#nan

Question 1: Single choice

hardAI-checkedPyTorch

Mathematically, $f(\mathbf{x}) = \lVert\mathbf{x}\rVert_2$ has the gradient $\mathbf{x}/\lVert\mathbf{x}\rVert_2$ for $\mathbf{x} \neq \mathbf{0}$ . What does x.grad contain after this code runs at $\mathbf{x} = \mathbf{0}$ ?

x = torch.zeros(3, requires_grad=True)
f = torch.sqrt((x ** 2).sum())
f.backward()

[1., 1., 1.], the limit of $\mathbf{x}/\lVert\mathbf{x}\rVert_2$ as $\mathbf{x}$ approaches $\mathbf{0}$ 1
A RuntimeError, because the norm is not differentiable at 02
[nan, nan, nan]: the chain rule multiplies 0 by the infinite slope of $\sqrt{u}$ at 03
[0., 0., 0.], because 0 is the minimum of the norm4

Timed test