Overview of GAT (Graph Attention Network)
Attention in deep learning, as described in “Attention in Deep Learning,” is a method for learning to pay attention to specific parts of an image or natural language, which is the approach used successfully in the EncoderDecoder model described in “Overview of Encoder/Decoder Models in GNN, Algorithms and Examples of Implementation“. The attention mechanism is an approach that can automatically determine the importance of each node based on the relationships and connection patterns among different nodes. computed as a weighted average of the combined features of the neighboring nodes, and this weight shall be computed and learned based on the importance of the relationships between the different nodes.
Such an attention in the EncoderDecoder model can map a set of query and key-value pairs to an output. Here, query, key, and value are all vectors, and the output is the weighted sum of the keys that match the query and their corresponding values. In the past, RNNs described in “Overview of RNNs, Algorithms, and Implementation Examples” were often used to learn such dependencies, but the Transformer described in “Overview of Transformer Models, Algorithms, and Implementation Examples” uses an attention The Transformer, described in “Overview of the Transformer Model, Algorithm, and Example Implementations,” uses an Encoder-Decoder model that uses the attention mechanism to successfully construct a model with improved accuracy and computational complexity without using RNNs or CNNs. This Transformer model is the basis for the most recent leading models in natural language processing, such as BERT (described in “BERT Overview, Algorithm, and Implementation Examples“) and GPT (described in “GPT Overview, Algorithm, and Implementation Examples“).
In graph convolutional aggregation, most of the information from neighbors is treated equally or given weights in advance, but the effects of neighbors are generally very different, and learning during training is a more natural approach than giving weights in advance. The GAT reported by Velickovic et al. in “Graph Attention Networks” applies attention, which is the de facto standard for sequence (e.g., natural language word sequences) tasks, to graph learning.
Velickovic et al. list the following features of using attention instead of convolution
- Efficient computation due to parallelizability.
- It can be applied to nodes of different degree by assigning arbitrary weights to the neighbors.
- The inductive approach makes the model generalizable to unknown graph structures.
The graph attention layer, which realizes attention in GAT, is a node feature set\(\mathbf{h}=\{\vec{h}_1,\vec{h}_2,\dots,\vec{h}_N\},\vec{h}_i\in\mathbb{R}^F\)( N is the number of nodes and F is the number of features for each node) and the graph as input, output a new node feature set\(\mathbf{h}’=\{\vec{h’}_1,\vec{h’}_2,\dots,\vec{h’}_N\}\ \vec{h’}_i\in\mathbb{R}^{F’}\) Output. In order to have sufficient expressive power to transform the input feature set, at least one learnable linear transformation is required, and for this purpose the weight matrix \(\mathbf{W}\in\mathbb{R}^{F’\times F}\) is applied to each node. Next, based on the attention coefficient (a:\mathbb{R}^{F’}\times\mathbb{R}^{F’}\rightarrow\mathbb{R}\), the attention coefficient is calculated as shown in the following formula. This indicates the importance of the feature of node j to node i. In other words, it expresses the strength of the relationship between two node expressions.
\[e_{ij}=a(\mathbf{W}\vec{h}_i,\ \mathbf{W}\vec{h}_j)\]
Since j is arbitrary here, we introduce masked attention that takes into account a graph structure that computes \(e_{ij}\) only for \(j\in N_i\), which is a neighborhood of node i in the graph. GAT considers a neighborhood with distance 1 (including i itself). In order to make it equivalent to the values of the other nodes, the following softmax function is used for normalization.
\[\alpha_{ij}=softmax x_j(e_{ij})=\frac{e^{e_{ij}}}{\sum_{k\in N_i}e^{e_{ik}}}\]
This framework is generic, independent of the choice of attention, but the GAT paper uses a one-layer forward propagating neural network as attention a, which can be represented as a weight vector of \(\vec{a}\in\mathbb{R}^{2F’}\). LeakyReLU is used as the activation function. The resulting \(\alpha_{ij}\) is calculated by the following equation where T represents transposition and || represents concatenation.
\[\alpha_{ij}=softmax x_j(e_{ij})=\frac{e^{LeakyReLU(\vec{a}^T[\mathbf{W}\vec{h}_i||\mathbf{W}\vec{h}_j])}}{\sum_{k\in N_i}e^{LeakyReLU((\vec{a}^T[\mathbf{W}\vec{h}_i[\mathbf{W}\vec{h}_k])}}\]
As with the Transformer, multi-head attention is very convenient for stabilizing the learning process of self-attention. K independent attentions, each with different parameters, are computed and their outputs are aggregated by concatenation and addition.
GAT is known to outperform conventional graph neural networks (GNNs) in learning the representation of nodes in graph data, and is considered to be a highly scalable and efficient learning method, especially for large graphs.
In the experiments reported in “Graph Attention Networks,” node classification was performed using Cora, Citeseer, and Pubmed as transductive learning methods, showing that GAT performs better than DeepWalk described in “DeepWalk Overview, Algorithms, and Example Implementations,”, ChebNet described in “Overview of ChebNet and Examples of Algorithms and Implementations“, GCN, and others. The results show that GAT performs highly accurate classification compared to DeepWalk, ChebNet, GCN, and others. Inductive learning is used to perform graph classification using protein-protein interaction (PPI) datasets, showing that GAT performs more accurate classification than MLP, GraphSAGE described in “Overview of GraphSAGE, Algorithms, and Examples of Implementations. Algorithms and Examples of Implementations“, and other methods.
The code available for GAT is available on the authors’ Git page.
Algorithms related to GAT (Graph Attention Network)
The GAT (Graph Attention Network) algorithm is designed to learn representations of nodes in a graph structure. The main points of the GAT algorithm are as follows.
1. input graph representation: GAT takes as input a graph in which feature representations of nodes are given. Each node is represented by a feature vector.
