Hi,guys,
x = torch.tensor([1.,2.,3.],requires_grad=True)
sum = x.sum()
y = x**2/sum
z = y[1]
z.sum().backward()
print(x.grad)
tensor([-0.1111, 0.5556, -0.1111])
x1 = torch.tensor([1.,2.,3.],requires_grad=True)
sum1 = x1.sum()
y1 = x1**2/sum1
z1 = y1
z1.sum().backward()
print(x1.grad)
tensor([-0.0556, 0.2778, 0.6111])
Any answer or idea will be appreciated!
I know how to get the first code array[1] grad,is 0.5556
I tried to answer in a gist, as it involves math expressions.
math.md
Answering https://discuss.pytorch.org/t/a-set-of-data-sum-as-the-dividend-how-to-find-grad/182303:
We can find $grad_x = \frac{dz}{dx}$ in the following way:
$$grad_x = \frac{dz}{dx} = \left[\frac{dz}{dx_0},\frac{dz}{dx_1}, \frac{dz}{dx_2}\right]$$
$$ = \frac{dz}{dx} = \left[\frac{dy}{dx_0}\frac{dz}{dy},\frac{dy}{dx_1}\frac{dz}{dy},\frac{dy}{dx_2}\frac{dz}{dy}\right]$$
Now let's concentrate on finding one element $\frac{dz}{dx_0} = \frac{dz}{dy}\frac{dy}{dx_0}$
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I see, thank you very much