Write pytorch-based Python code to implement a neural network that solves binary classification problem with an output layer of 3 weighted sub-networks. The first weight is Positive, the second is negative, which is random and take the opposite of the absolute value of the standard normal distribution, the third random weight obeys a standard normal distribution. The exact value of the 3 weights are obtained from the objective function by Back propagation. The activation function is set to tanh.

Sure! Here's the PyTorch-based Python code to implement a neural network that solves a binary classification problem with an output layer consisting of three weighted sub-networks:

import torch
import torch.nn as nn

class BinaryClassifier(nn.Module):
    def __init__(self, input_size, hidden_size):
        super(BinaryClassifier, self).__init__()
        
        self.hidden_layer = nn.Linear(input_size, hidden_size)
        self.output_layer = nn.Linear(hidden_size, 3)
        
        # Initialize the weights
        self.output_layer.weight.data[0] = torch.randn(3)
        self.output_layer.weight.data[1] = -torch.abs(torch.randn(3))
        self.output_layer.weight.data[2] = torch.randn(3)
        
    def forward(self, x):
        x = torch.tanh(self.hidden_layer(x))
        x = self.output_layer(x)
        
        return x

# Example usage
input_size = 10
hidden_size = 20
model = BinaryClassifier(input_size, hidden_size)

# Generate a random input tensor
input_tensor = torch.randn(1, input_size)

# Forward pass
output = model(input_tensor)
print(output)

In this code, we define a `BinaryClassifier` class that inherits from `nn.Module` in PyTorch. The class has two layers: a hidden layer and an output layer. The hidden layer is a linear transformation with the input size and hidden size specified. The output layer is also a linear transformation that maps the hidden layer's output to three classes.

We initialize the weights of the output layer as described in the question - the first weight is sampled from a standard normal distribution, the second weight is the negative absolute value of a standard normal distribution, and the third weight is also sampled from a standard normal distribution.

The forward method performs the forward pass of the network. The input tensor is passed through the hidden layer, followed by a tanh activation function. The result is then passed through the output layer, resulting in the final output.

Finally, we create an instance of the `BinaryClassifier` class with the desired input and hidden sizes. We generate a random input tensor and pass it through the model to obtain the output.