## 3 Materials and Methods
### \"Overfitting\" Training Strategy for SCF-CIL  
Nowadays, many mainstream incremental learning methods focus on preserving old knowledge to improve the performance. Among them, the distillation loss used in LWF is one of the most representative approaches. In addition, methods such as iCaRL, DER et al. also aim to preserve the feature representations of previous classes through different mechanisms. Similarly, our feature fusion method proposed in Section 3.1 is designed with the same goal in mind. In this section, we further conduct a theoretical analysis on how the degree of feature clustering affects the performance of incremental learning, under the assumption that the feature representations of previous classes have been sufficiently preserved. Fundamentally, classification is achieved by calculating and comparing the dot product of the feature vector with the weights of the last fully connected layer. This process determines which class the instance belongs to. For a \(p\)-class classification network, when an instance is input into the network, the classification result must fall into one of the \(p\) classes, even if the instance does not belong to any of these classes. In other words, after the normal training of the classification network, the whole feature space \(\Theta\) is divided into \(p\) part \(\Theta_{1},\Theta_{2},\cdots,\Theta_{p}\). After the feature extraction, the feature of the input instance must fall in one of the \(\Theta_{1},\Theta_{2},\cdots,\Theta_{p}\). When CIL proceeds to the next phase, the same feature space need to be divided into \(p+1\) part \(\Theta_{1},\Theta_{2},\cdots,\Theta_{p},\Theta_{p+1}\). If applying a method that only tries to protect the former knowledge, the new features will share a part of feature space of other classes, which is one of a main reasons the accuracy of the old classes decreases in CIL process. Now that the current classes need to share a part of the feature space with the new classes, one method that could mitigate this effect is to adjust the feature clustering degree. Observing the feature clustering performance in classification network training experiments, we can conclude that a deeper network fitting degree can enhance the clustering of features in feature space. The negative impact of overfitting essentially lies in the model focusing too much on noise, fine-grained details, or spurious patterns present in the training samples. As a result, when the model encounters the samples in the validation set with different depression degrees, it becomes more susceptible to noise and sample-specific features, leading to degraded performance. In this context, the stability of extracted features--meaning their reduced sensitivity to noise and sample-specific variations during the fitting process--plays a key role in enhancing generalization. Our feature fusion method proposed in Section 3.1 improves the stability of the extracted features, thereby effectively suppressing the negative impact of slight overfitting. Therefore, this section will analyze the distribution of features and focus on modifying them to enhance the performance of the method in CIL. Combining the conclusion about feature clustering with the description of feature space segmentation above, we can derive the schematic diagrams of feature space distribution under different conditions as shown in Figure 4a,b depict the clustering performance of features under different fitting degrees, where the scatters with different colors represent the instances from different classes. The transition from (a) to (b) illustrates the changes in feature clustering in feature space as the network fitting progresses, which can be observed during the network training process. Let us assume that the features of \(i\)-th class are distributed in the feature space with distribution \(g=R(f),f\in\Theta\), where \(g\) is the probability of the feature falling into the position \(f\) in the whole feature space \(\Theta\).