Focal-Loss

loss layer of implementation.
You can see "Focal Loss for Dense Object Detection" arXiv for more information.

Usage

// Focal Loss layer
optional FocalLossParameter focal_loss_param = 124;

// Focal Loss for Dense Object Detection
message FocalLossParameter {
  enum Type {
    ORIGIN = 0; // FL(p_t)  = -(1 - p_t) ^ gama * log(p_t), where p_t = p if y == 1 else 1 - p, whre p = sigmoid(x)
    LINEAR = 1; // FL*(p_t) = -log(p_t) / gama, where p_t = sigmoid(gama * x_t + beta), where x_t = x * y, y is the ground truth label {-1, 1}
  }
  optional Type type   = 1 [default = ORIGIN]; 
  optional float gamma = 2 [default = 2];
  // cross-categories weights to solve the imbalance problem
  optional float alpha = 3 [default = 0.25]; 
  optional float beta  = 4 [default = 1.0];
}

layer {
  name: "loss_cls"
  type: "FocalLoss"
  bottom: "cls_score"
  bottom: "labels"
  propagate_down: 1
  propagate_down: 0
  top: "loss_cls"
  include { phase: TRAIN }
  loss_weight: 1
  loss_param { ignore_label: -1 normalize: true }
  focal_loss_param { alpha: 0.25 gamma: 2 }
}

Derivative

see https://github.com/zimenglan-sysu-512/paper-note/blob/master/focal_loss.pdf

Done

All categories share the same alpha.

Sigmoid Form

Here use softmax instead of sigmoid function.
If you want see how to use sigmoid to implement Focal Loss, please see https://github.com/sciencefans/Focal-Loss to get more information.

MXNet Repo

https://github.com/unsky/focal-loss