RuntimeError: Trying to backward through the graph a second time, when we store the variable

autograd
1

Could you tell me why the error occurs here?

import torch

a = torch.rand(3,3, requires_grad=True)

L = []

for i in range(10):

b = a * a

d = b * b

e = d.sum()

L.append(e)

sum(L).backward()
2

Your code is unfortunately not formatted correctly, but I assume the backward() operation is performed inside the loop. The first backward pass would free the intermediate activations from the forward pass, so that you wouldn’t be able to call backward a second time (if this is needed, use retain_graph=True, but it’s usually not the case). Since you are storing the e tensor in the L list and calculating the sum afterwards, the next backward pass would then try to backpropagate through both e tensors (the one from the current iteration [e1] as well as the one from the previous iteration [e0]). However, since the computation graph from e0 is already freed the error is raised.

3

I don’t know why you wanna do this:

import torch
a = torch.rand(3,3, requires_grad=True)

L = []
for i in range(10):
    b = a * a
    d = b * b
    e = d.sum()
    L.append(e)
    sum(L).backward()

the more normal way is to have sum(L).backward() outside of loop.(and i think it really is the case)
But if your intention is to compute grad for what you asked, then you can go around using retain_graph = True with change in how you backward.

import torch
a = torch.rand(3,3, requires_grad=True)

L = []
for i in range(10):
    b = a * a
    d = b * b
    e = d.sum()
    e.backward(torch.tensor(10-i)) # if you really want to compute 
                                   # grad multiple times,
                                   # i.e. backward for 10 
                                   # times on first item of the list
    L.append(e.item())
sum(L)
# do some thing with a.grad and then
print(a.grad)

a.grad.fill_(0)

This way is more memory efficient.