Implement binary focal loss from raw logits:

loss = -alpha * (1 - p_t)**gamma * log(p_t)

where p = sigmoid(logits) and p_t is p for a positive target and 1 - p for a negative one. Return the mean over all elements.

The (1 - p_t)**gamma factor shrinks the contribution of examples already classified confidently, so training attends to the hard ones. Note that alpha here multiplies every term, positive and negative alike.

Input

logits = tensor([ 2.0000, -1.0000,  0.5000])
targets = tensor([1., 0., 1.])
alpha = 0.25
gamma = 2.0

Output

tensor(0.0077)