# AFGN: Adaptive Filtering Graph Neural Network for Few-Shot Learning
## 1 Introduction  
The success of deep learning in computer vision relies on a large amount of labeled data [1, 2, 3]. However, in practical scenarios, there are situations where labeling costs are high or the number of samples is limited. In situations where samples are scarce, a limited number of labeled samples are not sufficient to support model training, leading to overfitting and difficulty in generalizing to new data. Therefore, completing the training of the model under the premise of limited sample quantity is a challenging problem. The human ability to quickly learn from a small number of samples and generalize to new tasks has inspired the emergence of few-shot learning. Few-shot learning can acquire the ability to quickly adapt to new tasks in multi-task training, ultimately accomplishing the goal of \"learning to learn\" [4]. Initially, it was relatively challenging for few-shot models to extract useful information from limited data. With the rapid development of Graph Neural Networks in recent years, Graph-based Few-shot (GBFS) models have become a new research trend in few-shot learning. Graph Neural Networks combined with few-shot learning can provide effective solutions in situations with limited data. Specifically, the relationships between nodes and the graph structure can serve as additional information to alleviate the data limitation problem in few-shot tasks. Certainly, there is still room for improvement in model performance for GBFS models. This paper focusesprimarily on studying graph construction and graph convolution filtering to improve model performance. Constructing a suitable graph for graph networks is the basis for the model to get good learning performance. In few-shot tasks, episodic training strategy takes tasks as the basic unit of training, where a task includes support set and query set. These GBFS models establish a one-to-one correspondence between tasks and graphs, with nodes on the graph corresponding to samples in the tasks. In most GBFS models, sample features extracted from the backbone are directly utilized as the initial node features during graph construction, which focuses on the global features of the image, while ignoring the hidden dependency information within the image features. We found hidden correlations among the channels of the extracted tensor features. By utilizing theoretical knowledge in statistical probability, we can calculate the Brownian covariance between these channels, thereby obtaining representations of nodes. Subsequently, we initialize edge features based on these node representations, thus constructing the corresponding graphs for the few-shot tasks. Furthermore, based on the theory of spectral graph convolution, we realize that convolution on the graph is actually a filtering process of the graph signal in the frequency domain. Most existing GBFS models have not studied few-shot learning from the direction of graph convolution filtering. These models employ the message passing approach proposed in [5], after converting the graph convolution into the frequency domain, it was found that GCN constructs a stationary filter in the frequency domain, allowing all frequency components of the graph signal to pass through. where Graph Convolutional Network (GCN) constructs a stationary filter in the frequency domain, allowing all frequency components of the graph signal to pass through. However, in the message aggregation updates of graph networks, as much beneficial information for classification as possible should be aggregated. The current best method combining graph networks and filtering techniques is the HDGN proposed in our previous work [6]. HDGN designs a low-pass filter to help the model retain more low-frequency information among the nodes and less high-frequency information among the nodes in few-shot tasks. However, in practical scenarios, both low-frequency and high-frequency information have significant impacts on classification tasks.