Matrix Derivation Link

https://www.math.uwaterloo.ca/~hwolkowi/matrixcookbook.pdf

Complex Matrix-Derivative by Another Matrix

https://math.stackexchange.com/questions/3250317/derivative-of-axb-with-respect-to-x

import torch import torch.nn as nn import numpy as np

class FocalLoss(nn.Module): def init(self, alpha=1, gamma=2, reduction: str = 'mean'): super().init() if reduction not in ['mean', 'none', 'sum']: raise NotImplementedError('Reduction {} not implemented.'.format(reduction)) self.reduction = reduction self.alpha = alpha self.gamma = gamma

def forward(self, x, target):
    eps = np.finfo(float).eps
    x = torch.sigmoid(x)
    p_t = torch.where(target == 1, x, 1-x)
    fl = - 1 * (1 - p_t) ** self.gamma * torch.log(p_t + eps)
    fl = torch.where(target == 1, fl * self.alpha, fl * (1 - self.alpha))
    return self._reduce(fl)

def _reduce(self, x):
    if self.reduction == 'mean':
        return x.mean()
    elif self.reduction == 'sum':
        return x.sum()
    else:
        return x