Project: s41467-025-60989-7 | Function: Correlation_layer.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:** Implements the adjoint correlation mechanism that enables interaction between compound embeddings and endpoint embeddings. It correlates molecular representations with endpoint graph features to learn endpoint-aware compound representations.

**KEY TERMS:** {
  "input_mlp": "compound embeddings",
  "input_gcn": "endpoint embeddings",
  "W": "learnable weight matrix"
}

**CONTEXT CODE:** import torch
import torch.nn as nn
import torch.nn.functional as F
import numpy as np

class FCL(nn.Module):  # feed-forward layer
    def __init__(self, in_features, out_features, dropout_prob = 0):
        super(FCL, self).__init__()
        self.layers = nn.Sequential()
        self.layers.add_module('Linear',nn.Linear(in_features=in_features,
                                                  out_features=out_features,
                                                  bias=True))
        self.layers.add_module('BatchNorm',nn.BatchNorm1d(out_features))
        self.layers.add_module('Dropout', nn.Dropout(dropout_prob))
        # self.layers.add_module('Relu', nn.Tanh())
        self.layers.add_module('Relu', nn.ReLU())

    def forward(self, x):
        out  = self.layers(x)
        return out


class GCN_layer(nn.Module): # graph convolution layer
    def __init__(self, input_dim, output_dim, A, nonlinear=True):
        super(GCN_layer, self).__init__()
        self.input_dim = input_dim
        self.output_dim = output_dim
        self.A = A
        self.W = nn.Parameter(0.1 * (torch.rand(self.input_dim, self.output_dim)-0.5),
                              requires_grad=True)
        self.nonlinear_ = nonlinear

    def forward(self, x):
        # x: (num_nodes, input_dim)
        x = torch.mm(x, self.W)
        x = torch.mm(self.A, x)   #(num_nodes, output_dim)
        if self.nonlinear_ == True:
            x = F.leaky_relu(x, negative_slope=0.1)
        return x


class Correlation_layer(nn.Module):  # adjoint correlation layer
    def __init__(self, num_node, fea_dim):
        super(Correlation_layer, self).__init__()
        self.num_node = num_node
        self.fea_dim = fea_dim
        self.W = nn.Parameter(0.1 * (torch.rand(self.num_node, self.fea_dim)-0.5),
                              requires_grad=True)  # (num_nodes, batchsize)

    def forward(self, input_mlp, input_gcn):
        """
        Implements the adjoint correlation mechanism that enables interaction between compound embeddings
        and endpoint embeddings. It correlates molecular representations with endpoint graph features
        to learn endpoint-aware compound representations.
        """
        # MASKED: Implements the adjoint correlation mechanism that enables interaction between compound embeddings and endpoint embeddings by correlating molecular representations with endpoint graph features to learn endpoint-aware compound representations implementation
        raise NotImplementedError("This function is masked for testing purposes.")


class CorrelationNet(nn.Module):
    def __init__(self, opt):
        super(CorrelationNet, self).__init__()
        self.in_features_dnn = opt['in_features_dnn']  # 1024
        self.in_features_gcn = opt['in_features_gcn']  # 26
        self.out_features = opt['out_features']
        self.num_layers = opt['num_layers']
        self.Dropout_p = opt['Dropout_p']
        self.num_node = opt['num_task']

        A = self.init_adjacency_matrix()
        self.A = nn.Parameter(A, requires_grad=False)

        gcn_input = self.init_gcn_input()
        self.gcn_input = nn.Parameter(gcn_input, requires_grad=False)

        self.tail_w = nn.Parameter(0.1 * torch.rand(self.out_features[-1], self.num_node), requires_grad=True)

        if type(self.out_features) == int:
            self.out_features = [self.out_features for _ in range(self.num_layers)]
        assert (type(self.out_features) ==list and len(self.out_features) == self.num_layers)

        if type(self.Dropout_p) == float:
            self.Dropout_p =[self.Dropout_p for _ in range(self.num_layers)]
        assert(type(self.Dropout_p)==list and len(self.Dropout_p)==self.num_layers)

        num_features_dnn = [self.in_features_dnn, ] + self.out_features  # [1024, 768, 512, 384, 64]
        num_features_gcn = [self.in_features_gcn, ] + self.out_features  # [26, 768, 512, 384, 64]


        self.dnn = nn.ModuleList(
            [FCL(in_features =num_features_dnn[i],
                 out_features=num_features_dnn[i+1],
                 dropout_prob=self.Dropout_p[i]) for i in range(self.num_layers)]
        )


        self.gcn = nn.ModuleList(
            [GCN_layer(input_dim =num_features_gcn[i],
                       output_dim=num_features_gcn[i+1],
                       A = self.A,
                       nonlinear=False) for i in range(self.num_layers)]

        )


        self.correlation_net = nn.ModuleList(
            [Correlation_layer(num_node=self.num_node, fea_dim=d) for d in self.out_features]
        )


    def forward(self, x):
        """
        Main forward pass of ToxACoL model that processes compound features through multiple layers
        of DNN, GCN, and correlation layers in parallel to predict multi-condition acute toxicity endpoints.
        """
        # MASKED: Main forward pass of ToxACoL model that processes compound features through multiple layers of DNN, GCN, and correlation layers in parallel to predict multi-condition acute toxicity endpoints implementation
        raise NotImplementedError("This function is masked for testing purposes.")


Complete the function implementation replacing "raise NotImplementedError".