So I’m basically trying to fit a regression on the relation of the input and output of a neural network model. Then the idea is, that these estimated regression weights should be optimized to some specific target value (let’s say matrix of ones). So the weights are optimized, but have a direct relation to the neural network weights.
I think I have an issue with how I define the weights, as they probably don’t relate to the neural network the way I define them?
# Some arbitrary PyTorch model
my_nn = Net()

# Our target regression weights
target = torch.ones(2, 2)

# Optimizer for NN weights
optimizer = optim.Adam(my_nn.parameters(), lr=0.0001)

# weights for regression model
w1 = Variable(torch.randn(2, 2).type(torch.float), requires_grad=True)
# optimizer for regression model
optimizer1 = optim.SGD([w1], lr=0.001, momentum=0.9)

# Arbitrary loss function
criterion = nn.MSELoss()

# Training loop
my_nn.train()
for epoch in range(500):
    print('Running Epoch: ', epoch)
    # zero the parameter gradients
    optimizer.zero_grad()

    # output of model is 2-dim
    y_pred = my_nn(X)

    for nest_epoch in range(1000):
        optimizer1.zero_grad()
    
        y_hat = torch.mm(X, w1)
        loss = criterion(y_hat, y_pred)

        # Need to add retain_graph, as it doesn't work otherwise
        # but it does work, this loss will get close to 0
        loss.backward(retain_graph=True)
        optimizer1.step()

# this loss does not decrease
loss = criterion(target, w1)
print('Loss:', loss.item())
loss.backward()
optimizer.step()