Loss function which uses the derivative of the net w.r.t. input

[mhq]

Hey there,

i want to implement something probably related to :

Is it possible to use gradient w.r.t input in loss?

Hi, I need to construct a loss function that uses the gradient of the output of the NN w.r.t the input, i.e. something like: 1 output = NN(input, weight) 2 grad_input = output.backward(retain_variables=True) 3 loss = criterion(grad_input.grad.data, target_of_grad_input) 4 loss.backward() The problem is that after step 2, I can only have the numerical value of the gradient of output w.r.t to input (i.e. grad_input). Then it is no longer a function of the weight, and as a result the loss is…

but i am not quite sure how to do it.

I want to have a loss with multiple parts, one of which uses the derivative of the net with respect to an input value. The background is that i want to impose characteristics for the linearisations of the net at certain values of x.

Small examples with notation for clarification:

• nn(x) : R → R is our network
• x is the input
• y the true value
• x_1, x_2 are some values in R
• d_nn(x*) is the derivative of nn(x) w.r.t x at x*

and i want a loss which could for example look like :

a = nn(x_2) - nn(x_1) + d_nn(x_1)*x - d_nn(x_2)*x
b = d_nn(x_1) - d_nn(x2)

loss = (a/b - y )**2

I am still new to pytorch and all help is highly appreciated!

[mhq]

To get the derivative of your network (net) with respect to an input (x_1) use torch.autograd.grad() e.g.

dnet_by_dx1 = grad(net(x1), x1, create_graph=True)[0]

where x1 needs to be a torch.Variable.