Write pytorch-based Python code to implement a neural network that solves a regression problem with an output layer of a positively weighted sub-network plus a negatively weighted sub-network， where the negative weights are random and take the opposite of the absolute value of the standard normal distribution, the exact value of the weights are obtained from the objective function by Back propagation.

Sure! Here's an example of PyTorch code that implements a neural network with a positively weighted sub-network and a negatively weighted sub-network for solving a regression problem:

import torch
import torch.nn as nn
import torch.optim as optim

# Define the neural network architecture
class RegressionNet(nn.Module):
    def __init__(self, input_size, hidden_size):
        super(RegressionNet, self).__init__()
        self.positive_net = nn.Linear(input_size, hidden_size)
        self.negative_net = nn.Linear(input_size, hidden_size)
        self.output_layer = nn.Linear(hidden_size, 1)

    def forward(self, x):
        positive_output = torch.relu(self.positive_net(x))
        negative_output = torch.relu(self.negative_net(x))
        output = self.output_layer(positive_output - negative_output)
        return output

# Define the objective function
def objective_function(y_pred, y_true):
    loss = nn.MSELoss()
    return loss(y_pred, y_true)

# Generate random negative weights
negative_weights = -torch.abs(torch.randn(1))

# Create the neural network
input_size = 10
hidden_size = 20
net = RegressionNet(input_size, hidden_size)

# Define the optimizer
optimizer = optim.SGD(net.parameters(), lr=0.01)

# Training loop
for epoch in range(num_epochs):
    # Forward pass
    outputs = net(inputs)
    
    # Compute the loss
    loss = objective_function(outputs, labels)
    
    # Backward and optimize
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    
    # Update negative weights
    negative_weights.data = -torch.abs(net.negative_net.weight.data.mean())

In this code, we define a `RegressionNet` class that consists of a positively weighted sub-network and a negatively weighted sub-network. The `forward` method implements the forward pass of the neural network. We also define the `objective_function` that computes the mean squared error loss.

During the training loop, we compute the forward pass, compute the loss, perform backward propagation, and update the weights using the optimizer. After each iteration, we update the negative weights by taking the opposite of the absolute value of the mean of the weights in the negative sub-network.

Please note that this is a simplified example, and you may need to modify it according to your specific regression problem and data.