Gradient error when calculating - pytorch - numpy

Question

I am learning to use pytorch (0.4.0) to automate the gradient calculation, however I did not quite understand how to use the backward () and grad, as I'm doing an exercise I need to calculate df / dw using pytorch and
making the derivative analytically, returning respectively auto_grad, user_grad, but I did not quite understand the use of automatic differentiation, in the code I made f.backward () and did w.grad to find df / dw, in addition the two calculations are not corresponding, if I even erred the derivative, it follows the graph that I am using and the code that I am trying to do:
import numpy as np
import torch
import torch.nn.functional as F
def graph2(W_np, x_np, b_np):
W = torch.Tensor(W_np)
W.requires_grad = True
x = torch.Tensor(x_np)
b = torch.Tensor(b_np)
u = torch.matmul(W, x) + b
g = F.sigmoid(u)
f = torch.sum(g)
user_grad = (sigmoid(W_np*x_np + b_np)*(1 - sigmoid(W_np*x_np + b_np))).T*x_np
f.backward(retain_graph=True)
auto_grad = W.grad
print(auto_grad)
print(user_grad)
# raise NotImplementedError("falta completar a função graph2")
# END YOUR CODE
return f, auto_grad, user_grad
test:
iterations = 1000
sizes = np.random.randint(2,10, size=(iterations))
for i in range(iterations):
size = sizes[i]
W_np = np.random.rand(size, size)
x_np = np.random.rand(size, 1)
b_np = np.random.rand(size, 1)
f, auto_grad, user_grad = graph2(W_np, x_np, b_np)
manual_f = np.sum(sigmoid(np.matmul(W_np, x_np) + b_np))
assert np.isclose(f.data.numpy(), manual_f, atol=1e-4), "f not correct"
assert np.allclose(auto_grad.numpy(), user_grad), "Gradient not correct"

Answer 1

I think you computed the gradients in the wrong way. Try this.
import numpy as np
import torch
from torch.autograd import Variable
import torch.nn.functional as F
def sigmoid(x):
return 1.0 / (1.0 + np.exp(-x))
def graph2(W_np, x_np, b_np):
W = Variable(torch.Tensor(W_np), requires_grad=True)
x = torch.tensor(x_np, requires_grad=True).type(torch.FloatTensor)
b = torch.tensor(b_np, requires_grad=True).type(torch.FloatTensor)
u = torch.matmul(W, x) + b
g = F.sigmoid(u)
f = torch.sum(g)
user_grad = (sigmoid(np.matmul(W_np, x_np) + b_np)*(1 - sigmoid(np.matmul(W_np, x_np) + b_np)))*x_np.T
f.backward(retain_graph=True)
auto_grad = W.grad
print("auto_grad", auto_grad)
print("user_grad", user_grad)
# END YOUR CODE
return f, auto_grad, user_grad
iterations = 1000
sizes = np.random.randint(2,10, size=(iterations))
for i in range(iterations):
size = sizes[i]
print("i, size", i, size)
W_np = np.random.rand(size, size)
x_np = np.random.rand(size, 1)
b_np = np.random.rand(size, 1)
f, auto_grad, user_grad = graph2(W_np, x_np, b_np)
manual_f = np.sum(sigmoid(np.matmul(W_np, x_np) + b_np))
assert np.isclose(f.data.numpy(), manual_f, atol=1e-4), "f not correct"
assert np.allclose(auto_grad.numpy(), user_grad), "Gradient not correct"