# Fused Node-Level Residual Structure Edge Graph Neural Network for Few-Shot Image Classification
## 3 Methods
### EGNN + Node Hierarchical Residual Model Architecture
In the 5-way 5-shot setting on the mini-ImageNet dataset, EGNN-NHR improved by 0.89% over EGNN, and EGNN-NHR\({}_{0}\) improved by 2.18%. However, an interesting phenomenon was seen: models with convolutional structures showed more improvement in the 5-way 1-shot experiments compared to the 5-way 5-shot experiments. It is possible that if different structures are appropriately designed for each layer, residual connections with convolutional structures might show more improvement with smaller support sets, while linear residual structures could provide more improvement with larger support sets. In the public dataset tiered-ImageNet (as shown in Table 2), the experiments in the 5-way 1-shot setting showed an increase of 1.17%, while there was a slight decrease in the 5-way 5-shot setting. In tiered-ImageNet experiments, since this dataset is relatively large, it's possible to fine-tune the knowledge learned from mini-ImageNet directly. In the public dataset, we observed some intriguing phenomena and results that warrant further in-depth exploration and explanation. A more detailed discussion follows:

Impact of Convolutional and Linear Residual Structures: The experimental results have demonstrated a significant enhancement in model performance upon introducing convolutional and linear residual connections, marking a noteworthy finding. In the context of the 5-way 1-shot task, both EGNN-NHR and EGNN-NHR0 exhibited substantial improvements of 2.70% and 2.54%, respectively. However, in the 5-way 5-shot task, the improvements were comparatively modest, with EGNN-NHR achieving 0.89% and EGNN-NHR0 showing a 2.18% boost. This variance in performance enhancement may be attributed to the varying characteristics of different tasks and datasets. Further research can delve into the underlying reasons why convolutional structures excel in few-shot tasks, while linear residual structures prove more effective in larger-sample scenarios. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mode** & **1-Shot** & **5-Shot** \\ \hline \multirow{5}{*}{GNN methods} & GNN [17] & 50.30 & 66.40 \\  & TPN [38] & 55.51 & 69.86 \\  & EGNN [19] & 58.98 & 76.37 \\ \cline{1-1}  & EGNN [19]\({}^{\star}\) & 58.34 & 76.80 \\ \cline{1-1}  & wDAE-GNN [23] & 61.07 \(\pm\) 0.15 & 76.75 \(\pm\) 0.11 \\ \cline{1-1}  & **EGNN-NHR\({}_{0}\)** & **61.68** & 77.26 \\ \cline{1-1}  & **EGNN-NHR\({}_{0}\)** & 61.52 & **78.55** \\ \hline \hline \end{tabular} \({}^{\star}\)—we implemented using pre-trained feature extractor.

\end{table} 
Table 1: The 1-shot and 5-shot classification results on the mini-ImageNet dataset under the 5-way setting. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Mode** & **1-Shot** & **5-Shot** \\ \hline \multirow{3}{*}{GNN methods} & GNN [17] & 42.36 & 48.79 \\  & EGNN [19] & 49.47 & 57.58 \\ \cline{1-1}  & **EGNN-NHR\({}_{0}\)** & **60.61** & **66.88** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The 1-shot and 5-shot classification results on the CBAC dataset under the 5-way setting. Explaining the Performance Dip: A slight decline in performance was observed in the 5-way 5-shot task. This phenomenon might be linked to the complexity of the task and the model's capacity. More intricate tasks often demand increased learning and representation capabilities, and the relatively larger support sets in 5-shot tasks may contribute to potential overfitting by the model. Additionally, factors such as dataset properties or hyperparameter choices during training could also influence performance. Future Research Directions: Given the substantial performance gains achieved through the introduction of residual connection structures, future research avenues could explore additional types of residual structures or combinations to further enhance model performance. Diversifying the model by experimenting with different convolutional kernel sizes, channel numbers, or other variants could be considered.