#non-scalar-backward

Question 1: Single choice

hardAI-checkedPyTorch

f doubles its input until the norm reaches 1000 and multiplies by 100 if the sum is not positive. Now a is a vector:

def f(a):
    b = a * 2
    while b.norm() < 1000:
        b = b * 2
    if b.sum() > 0:
        c = b
    else:
        c = 100 * b
    return c

a = torch.randn(3, requires_grad=True)
d = f(a)

Which statement is correct?

After d.sum().backward(), each entry of a.grad has a different value, one per entry of a1
d.backward() fails; after d.sum().backward(), all entries of a.grad equal d[0] / a[0]2
d.backward() works and fills a.grad with the 3 × 3 Jacobian matrix of d with respect to a3
No gradient exists, because the number of loop iterations and the branch both depend on a4

#non-scalar-backward

Timed test