Handling Memory Insufficiency in Graph Convolutional Network (GCN) for Large Graphs

Question

I am working with a large graph consisting of 770,000 nodes and utilizing a Graph Convolutional Network (GCN) to learn an 8-dimensional feature representation for each node. My goal is to reconstruct the feature matrix and compute the reconstruction loss between this reconstructed matrix and the adjacency matrix, as per the following formula: enter image description here enter image description here The feature matrix is then used to compute a reconstruction matrix (A_hat) by multiplying the feature matrix with its transpose. This results in a 770,000 x 770,000 matrix. The reconstruction loss is calculated between this matrix and an adjacency matrix of the same size.

Here is the code for the GCN model and the training loop:

class GcnNet(nn.Module):
    def __init__(self, input_dim=8, hidden_dim=16, output_dim=8):
        super(GcnNet, self).__init__()
        self.gcn1 = GCNConv(input_dim, hidden_dim)
        self.gcn2 = GCNConv(hidden_dim, hidden_dim)
        self.gcn3 = GCNConv(hidden_dim, output_dim)

    def forward(self, feature, edge_index):
        h1 = F.relu(self.gcn1(feature, edge_index))
        h2 = F.relu(self.gcn2(h1, edge_index))
        out = self.gcn3(h2, edge_index)
        A_ = torch.sigmoid(torch.matmul(out, out.t()))
        return out, A_

def train(model, train_data, optimizer, val_data, num_epochs):
    for epoch in range(num_epochs):
        model.train()
        out, A_ = model(train_data.x, train_data.edge_index)  
        A_ = A_.to_dense()
        train_data.adj_matrix = train_data.adj_matrix.to_dense()
        loss = F.mse_loss(train_data.adj_matrix, A_)
        optimizer.zero_grad()
        loss.backward() 
        optimizer.step()

My issue is severe memory shortage. While computing the reconstruction matrix as well as the loss, the required memory far exceeds the capacity of ordinary hardware, requiring several terabytes of memory. What strategies could I use to address this memory issue?

Some considerations:

Are there efficient ways to perform these computations that avoid creating such large intermediate matrices? Would sparse matrix representations or incremental calculations be a feasible solution? Are there any known libraries or frameworks specifically designed to handle this type of large-scale graph data? I appreciate any insights or suggestions on how to overcome this challenge.

To address the computational challenge of the reconstruction matrix, I have attempted to implement a for-loop that multiplies each row of the GCN-generated feature matrix with its transpose to avoid the multiplication of two large matrices. However, this approach has significant drawbacks:

Computation Speed: The process is extremely slow - it takes approximately ten minutes to compute just 5,000 rows. Given the size of the entire graph, this approach is not practical for my use case.

Memory for Backpropagation: Since I need to compute the loss for backpropagation, accumulating the loss over the iterations still poses a substantial memory issue. The memory requirement for the cumulative loss grows excessively large as the number of rows increases.

I am seeking alternatives that can handle the multiplication and loss computation in a memory-efficient manner while also being computationally feasible for a graph of this scale. Strategies that allow for backpropagation without requiring the storage of huge intermediate matrices would be ideal.

Suggestions for optimization techniques, memory-efficient algorithms, or even parallel computing frameworks that could distribute the workload effectively are highly welcome.