How to take gradients with respect to model parameters on a loss function already defined in terms of gradients of inputs?

autograd
1

The problem I am trying to solve has the following setup. Let f(x; theta) and g(y; phi) be two neural networks whose outputs are scalar and theta, phi are the parameters I want to learn. x,y are vector valued inputs to these networks. In order to train the parameters, the loss function I have is the following:

CodeCogsEqn

The issue I have is that since the loss L already has gradients with respect to input y in the form of nabla g(y), I am wondering if it’s possible to compute the gradient again with respect to both theta and phi. The tentative code I have is the following but I am not sure if it’ll work:

x, y = Variable(torch.randn(1,2), requires_grad= True), Variable(torch.randn(1,2), requires_grad= True)

# Assuming that f_theta and g_phi are predefined neural networks

g_y = g_phi(y)

g_phi(y).backward()

grad_g_y = y.grad

f_grad_g_y = f_theta(grad_g_y)

f_x = f_theta(x)

loss = f_grad_g_y - f_x - torch.sum(y*grad_g_y ,dim=1)


# Computing gradient with respect to theta and phi

loss.backward()
print(theta.grad, phi.grad)
2

Hello,

In my shallow view, it will work, but we should fix something manaully, see this thread which computing Hessian product and do backward, I think it is similar to you, do backward on a gradient.

So, did you have a try on the snippet above?

3

Hi ,so is your tentative code working correctly?