2. definition of an attention mechanism: GAT uses an attention mechanism to represent the relationship between different nodes. Usually, a function is defined for each pair of nodes to determine the weight of attention.
3. Computation of attention: In GAT, the attention mechanism of each node computes the weight of attention between that node and its neighbors. This weight is determined based on the similarity and importance of the features of that node and its neighbors, and typically this is computed using the inner product of the node’s feature vectors or a similarity function.
4. weighted feature aggregation: Using the calculated attention weights, features from each node’s neighbors are aggregated in a weighted manner. This yields a new representation of each node. Typically, a weighted average is used.
5. nonlinear transformation and output: The aggregated features are passed through a nonlinear transformation layer (e.g., ReLU) to obtain a final representation of the nodes. These representations are passed to different architectures depending on the task.
6. learning and optimization: GAT is typically trained to minimize the loss function using a labeled dataset given a representation of the nodes. Typically, the gradient descent method or its variants are used.
In this way, GATs are able to learn representations of nodes for graph data and use those representations to solve a variety of graph-related tasks.
Application examples of GAT (Graph Attention Network)
GAT (Graph Attention Network) has been widely applied in various domains due to its flexibility and high performance. The following are examples of GAT applications.
1. graph classification: GAT is used for tasks that classify nodes or graphs into categories based on the overall graph structure. Examples include user group classification in social networks and protein classification in biological networks.
2. node classification: GAT is also used for the task of predicting labels for each node, for example, predicting user attributes for a social network or predicting the activity of a compound based on the structure of a chemical molecule.
3. recommendation: GAT is used to represent relationships between users and items, and has been applied to recommend items to users in recommendation systems.
4. graph generation: GAT is used to learn existing graph structures and generate new graphs, for example, the generation of molecular graph structures or data extensions of graph data.
5. transfer learning: GAT is used to transfer knowledge between different graph domains, e.g., when a model learned in one domain is transferred to another domain.
Examples of GAT (Graph Attention Network) implementations
Example implementation of a Graph Attention Network (GAT) is shown using Python and PyTorch. The code below is an implementation of the GAT model for solving a simple graph classification task; this example uses the Cora dataset.
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch_geometric.nn import GATConv
from torch_geometric.datasets import Planetoid
import torch.optim as optim
from torch.utils.data import DataLoader
# Definition of the GAT model
class GAT(nn.Module):
def __init__(self, num_features, hidden_dim, num_classes, num_heads):
super(GAT, self).__init__()
self.conv1 = GATConv(num_features, hidden_dim, heads=num_heads, dropout=0.6)
self.conv2 = GATConv(hidden_dim * num_heads, num_classes, dropout=0.6)
def forward(self, data):
x, edge_index = data.x, data.edge_index
x = F.dropout(x, p=0.6, training=self.training)
x = F.elu(self.conv1(x, edge_index))
x = F.dropout(x, p=0.6, training=self.training)
x = self.conv2(x, edge_index)
return F.log_softmax(x, dim=1)
# Loading Data Sets
dataset = Planetoid(root='/tmp/Cora', name='Cora')
data = dataset[0]
# Model initialization and training
device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
model = GAT(dataset.num_features, hidden_dim=8, num_classes=dataset.num_classes, num_heads=8).to(device)
optimizer = optim.Adam(model.parameters(), lr=0.005, weight_decay=5e-4)
criterion = nn.NLLLoss()
def train(epoch):
model.train()
optimizer.zero_grad()
out = model(data)
loss = criterion(out[data.train_mask], data.y[data.train_mask])
loss.backward()
optimizer.step()
print(f'Epoch: {epoch}, Loss: {loss.item()}')
for epoch in range(1, 201):
train(epoch)
# test
model.eval()
_, pred = model(data).max(dim=1)
correct = int(pred[data.test_mask].eq(data.y[data.test_mask]).sum().item())
acc = correct / int(data.test_mask.sum())
print(f'Test Accuracy: {acc}')This code implements GAT using PyTorch Geometric to train and test models on the Cora dataset.
GAT (Graph Attention Network) Challenges and Measures to Address Them
Although GAT (Graph Attention Network) has excellent performance, it faces several challenges. The challenges and their countermeasures are described below.
1. increased computational load:
Challenge: GAT tends to be computationally expensive because it uses attention mechanisms to model relationships between different nodes, especially for large graphs or when many attention heads are used.
Solution: Techniques such as mini-batching, graph sampling, and reducing the number of parameters in the model can be used to reduce the computational load. Improving hardware performance and using distributed processing can also be effective.
2. over-learning:
Challenge: Because GAT is a very flexible model for large graphs and complex data, there is a risk of over-learning, especially when the number of nodes is large or the data contains noise.
Solution: Overlearning can be prevented by using methods such as dropouts, regularization, data expansion, or adjusting the complexity of the model. It is also important to improve the generalization performance of the model by using techniques such as cross-validation and early stopping.
3. graphs at different scales:
Challenge: GAT may have difficulty in properly weighting graphs of different scales and densities, especially when the number of nodes and edges in the graphs are different.
Solution: Graph preprocessing and feature engineering to homogenize node and edge characteristics can be used to deal with graphs of different scales. Robust model design for graphs of different scales and the use of scaling and normalization techniques can also be helpful.
Reference Information and Reference Books
For more information on graph data, see “Graph Data Processing Algorithms and Applications to Machine Learning/Artificial Intelligence Tasks. Also see “Knowledge Information Processing Techniques” for details specific to knowledge graphs. For more information on deep learning in general, see “About Deep Learning.
Reference book is
“Graph Neural Networks: Foundations, Frontiers, and Applications“等がある。
“Introduction to Graph Neural Networks“
“Graph Neural Networks in Action“
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