# Fused Node-Level Residual Structure Edge Graph Neural Network for Few-Shot Image Classification
## 3 Methods
### EGNN + Node Hierarchical Residual Model Architecture
This architecture contains no leftover connections. Each convolutional block is made up of a batch normalization step, a 3 \(\times\) 3 convolution layer, and a LeakyReLU activation. Figure 2 provides comprehensive descriptions of each network design used in EGNN + Node Hierarchical Residual. **Training:** The Adam optimizer is used to train the model on the public datasets, with an initial learning rate of \(10^{-3}\) and a weight decay of \(10^{-6}\). The initial learning rate is set to \(10^{-4}\) on the CBAC dataset, while the weight decay is set at \(10^{-6}\). The batch size for contrastive meta-training tasks is set at 40 in all studies to guarantee a fair comparison with the original EGNN. For mini-ImageNet, the learning rate is reduced by half every 15,000 episodes, while for tiered-ImageNet and CBAC, transfer learning is applied directly from mini-ImageNet, and the learning rate is reduced by half every 20,000 episodes for tiered-ImageNet and every 10,000 episodes for CBAC since it is a larger dataset that requires more iterations to converge. All code implementations are conducted in PyTorch [37] and executed on an NVIDIA A100 Tensor Core GPU. For the tiered-ImageNet dataset, which is relatively large, it requires physically splitting the dataset into two parts and loading them together, involving at least two NVIDIA A100 GPUs working in parallel. **Residual Structures:** In the experiments on the mini-ImageNet dataset, two residual structures are used. The first one is a direct linear connection, and the second one includes a convolutional layer, as illustrated in Figure 3.

### Results and Analysis

Tables 1 and 2 present our experimental results on the mini-ImageNet and tiered-ImageNet datasets, respectively. These tables are sorted by method categories. Table 3 displays three comparative experimental results on the CBAC dataset. Note that the results only compare edge-conditioned Graph Neural Networks with prior relevant methods in few-shot image classification. The results in the table are the corresponding accuracies in %. The terms \"5-ways 1-shot\" and \"5-ways 5-shot\" are commonly used in the context of few-shot learning. The term \"5-ways 1-shot\" signifies that the model is exposed to only one sample (i.e., one image) from each class within each training set and is subsequently evaluated on its classification capability for these classes in the test set. This implies that the model needs to learn effective feature representations from a limited number of samples to correctly classify new instances. On the other hand, \"5-ways 5-shot\" indicates that the model is presented with five samples (i.e., five images) from each class within each training set and is then assessed on its classification performance for these classes in the test set. In contrast to \"5-ways 1-shot\", \"5-ways 5-shot\" provides more training samples, enabling the model to acquire richer feature representations. In experiments, \"5-ways 1-shot\" and \"5-ways 5-shot\" tasks are typically employed to evaluate the performance of models, facilitating the comparison of different models in the context of few-shot learning scenarios. These tasks impose significant demands on a model's generalization and learning capabilities as the model must learn effective feature representations from a limited number of samples and be capable of accurate classification on new instances. In the table, \"EGNN-NHR\" refers to the EGNN model with convolutional residual structure (as shown in Figure 3), while \"EGNN-NHR\({}_{0}\)\" refers to the EGNN model with a linear residual structure. **Result Analysis:**

In the public dataset mini-ImageNet (as shown in Table 1), both residual connections with convolutional structures and linear residual structures showed significant improvements in experiments. For instance, in the 5-way 1-shot setting on the mini-ImageNet dataset, EGNN-NHR improved by 2.70% over EGNN, while EGNN-NHR\({}_{0}\) improved by 2.54%.