【PyG】图神经网络GAT代码自学

图方法分为谱方法和空间方法，空间方法是直接在图上进行操作，代表方法之一GAT；谱方法是将图映射到谱域上，例如拉普拉斯矩阵经过特征分解得到的空间，代表方法之一是GCN。本文介绍GAT的代码实现。

本文参考论文原作者代码https://github.com/PetarV-/GAT

论文原图与核心公式

utils相关代码分析

见之前写的GCN那篇博客

https://blog.csdn.net/qq_42859088/article/details/124669794?spm=1001.2014.3001.5501

train相关代码分析

train.py

感觉和之前的gcn没有区别，先setting，再cuda，load_data，然后train，eval，test

from __future__ import division
from __future__ import print_function

import os
import glob
import time
import random
import argparse
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
import torch.optim as optim
from torch.autograd import Variable

from utils import load_data, accuracy
from models import GAT, SpGAT

# Training settings
parser = argparse.ArgumentParser()
parser.add_argument('--no-cuda', action='store_true', default=False, help='Disables CUDA training.')
parser.add_argument('--fastmode', action='store_true', default=False, help='Validate during training pass.')
parser.add_argument('--sparse', action='store_true', default=False, help='GAT with sparse version or not.')
parser.add_argument('--seed', type=int, default=72, help='Random seed.')
parser.add_argument('--epochs', type=int, default=200, help='Number of epochs to train.')
parser.add_argument('--lr', type=float, default=0.005, help='Initial learning rate.')
parser.add_argument('--weight_decay', type=float, default=5e-4, help='Weight decay (L2 loss on parameters).')
parser.add_argument('--hidden', type=int, default=8, help='Number of hidden units.')
parser.add_argument('--nb_heads', type=int, default=8, help='Number of head attentions.')
parser.add_argument('--dropout', type=float, default=0.6, help='Dropout rate (1 - keep probability).')
parser.add_argument('--alpha', type=float, default=0.2, help='Alpha for the leaky_relu.')
parser.add_argument('--patience', type=int, default=100, help='Patience')

args = parser.parse_args()
args.cuda = not args.no_cuda and torch.cuda.is_available()

random.seed(args.seed)
np.random.seed(args.seed)
torch.manual_seed(args.seed)
if args.cuda:
    torch.cuda.manual_seed(args.seed)

# Load data
adj, features, labels, idx_train, idx_val, idx_test = load_data()

# Model and optimizer
args.sparse = False
if args.sparse:
    model = SpGAT(nfeat=features.shape[1], 
                nhid=args.hidden, 
                nclass=int(labels.max()) + 1, 
                dropout=args.dropout, 
                nheads=args.nb_heads, 
                alpha=args.alpha)
else:
    model = GAT(nfeat=features.shape[1], 
                nhid=args.hidden, 
                nclass=int(labels.max()) + 1, 
                dropout=args.dropout, 
                nheads=args.nb_heads, 
                alpha=args.alpha)
optimizer = optim.Adam(model.parameters(), 
                       lr=args.lr, 
                       weight_decay=args.weight_decay)

if args.cuda:
    model.cuda()
    features = features.cuda()
    adj = adj.cuda()
    labels = labels.cuda()
    idx_train = idx_train.cuda()
    idx_val = idx_val.cuda()
    idx_test = idx_test.cuda()

# features, adj, labels = Variable(features), Variable(adj), Variable(labels)


def train(epoch):
    t = time.time()
    model.train()
    optimizer.zero_grad()
    output = model(features, adj)  # GAT模块
    loss_train = F.nll_loss(output[idx_train], labels[idx_train])
    acc_train = accuracy(output[idx_train], labels[idx_train])
    loss_train.backward()
    optimizer.step()

    if not args.fastmode:
        # Evaluate validation set performance separately,
        # deactivates dropout during validation run.
        model.eval()
        output = model(features, adj)

