Project: s41467-024-48446-3 | Function: forward (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Variational Graph Autoencoder (VGAE) forward pass implementing the core self-supervised learning module of TransDSI framework for protein sequence feature embedding, combining graph convolutional network encoding with variational inference for latent protein representation learning

**KEY TERMS:** {
  "mu": "mean parameter μ from variational encoder",
  "logstd": "log standard deviation logσ from variational encoder",
  "z": "latent representation Z after reparameterization",
  "encode": "GCN-based encoder for feature extraction",
  "decode": "decoder reconstructing adjacency matrix",
  "reparameterize": "variational inference reparameterization trick"
}

**CONTEXT CODE:** import torch
import torch.nn as nn
import torch.nn.functional as F
from tqdm import tqdm
from torch_geometric.utils import k_hop_subgraph
import numpy as np
import scipy.sparse as sp

EPS = 1e-15

class GCNLayer(nn.Module):
    """
    Simple GCN layer, similar to https://arxiv.org/abs/1609.02907
    """
    def __init__(self, in_features, out_features, dropout=0.):
        super(GCNLayer, self).__init__()
        self.in_features = in_features
        self.out_features = out_features
        self.dropout = dropout
        self.weight = nn.Parameter(torch.FloatTensor(in_features, out_features))
        self.reset_parameters()

    def reset_parameters(self):
        torch.nn.init.xavier_uniform_(self.weight)

    def forward(self, x, adj):
        input = F.dropout(x, self.dropout, self.training)
        support = torch.mm(input, self.weight)
        output = torch.spmm(adj, support)
        return output

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


class VGAE(nn.Module):
    """
    The self-supervised module of DeepDSI
    """
    def __init__(self, input_feat_dim, hidden_dim1, hidden_dim2, dropout):
        super(VGAE, self).__init__()
        self.gc1 = GCNLayer(input_feat_dim, hidden_dim1, dropout)   # F.relu
        self.gc2 = GCNLayer(hidden_dim1, hidden_dim2, dropout)    # lambda x: x
        self.gc3 = GCNLayer(hidden_dim1, hidden_dim2, dropout)
        self.act1 = nn.ReLU()

    def encode(self, x, adj):
        hidden1 = self.act1(self.gc1(x, adj))
        return self.gc2(hidden1, adj), self.gc3(hidden1, adj)

    def reparameterize(self, mu, logstd):
        std = torch.exp(logstd)
        eps = torch.randn_like(std)
        return eps.mul(std).add_(mu)

    def decode(self, z):
        adj_hat = torch.mm(z, z.t())
        return adj_hat

    def forward(self, x, adj, sigmoid: bool = True):
        """Variational Graph Autoencoder (VGAE) forward pass implementing the core self-supervised learning module of TransDSI framework for protein sequence feature embedding"""
        raise NotImplementedError("Function has been masked for testing purposes")


class DSIPredictor(nn.Module):
    """
    The semi-supervised module of DeepDSI
    """
    def __init__(self, in_features, out_features):
        super(DSIPredictor, self).__init__()

        self.gc1 = GCNLayer(343, 343, 0.1)
        self.gc2 = GCNLayer(343, 343, 0.1)

        self.fc1 = nn.Linear(in_features, 512)
        self.bn1 = nn.BatchNorm1d(512)
        self.fc2 = nn.Linear(512, 256)
        self.bn2 = nn.BatchNorm1d(256)
        self.fc3 = nn.Linear(256, 64)
        self.bn3 = nn.BatchNorm1d(64)
        self.fc4 = nn.Linear(64, out_features)
        self.dropout = nn.Dropout(p=0.4)
        self.act1 = nn.ReLU()
        self.act2 = nn.Mish()

    def forward(self, x, adj, pro1_index, pro2_index, sigmoid: bool = True):
        x1 = self.act1(self.gc1(x, adj))
        x2 = self.gc2(x1, adj)

        pro1 = x2[pro1_index]
        pro2 = x2[pro2_index]

        dsi = torch.cat([pro1, pro2], dim = 1)

        h1 = self.dropout(self.bn1(self.act2(self.fc1(dsi))))
        h2 = self.dropout(self.bn2(self.act2(self.fc2(h1))))
        h3 = self.dropout(self.bn3(self.act2(self.fc3(h2))))
        h4 = self.fc4(h3)

        return torch.sigmoid(h4) if sigmoid else h4


class AE(nn.Module):
    def __init__(self):
        super(AE, self).__init__()
        self.encoder = nn.Linear(20398, 343)
        self.decoder = nn.Linear(343, 20398)

    def forward(self, x):
        x = self.encoder(x)
        x = self.decoder(x)
        return x


class Classifier(nn.Module):
    # __constants__ = ['in_features', 'out_features']
    def __init__(self, in_features, out_features):
        super(Classifier, self).__init__()

        self.fc1 = nn.Linear(in_features, 512)
        self.bn1 = nn.BatchNorm1d(512)
        self.fc2 = nn.Linear(512, 256)
        self.bn2 = nn.BatchNorm1d(256)


Complete the function implementation replacing "raise NotImplementedError".