[Python] PyTorch, why am I getting RuntimeError: Trying to backward through the graph a second...

I have pretty simple code

import torch
import random

image_width, image_height = 128, 128

def apply_ellipse_mask(img, pos, axes):
r = torch.arange(image_height)[:, None]
c = torch.arange(image_width)[None, :]
val_array = ((c - pos[0]) ** 2) / axes[0] ** 2 + ((r - pos[1]) ** 2) / axes[1] ** 2
mask = torch.where((0.9 < val_array) & (val_array < 1), torch.tensor(1.0), torch.tensor(0.0))

return img * (1.0 - mask) + mask


random.seed(0xced)

sphere_radius = image_height / 3
sphere_position = torch.tensor([image_width / 2, image_height / 2 ,0], requires_grad=True)

ref_image = apply_ellipse_mask(torch.zeros(image_width, image_height, requires_grad=True), sphere_position, [sphere_radius, sphere_radius, sphere_radius])

ellipsoid_pos = torch.tensor([sphere_position[0], sphere_position[1], 0], requires_grad=True)
ellipsoid_axes = torch.tensor([image_width / 3 + (random.random() - 0.5) * image_width / 5, image_height / 3 + (random.random() - 0.5) * image_height / 5, image_height / 2], requires_grad=True)

optimizer = torch.optim.Adam([ellipsoid_axes], lr=0.1)
criterion = torch.nn.MSELoss()
for _ in range(100):

optimizer.zero_grad()
current_image = torch.zeros(image_width, image_height, requires_grad=True)
current_image = apply_ellipse_mask(current_image, ellipsoid_pos, ellipsoid_axes)

loss = criterion(current_image, ref_image)
loss.backward()
print(_, loss)
optimizer.step()



However, I'm encountering an issue that as a Pytorch beginner I find hard to understand.

RuntimeError: Trying to backward through the graph a second time (or directly access saved tensors after they have already been freed). Saved intermediate values of the graph are freed when you call .backward() or autograd.grad(). Specify retain_graph=True if you need to backward through the graph a second time or if you need to access saved tensors after calling backward.
​

I don't understand why it would be trying to backward through the same graph a second time? or am I directly accessing saved tensors after they were freed? I don't understand why this happens.

Continue reading...