## 2 Materials and Methods
### Involved CNN Models
#### 2.3.1 2D CNN Models  
The first 2D CNN model is ResNet34 [28], which is widely used as the backbone of many advanced networks in image classification and medical diagnosis [5; 36]. Figure 3 shows the repeated residual blocks that use convolution layers for hierarchical representation and skip connections to mitigate the vanishing gradient problem. And consequently, deep neural networks can be straightforward, computationally efficient, and trained with fast convergence.  
Figure 3: ResNet34. It uses skip connections of convolutional layers to avoid vanishing gradient. The structure of skip connections (red arrows) enables the building and training of very deep networks.  
The second 2D CNN model is MedMamba [31] that combines both CNNs and Transformers. It is made up of patch embedding layers, stacked SS-Conv-SSM blocks, patch merging layers, and a feature classifier, as shown in Figure 4. It is similar to Vision Transformers [37] in that MedMamba splits the input image into non-overlapping patches. It builds hierarchical representations using four SS-Conv-SSM blocks for image down-sampling. Specifically, the basic block SS-Conv-SSM includes channel-split, convolutional layers, structured state-space model (SSM) layers, and channel-shuffle in two branches of Conv-Branch and SSM-Branch for local and global information processing.  
The third 2D CNN model is MedViT [29]. It introduces the multi-head convolutional attention (MHCA), local feed-forward network (LFNN), and efficient self-attention (ESA), and the model is built based on the efficient convolutional blocks (ECBs) and local-token block (LTB), as shown in Figure 5. Specifically, MHCA decomposes an image into multiple regions or tokens and captures long-range dependencies, LFNN token-wisely rearranges the feature maps and token sequences converted by Seq2 Img and Img2 Seq, and ECBd benefit residual blocks of detail preservation while integrating the Transformer for deep feature representation. At the same time, LTB combines both local features from ECBs and global features from MHCA and ESA, and patch momentum changer is used for data diversity augmentation and improved model robustness. After progressive feature extraction and fusion, the malignancy is predicted by using simple batch normalization, global average pooling, and a full connection layer.  
Figure 4: MedMamba. It designs two branches to form the SS-Conv-SSM block, and tumor lesions are progressively represented by the blocks for malignancy prediction.  
Figure 5: MedViT. It forms ECBs and LTB by using LFNN, MHCA, and ESA for progressively local and global feature extraction, long-range dependency capturing, and information fusion.  
The fourth 2D CNN model is HiFuse [30]. It develops three-branch hierarchical integration of multi-scale features. Self-attention-based Transformer and CNN are combined without destroying the respective modeling. As shown in Figure 6, a parallel hierarchy structure with local and global feature blocks is designed for efficient representations of local and global semantic cues, and an adaptive hierarchical feature fusion (HFF) block is proposed to integrate the multi-scale features comprehensively. Specifically, the HFF block uses small modules, including spatial attention, channel attention, residual inverted multi-layer perceptron (MLP), and shortcut, to integrate the semantic features of each branch. At last, global average pooling and a layer-normalized linear classifier are used for lesion malignancy prediction.  
It is observed that ResNet34 uses four different sizes of residual blocks (Figure 3), and MedViT, HiFuse, and MedMamba repeat four specific designs of blocks (Figures 4-6) for hierarchical data representation, progressive feature fusion, and object classification. Full technical details of these 2D-input networks can be found in the relevant publications and code implementations.