    loss_val = F.nll_loss(output[idx_val], labels[idx_val])
    acc_val = accuracy(output[idx_val], labels[idx_val])
    print('Epoch: {:04d}'.format(epoch+1),
          'loss_train: {:.4f}'.format(loss_train.data.item()),
          'acc_train: {:.4f}'.format(acc_train.data.item()),
          'loss_val: {:.4f}'.format(loss_val.data.item()),
          'acc_val: {:.4f}'.format(acc_val.data.item()),
          'time: {:.4f}s'.format(time.time() - t))

    return loss_val.data.item()


def compute_test():
    model.eval()
    output = model(features, adj)
    loss_test = F.nll_loss(output[idx_test], labels[idx_test])
    acc_test = accuracy(output[idx_test], labels[idx_test])
    print("Test set results:",
          "loss= {:.4f}".format(loss_test.item()),
          "accuracy= {:.4f}".format(acc_test.item()))

# Train model
t_total = time.time()
loss_values = []
bad_counter = 0
best = args.epochs + 1
best_epoch = 0
for epoch in range(args.epochs):
    loss_values.append(train(epoch))

    torch.save(model.state_dict(), '{}.pkl'.format(epoch))
    if loss_values[-1] < best:
        best = loss_values[-1]
        best_epoch = epoch
        bad_counter = 0
    else:
        bad_counter += 1

    if bad_counter == args.patience:
        break

    files = glob.glob('*.pkl')
    for file in files:
        epoch_nb = int(file.split('.')[0])
        if epoch_nb < best_epoch:
            os.remove(file)

files = glob.glob('*.pkl')
for file in files:
    epoch_nb = int(file.split('.')[0])
    if epoch_nb > best_epoch:
        os.remove(file)

print("Optimization Finished!")
print("Total time elapsed: {:.4f}s".format(time.time() - t_total))

# Restore best model
print('Loading {}th epoch'.format(best_epoch))
model.load_state_dict(torch.load('{}.pkl'.format(best_epoch)))

# Testing
compute_test()

models.py

import torch
import torch.nn as nn
import torch.nn.functional as F
from layers import GraphAttentionLayer, SpGraphAttentionLayer


class GAT(nn.Module):
    def __init__(self, nfeat, nhid, nclass, dropout, alpha, nheads):
        """Dense version of GAT."""
        super(GAT, self).__init__()
        self.dropout = dropout

        self.attentions = [GraphAttentionLayer(nfeat, nhid, dropout=dropout, alpha=alpha, concat=True) for _ in range(nheads)]
        #nfeat为feature大小也就是idx_features_labels[:, 1:-1]第二列到倒数第二列，nhid自己设定
        #for _ in range(nheads)多头注意力机制，这里面nheads为8
        for i, attention in enumerate(self.attentions):
            self.add_module('attention_{}'.format(i), attention)
        #创建8个多头注意力机制模块

        self.out_att = GraphAttentionLayer(nhid * nheads, nclass, dropout=dropout, alpha=alpha, concat=False)  # 第二层(最后一层)的attention layer
        #nhid * nheads输入维度8*8，输出维度当时分的类，这个数据集里面是7个
    def forward(self, x, adj):
        x = F.dropout(x, self.dropout, training=self.training)
        x = torch.cat([att(x, adj) for att in self.attentions], dim=1)  # 将每层attention拼接
        x = F.dropout(x, self.dropout, training=self.training)
        x = F.elu(self.out_att(x, adj))   # 第二层的attention layer
        return F.log_softmax(x, dim=1)

layers.py

import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F


class GraphAttentionLayer(nn.Module):
    """
    Simple GAT layer, similar to https://arxiv.org/abs/1710.10903
    """
    def __init__(self, in_features, out_features, dropout, alpha, concat=True):
        super(GraphAttentionLayer, self).__init__()
        self.dropout = dropout
        self.in_features = in_features
        self.out_features = out_features
        self.alpha = alpha
        self.concat = concat

