Is this the correct formula for delta focal loss?

[AlexeyAB]

Hi @unsky
Please, can you check, did I read your Focal Loss formulas correctly?

For CE, delta is:

• if (i == j) then delta = 1-p
• if (i != j) then delta = -p

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For Focal Loss (when gamm=2), delta is:

• if (i == j) then delta = (1-p)* alpha * (1 - pt) * (2 * pt * log(pt) + pt - 1)
• if (i != j) then delta = (-p)* alpha * (1 - pt) * (2 * pt * log(pt) + pt - 1)

Where are:

• pt = softmax(i) - is a probability of the correct class id.
• p = softmax(j)
  where is i = label truth class id.

[AlexeyAB]

Or is it correct as written here? https://blog.csdn.net/linmingan/article/details/77885832

For Focal Loss (when gamm=2), delta is:

• if (i == j) then delta = (1-p)* -1 *alpha * (1 - pt) * (2 * pt * log(pt) + pt - 1)
• if (i != j) then delta = (-p)* -1 *alpha * (1 - pt) * (2 * pt * log(pt) + pt - 1)

Because:
float grad =-2*(1-output[ti])*logf(fmaxf(output[ti],0.0000001))*output[ti]+(1-output[ti])*(1-output[ti]);

Or the same:
float grad =
-2*(1-pt)*log(pt)*pt + (1-pt)*(1-pt) =
(1-pt)*-2*pt*log(pt) + 1-pt)*(1-pt) =
(1-pt)*(-2*pt*log(pt) + (1-pt)) =
-1 * (1-pt)*(2*pt*log(pt) + pt - 1)