Compute cross-entropy with label smoothing. Instead of putting all the probability mass on the true class, the target distribution gives it 1 - epsilon + epsilon/C and every other class epsilon/C, where C is the number of classes.

logits is (B, C) and targets is (B,). Return the mean loss. At epsilon = 0 it must equal ordinary cross-entropy exactly.

Smoothing stops the model driving the true logit to infinity, which is where overconfidence comes from.

Input

logits =
tensor([[2.0000, 1.0000, 0.1000],
        [0.5000, 2.5000, 0.3000]])
targets = tensor([0, 1])
epsilon = 0.1

Output

tensor(0.4369)