        self.W = nn.Parameter(torch.empty(size=(in_features, out_features)))
        nn.init.xavier_uniform_(self.W.data, gain=1.414)
        #初始化in_features行，out_features列的权重矩阵
        self.a = nn.Parameter(torch.empty(size=(2*out_features, 1)))  # concat(V,NeigV)
        nn.init.xavier_uniform_(self.a.data, gain=1.414)
        #初始化α，大小为两个out_features拼接起来


        self.leakyrelu = nn.LeakyReLU(self.alpha)

    def forward(self, h, adj):
        Wh = torch.mm(h, self.W) # h.shape: (N, in_features), hW.shape: (N, out_features)
        a_input = self._prepare_attentional_mechanism_input(Wh)  # 每一个节点和所有节点，特征。(Vall, Vall, feature)
        e = self.leakyrelu(torch.matmul(a_input, self.a).squeeze(2))
        # 之前计算的是一个节点和所有节点的attention，其实需要的是连接的节点的attention系数
        zero_vec = -9e15*torch.ones_like(e)
        attention = torch.where(adj > 0, e, zero_vec)    # 将邻接矩阵中小于0的变成负无穷
        attention = F.softmax(attention, dim=1)  # 按行求softmax。 sum(axis=1) === 1
        attention = F.dropout(attention, self.dropout, training=self.training)
        h_prime = torch.matmul(attention, Wh)   # 聚合邻居函数

        if self.concat:
            return F.elu(h_prime)   # elu-激活函数
        else:
            return h_prime

    def _prepare_attentional_mechanism_input(self, Wh):
        N = Wh.size()[0] # number of nodes

        # Below, two matrices are created that contain embeddings in their rows in different orders.
        # (e stands for embedding)
        # These are the rows of the first matrix (Wh_repeated_in_chunks): 
        # e1, e1, ..., e1,            e2, e2, ..., e2,            ..., eN, eN, ..., eN
        # '-------------' -> N times  '-------------' -> N times       '-------------' -> N times
        # 
        # These are the rows of the second matrix (Wh_repeated_alternating): 
        # e1, e2, ..., eN, e1, e2, ..., eN, ..., e1, e2, ..., eN 
        # '----------------------------------------------------' -> N times
        # 
        
        Wh_repeated_in_chunks = Wh.repeat_interleave(N, dim=0)  # 复制
        Wh_repeated_alternating = Wh.repeat(N, 1)
        # Wh_repeated_in_chunks.shape == Wh_repeated_alternating.shape == (N * N, out_features)

        # The all_combination_matrix, created below, will look like this (|| denotes concatenation):
        # e1 || e1
        # e1 || e2
        # e1 || e3
        # ...
        # e1 || eN
        # e2 || e1
        # e2 || e2
        # e2 || e3
        # ...
        # e2 || eN
        # ...
        # eN || e1
        # eN || e2
        # eN || e3
        # ...
        # eN || eN

        all_combinations_matrix = torch.cat([Wh_repeated_in_chunks, Wh_repeated_alternating], dim=1)
        # all_combinations_matrix.shape == (N * N, 2 * out_features)

        return all_combinations_matrix.view(N, N, 2 * self.out_features)

    def __repr__(self):
        return self.__class__.__name__ + ' (' + str(self.in_features) + ' -> ' + str(self.out_features) + ')'

原始GAT代码debug调试

GAT初始化

第一层初始化结果

第二层初始化结果

此时多头注意力机制生成8个attention

第一次训练结果

此时代码debug到layers.py的class GraphAttentionLayer(nn.Module)中forward(self, h, adj)函数

wh为两个矩阵相乘，h.shape: (N, in_features), hW.shape: (N, out_features)

_prepare_attentional_mechanism_input这个函数做的是矩阵拼接操作，每一个节点和所有节点，特征。(Vall, Vall, feature)

各变量结果如下，此段代码实现了矩阵的拼接，得到矩阵torch.Size([2708, 2708, 16])




e = self.leakyrelu(torch.matmul(a_input, self.a).squeeze(2))， 之前计算的是一个节点和所有节点的attention，其实需要的是连接的节点的attention系数

