(a), responsible for making precise predictions for \(P_{O}\); the other is STCPSGN, which is responsible for screening \(P_{P}\) and refinement to produce high-quality pseudo-samples. These pseudo-samples are incorporated into the training set to guide the predictions of the original BBH. Similarly to STPPGN, STCPSGN consists of two submodules: teacher bounding box-head (teacher BBH) and student bounding box-head (student BBH). Its structure is shown in Figure 1c. Teacher BBH is updated using the exponential moving average [48] of the student BBH weights. Their structure is consistent with the original BBH, including an ROI feature extraction layer, a bounding box classifier, and a regressor. \(P_{P}\) undergoes RoI pooling first and then sends them to the STCPSGN to generate the final high-quality pseudo-samples that are integrated into the training set. STCPSGN has distinct parameters from the original BBH, focusing on pseudo-proposal processing, thereby resolving feature interference issues in ST-FSOD [23]. Teacher BBH generates teacher pseudo-samples \(D_{th}\) with confidence above the threshold \(\tau_{cls}\). Student BBH uses \(D_{th}\) as supervision to produce student predictions \(D_{stu}\) for computing the loss \(\mathcal{L}_{stu}^{BBH}\). \[\mathcal{L}_{stu}^{BBH}=\mathcal{L}_{stu-BBH}^{\text{cls}}(D_{stu},D_{th})+ \lambda\mathcal{L}_{stu-BBH}^{\text{reg}}(D_{stu},D_{th}) \tag{7}\]  
where \(\mathcal{L}_{stu-BBH}^{\text{cls}}\) represents the classification loss of student box-head while \(\mathcal{L}_{stu-BBH}^{\text{reg}}\) denotes the regression loss. The coefficient \(\lambda\) is used to adjust the regression loss. Subsequently, \(D_{stu}\) are subjected to a filtering and refinement process to generate pseudo-samples \(D_{s}=\{(X_{s},Y_{s})\}\), \(X_{\text{S}}\) is the region where the student box-head identifies as containing an instance, \(Y_{s}=\{(B_{s},C_{s})\}\) is its labels, where \(B_{s}=\{(x_{s},y_{s},h_{s},w_{s})\}\) indicates the bounding box coordinates, and \(C_{\text{S}}\) signifies the class label. If the predictions of the original BBH have bounding boxes that exhibit a high IoU with the pseudo-samples, it indicates the prediction is valid and should be updated with its class label. Specifically, when a sample with a ground truth class \(C\) is predicted as the background by the original BBH and it significantly overlaps with pseudo-samples, its label is replaced with the label of the pseudo-samples, and the loss is computed. The loss function for the original BBH \(\mathcal{L}_{orig}^{\text{BBH}}\) can be expressed as follows:  
\[\mathcal{L}_{\text{orig}}^{BBH}=\mathcal{L}_{\text{cls}}(u_{\text{orig}},D_{s },C)+\mathcal{L}_{\text{reg}}(u_{\text{orig}},D_{s},C) \tag{8}\]  
\[\mathcal{L}_{\text{cls}}(u_{\text{orig}},D_{s},C)= \begin{cases}\mathcal{L}_{ \text{cls}}(u_{\text{orig}},C_{s}),&\text{if $C=C_{bg}$ and $IoU(u_{\text{orig}},B_{s})>\tau_{IoU}$,}\\ \mathcal{L}_{\text{cls}}(u_{\text{orig}},C),&\text{otherwise.}\end{cases}  \tag{9}\]  
\[\mathcal{L}_{\text{reg}}(u_{\text{orig}},D_{s},C)= \begin{cases}\mathcal{L}_{ \text{reg}}(u_{\text{orig}},B_{s}),&\text{if $C=C_{bg}$ and $IoU(u_{\text{orig}},B_{s})>\tau_{IoU}$,}\\ \mathcal{L}_{\text{reg}}(u_{\text{orig}},B),&\text{if $C\
eq C_{bg}$,}\\ 0,&\text{otherwise.}\end{cases}  \tag{10}\]  
where \(\mathcal{L}_{cls}(u_{\text{orig}},D_{s},C)\) denotes the classification loss of the original BBH, and \(\mathcal{L}_{res}(u_{\text{orig}},D_{s},C)\) represents the regression loss. \(u_{\text{orig}}\) is the original prediction of the original BBH. \(C_{bg}\) is the label for the background.