# Getting RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn even if I included 'requires_grad = True'

Hi, I started studying pytorch recently and I’m stuck in a problem. The codes below trains w[0], …, w[8] which are the 2 * 2 elements of a weight matrix. The weight matrix is in the function named forward. I want to train w[1], …, w[8] to produce y from a. But after operating the codes, an error occurred. It is ‘RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn.’ I had tried to find causes but I can’t find and understand them. The original code is much more long, the code below is a simplified version. Would you help me how to fix the problem? Any help would be highly appreciated.

import torch
eta_n = torch.arange(1.0, 0, - 0.1)
#eta_n = torch.cat([torch.arange(1.0, 0.2, -0.1), torch.arange(0.2, 0, -0.01)], dim = 0)
delta_eta = eta_n[1:] - eta_n[0:-1] #Difference between the elements of eta_n. In this case, every element is -0.1.
eta_fin = eta_n[-1]
print('eta_n:', eta_n)
print('len(eta_n):', len(eta_n))
print('delta_eta:', delta_eta)
print('len(delta_eta) which is the no. of forward propagations:', len(delta_eta))
print('eta_fin:', eta_fin)

eta_n: tensor([1.0000, 0.9000, 0.8000, 0.7000, 0.6000, 0.5000, 0.4000, 0.3000, 0.2000, 0.1000])
len(eta_n): 10
delta_eta: tensor([-0.1000, -0.1000, -0.1000, -0.1000, -0.1000, -0.1000, -0.1000, -0.1000, -0.1000])
len(delta_eta) which is the no. of forward propagations: 9
eta_fin: tensor(0.1000)

#Activation function in hidden layers
def acti1(coordinate, layer_no):#layer_no from 0 to '(the length of eta_n) - 1'
x = coordinate[0]
y = coordinate[1]

return torch.cat([x.reshape(1, -1), (y + delta_eta[layer_no] * x ** 3).reshape(1, -1)], dim = 0)
#Activation function on the output layer
def acti2(coordinate):
y = coordinate[1]
F = y
return (torch.tanh(100 * (F - 0.1)) - torch.tanh(100 * (F + 0.1)) + 2) / 2
#The result is 0 when F is between -0.5 and 0.5 and for the other F, the result is 1
#This function is steep but continuous and differentiable
def forward(coordinate, w, layer_no):#layer_no from 0 to '(the length of eta_n) - 1'
matrix = torch.Tensor([[1, delta_eta[layer_no]], [- delta_eta[layer_no], 1 - delta_eta[layer_no] * w]])

return acti1(matrix.mm(coordinate), layer_no)
y = torch.Tensor([0, 0, 1, 1]) #I want y_pred(later mentioned) to be this value
the_no_of_iterations = 10
learning_rate = 0.01

a = torch.Tensor([[0.5528, 0.8563, 1.0779, 0.5932], [-0.1109, -0.0569, 0.0904, 0.1435]])

torch.manual_seed(1)
w = torch.randn(9, requires_grad = True) #What I want to train to produce y from a
print('w:', w)

optimizer = torch.optim.Adam([w], lr = learning_rate)

for i in range(the_no_of_iterations):
#Forward propagation
for j in range(9):
a = acti1(forward(a, w[j], j), j)
print('a:', a)

y_pred =acti2(a)
print('y_pred:', y_pred)

#Loss calculation
loss = (y - y_pred).abs().sum()
print('loss:', loss.item())

loss.backward()
optimizer.step()

w: tensor([ 0.6614, 0.2669, 0.0617, 0.6213, -0.4519, -0.1661, -1.5228, 0.3817, -1.0276], requires_grad=True)
a: tensor([[ 0.5961, 1.1220, 1.6414, 0.3710],
[ 0.0363, -0.7368, -2.2987, 0.3278]])
y_pred: tensor([2.9206e-06, 1.0000e+00, 1.0000e+00, 1.0000e+00])
loss: 1.0000028610229492

If you create a new tensor, you will detach the inputs from the computation graph.
The creation of your matrix tensor might be the issue here.
Could you try to rewrite the creation using torch.cat instead?

Let me know, if that helps or if we need to dig a bit deeper.

Thank you.
I fixed the function named forward like below.

def forward(coordinate, w, layer_no):#layer_no from 0 to '(the length of eta_n) - 1'
row1 = torch.Tensor([[1, delta_eta[layer_no]]])
row2_col1 = torch.Tensor([- delta_eta[layer_no]])
row2_col2 = w
row2 = torch.cat([row2_col1, row2_col2], dim = 0).reshape(1, -1)
matrix = torch.cat([row1, row2], dim = 0)

return acti1(matrix.mm(coordinate), layer_no)

Also, I fixed

w = torch.randn(9, requires_grad = True)

into

w = torch.randn((9, 1) requires_grad = True)

in accordance with the change in function named forward. And the error was solved.

However, another error which is ‘RuntimeError: Trying to backward through the graph a second time, but the buffers have already been freed. Specify retain_graph=True when calling backward the first time’ appeared. I reconstructed all codes to avoid the error what I can’t find a solution and the result is the simplified codes above. However the error appeared again. Would you help me again? I have done many googlings, but I couldn’t understand. And specifying retain_graph = True resulted in exponentially increasing operation time.