第一个attention将邻接矩阵中小于0的变成负无穷

第二个attention，按行求softmax，sum(axis=1) === 1

第三个attention聚合邻居函数，h_prime经过激活函数激活的结果


上方代码运行8次，然后拼接起来，此时gpu内存溢出报错，转为使用SpGAT代码。

SpGAT代码

models.py

class SpGAT(nn.Module):
    def __init__(self, nfeat, nhid, nclass, dropout, alpha, nheads):
        """Sparse version of GAT."""
        super(SpGAT, self).__init__()
        self.dropout = dropout

        self.attentions = [SpGraphAttentionLayer(nfeat, 
                                                 nhid, 
                                                 dropout=dropout, 
                                                 alpha=alpha, 
                                                 concat=True) for _ in range(nheads)]
        for i, attention in enumerate(self.attentions):
            self.add_module('attention_{}'.format(i), attention)

        self.out_att = SpGraphAttentionLayer(nhid * nheads, 
                                             nclass, 
                                             dropout=dropout, 
                                             alpha=alpha, 
                                             concat=False)

    def forward(self, x, adj):
        x = F.dropout(x, self.dropout, training=self.training)
        x = torch.cat([att(x, adj) for att in self.attentions], dim=1)
        x = F.dropout(x, self.dropout, training=self.training)
        x = F.elu(self.out_att(x, adj))
        return F.log_softmax(x, dim=1)

layers.py

class SpecialSpmmFunction(torch.autograd.Function):
    """Special function for only sparse region backpropataion layer."""
    @staticmethod
    def forward(ctx, indices, values, shape, b):
        assert indices.requires_grad == False
        a = torch.sparse_coo_tensor(indices, values, shape)
        ctx.save_for_backward(a, b)
        ctx.N = shape[0]
        return torch.matmul(a, b)

    @staticmethod
    def backward(ctx, grad_output):
        a, b = ctx.saved_tensors
        grad_values = grad_b = None
        if ctx.needs_input_grad[1]:
            grad_a_dense = grad_output.matmul(b.t())
            edge_idx = a._indices()[0, :] * ctx.N + a._indices()[1, :]
            grad_values = grad_a_dense.view(-1)[edge_idx]
        if ctx.needs_input_grad[3]:
            grad_b = a.t().matmul(grad_output)
        return None, grad_values, None, grad_b


class SpecialSpmm(nn.Module):
    def forward(self, indices, values, shape, b):
        return SpecialSpmmFunction.apply(indices, values, shape, b)

    
class SpGraphAttentionLayer(nn.Module):
    """
    Sparse version GAT layer, similar to https://arxiv.org/abs/1710.10903
    """

    def __init__(self, in_features, out_features, dropout, alpha, concat=True):
        super(SpGraphAttentionLayer, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.alpha = alpha
        self.concat = concat

        self.W = nn.Parameter(torch.zeros(size=(in_features, out_features)))
        nn.init.xavier_normal_(self.W.data, gain=1.414)
                
        self.a = nn.Parameter(torch.zeros(size=(1, 2*out_features)))
        nn.init.xavier_normal_(self.a.data, gain=1.414)

        self.dropout = nn.Dropout(dropout)
        self.leakyrelu = nn.LeakyReLU(self.alpha)
        self.special_spmm = SpecialSpmm()

    def forward(self, input, adj):
        dv = 'cuda' if input.is_cuda else 'cpu'

        N = input.size()[0]
        edge = adj.nonzero().t()

        h = torch.mm(input, self.W)
        # h: N x out
        assert not torch.isnan(h).any()

