图注意力网络论文详解和PyTorch实现

import torch from torch import nn # in_features -> F and out_feature -> 
F' in_features = ... out_feature = ... # instanciate the learnable weight matrix 
W (FxF') W = nn.Parameter(torch.empty(size=(in_features, out_feature))) # 
Initialize the weight matrix W nn.init.xavier_normal_(W) # multiply W and h (h 
is input features of all the nodes -> NxF matrix) h_transformed = torch.mm(h, 
W)

# instanciate the learnable attention parameter vector `a` a = 
nn.Parameter(torch.empty(size=(2 * out_feature, 1))) # Initialize the parameter 
vector `a` nn.init.xavier_normal_(a) # we obtained `h_transformed` in the 
previous code snippet # calculating the dot product of all node embeddings # and 
first half the attention vector parameters (corresponding to neighbor messages) 
source_scores = torch.matmul(h_transformed, self.a[:out_feature, :]) # 
calculating the dot product of all node embeddings # and second half the 
attention vector parameters (corresponding to target node) target_scores = 
torch.matmul(h_transformed, self.a[out_feature:, :]) # broadcast add e = 
source_scores + target_scores.T e = self.leakyrelu(e)

connectivity_mask = -9e16 * torch.ones_like(e) # adj_mat is the N by N 
adjacency matrix e = torch.where(adj_mat > 0, e, connectivity_mask) # masked 
attention scores # attention coefficients are computed as a softmax over the 
rows # for each column j in the attention score matrix e attention = 
F.softmax(e, dim=-1)

# final node embeddings are computed as a weighted average of the features of 
its neighbors h_prime = torch.matmul(attention, h_transformed)

import torch from torch import nn import torch.nn.functional as F 
################################ ### GAT LAYER DEFINITION ### 
################################ class GraphAttentionLayer(nn.Module): def 
__init__(self, in_features: int, out_features: int, n_heads: int, concat: bool = 
False, dropout: float = 0.4, leaky_relu_slope: float = 0.2): 
super(GraphAttentionLayer, self).__init__() self.n_heads = n_heads # Number of 
attention heads self.concat = concat # wether to concatenate the final attention 
heads self.dropout = dropout # Dropout rate if concat: # concatenating the 
attention heads self.out_features = out_features # Number of output features per 
node assert out_features % n_heads == 0 # Ensure that out_features is a multiple 
of n_heads self.n_hidden = out_features // n_heads else: # averaging output over 
the attention heads (Used in the main paper) self.n_hidden = out_features # A 
shared linear transformation, parametrized by a weight matrix W is applied to 
every node # Initialize the weight matrix W self.W = 
nn.Parameter(torch.empty(size=(in_features, self.n_hidden * n_heads))) # 
Initialize the attention weights a self.a = 
nn.Parameter(torch.empty(size=(n_heads, 2 * self.n_hidden, 1))) self.leakyrelu = 
nn.LeakyReLU(leaky_relu_slope) # LeakyReLU activation function self.softmax = 
nn.Softmax(dim=1) # softmax activation function to the attention coefficients 
self.reset_parameters() # Reset the parameters def reset_parameters(self): 
nn.init.xavier_normal_(self.W) nn.init.xavier_normal_(self.a) def 
_get_attention_scores(self, h_transformed: torch.Tensor): source_scores = 
torch.matmul(h_transformed, self.a[:, :self.n_hidden, :]) target_scores = 
torch.matmul(h_transformed, self.a[:, self.n_hidden:, :]) # broadcast add # 
(n_heads, n_nodes, 1) + (n_heads, 1, n_nodes) = (n_heads, n_nodes, n_nodes) e = 
source_scores + target_scores.mT return self.leakyrelu(e) def forward(self, h: 
torch.Tensor, adj_mat: torch.Tensor): n_nodes = h.shape[0] # Apply linear 
transformation to node feature -> W h # output shape (n_nodes, n_hidden * 
n_heads) h_transformed = torch.mm(h, self.W) h_transformed = 
F.dropout(h_transformed, self.dropout, training=self.training) # splitting the 
heads by reshaping the tensor and putting heads dim first # output shape 
(n_heads, n_nodes, n_hidden) h_transformed = h_transformed.view(n_nodes, 
self.n_heads, self.n_hidden).permute(1, 0, 2) # getting the attention scores # 
output shape (n_heads, n_nodes, n_nodes) e = 
self._get_attention_scores(h_transformed) # Set the attention score for 
non-existent edges to -9e15 (MASKING NON-EXISTENT EDGES) connectivity_mask = 
-9e16 * torch.ones_like(e) e = torch.where(adj_mat > 0, e, connectivity_mask) 
# masked attention scores # attention coefficients are computed as a softmax 
over the rows # for each column j in the attention score matrix e attention = 
F.softmax(e, dim=-1) attention = F.dropout(attention, self.dropout, 
training=self.training) # final node embeddings are computed as a weighted 
average of the features of its neighbors h_prime = torch.matmul(attention, 
h_transformed) # concatenating/averaging the attention heads # output shape 
(n_nodes, out_features) if self.concat: h_prime = h_prime.permute(1, 0, 
2).contiguous().view(n_nodes, self.out_features) else: h_prime = 
h_prime.mean(dim=0) return h_prime

class GAT(nn.Module): def __init__(self, in_features, n_hidden, n_heads, 
num_classes, concat=False, dropout=0.4, leaky_relu_slope=0.2): super(GAT, 
self).__init__() # Define the Graph Attention layers self.gat1 = 
GraphAttentionLayer( in_features=in_features, out_features=n_hidden, 
n_heads=n_heads, concat=concat, dropout=dropout, 
leaky_relu_slope=leaky_relu_slope ) self.gat2 = GraphAttentionLayer( 
in_features=n_hidden, out_features=num_classes, n_heads=1, concat=False, 
dropout=dropout, leaky_relu_slope=leaky_relu_slope ) def forward(self, 
input_tensor: torch.Tensor , adj_mat: torch.Tensor): # Apply the first Graph 
Attention layer x = self.gat1(input_tensor, adj_mat) x = F.elu(x) # Apply ELU 
activation function to the output of the first layer # Apply the second Graph 
Attention layer x = self.gat2(x, adj_mat) return F.softmax(x, dim=1) # Apply 
softmax activation function