        # Self-attention on the nodes - Shared attention mechanism
        edge_h = torch.cat((h[edge[0, :], :], h[edge[1, :], :]), dim=1).t()
        # edge: 2*D x E

        edge_e = torch.exp(-self.leakyrelu(self.a.mm(edge_h).squeeze()))
        assert not torch.isnan(edge_e).any()
        # edge_e: E

        e_rowsum = self.special_spmm(edge, edge_e, torch.Size([N, N]), torch.ones(size=(N,1), device=dv))
        # e_rowsum: N x 1

        edge_e = self.dropout(edge_e)
        # edge_e: E

        h_prime = self.special_spmm(edge, edge_e, torch.Size([N, N]), h)
        assert not torch.isnan(h_prime).any()
        # h_prime: N x out
        
        h_prime = h_prime.div(e_rowsum)
        # h_prime: N x out
        assert not torch.isnan(h_prime).any()

        if self.concat:
            # if this layer is not last layer,
            return F.elu(h_prime)
        else:
            # if this layer is last layer,
            return h_prime

    def __repr__(self):
        return self.__class__.__name__ + ' (' + str(self.in_features) + ' -> ' + str(self.out_features) + ')'

SpGAT代码debug调试

SpGAT初始化

和GAT基本一致，最后一步多了SpecialSpmm类调用SpecialSpmmFunction方法。

第一次训练第一层结果

    N = input.size()[0]#行数 2708
        edge = adj.nonzero().t()#稀疏矩阵coo创建，edge[0]代表行，edge[1]代表列

        h = torch.mm(input, self.W)#  等价于求Wh
         # h: N x out
        assert not torch.isnan(h).any(),'可以提示h里面有空值'

        # Self-attention on the nodes - Shared attention mechanism
        edge_h = torch.cat((h[edge[0, :], :], h[edge[1, :], :]), dim=1).t()
        # edge: 2*D x E

edge_h做的是下图矩阵拼接

edge_e = torch.exp(-self.leakyrelu(self.a.mm(edge_h).squeeze()))#squeeze把维度=1的压缩
        assert not torch.isnan(edge_e).any()
        # edge_e: E

这段代码实现的是下图：

仅针对稀疏区域反向传播层的特殊功能

class SpecialSpmmFunction(torch.autograd.Function):
    """Special function for only sparse region backpropataion layer."""
    @staticmethod
    def forward(ctx, indices, values, shape, b):
        #对应ctx,edge, edge_e, torch.Size([N, N]), torch.ones(size=(N,1), device=dv)
        assert indices.requires_grad == False
        a = torch.sparse_coo_tensor(indices, values, shape)#创建coo格式的稀疏矩阵
        ctx.save_for_backward(a, b)#反向传播用的
        ctx.N = shape[0]#batchsize
        return torch.matmul(a, b)

    @staticmethod
    def backward(ctx, grad_output):
        a, b = ctx.saved_tensors
        grad_values = grad_b = None
        if ctx.needs_input_grad[1]:
            grad_a_dense = grad_output.matmul(b.t())
            edge_idx = a._indices()[0, :] * ctx.N + a._indices()[1, :]
            grad_values = grad_a_dense.view(-1)[edge_idx]
        if ctx.needs_input_grad[3]:
            grad_b = a.t().matmul(grad_output)
        return None, grad_values, None, grad_b

e_rowsum = self.special_spmm(edge, edge_e, torch.Size([N, N]), torch.ones(size=(N,1), device=dv))
       # e_rowsum: N x 1

        edge_e = self.dropout(edge_e)#丢一点特征，相当于正则化，防止过拟合
        # edge_e: E

        h_prime = self.special_spmm(edge, edge_e, torch.Size([N, N]), h)
        #实现αWh
        assert not torch.isnan(h_prime).any()
        # h_prime: N x out
        
        h_prime = h_prime.div(e_rowsum)
        #相当于归一化
        # h_prime: N x out
        assert not torch.isnan(h_prime).any()

        if self.concat:
            # if this layer is not last layer,
            return F.elu(h_prime)
        else:
            # if this layer is last layer,
            return h_prime

self.attentions.shape=8，将上述过程进行8次，结果如下：

第一次训练第二层结果

之后反向传播循环epoch次。

实验结果