Focal loss 以及 pytorch实现

Focal loss 是在 Focal Loss for Dense Object Detection 中为了解决数据类别不平衡而提出的。

它是一个动态缩放的交叉熵损失，其中缩放因子随着正确类的置信度的增加衰减到零。因此可以在训练过程中自动降低简单示例的贡献，并快速将模型集中在困难示例上。

Focal loss 定义为：

其中 为模型对样本的正确类别估计概率。

当误分类时，很小，调制因子接近1，loss 不受影响。当 →1，因子趋近于0，分类良好的样本的损失权重下降，如上图。

当 ， Focal loss 相当于 Cross Entropy loss。实际应用中一般取 。

另一种平衡版本的 focal loss， 在论文的实验中能获得更好的结果：

pytorch 实现：

https://github.com/facebookresearch/fvcore/blob/main/fvcore/nn/focal_loss.py

# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.

import torch
from torch.nn import functional as F


def sigmoid_focal_loss(
    inputs: torch.Tensor,
    targets: torch.Tensor,
    alpha: float = -1,
    gamma: float = 2,
    reduction: str = "none",
) -> torch.Tensor:
    """
    Loss used in RetinaNet for dense detection: https://arxiv.org/abs/1708.02002.
    Args:
        inputs: A float tensor of arbitrary shape.
                The predictions for each example.
        targets: A float tensor with the same shape as inputs. Stores the binary
                 classification label for each element in inputs
                (0 for the negative class and 1 for the positive class).
        alpha: (optional) Weighting factor in range (0,1) to balance
                positive vs negative examples. Default = -1 (no weighting).
        gamma: Exponent of the modulating factor (1 - p_t) to
               balance easy vs hard examples.
        reduction: 'none' | 'mean' | 'sum'
                 'none': No reduction will be applied to the output.
                 'mean': The output will be averaged.
                 'sum': The output will be summed.
    Returns:
        Loss tensor with the reduction option applied.
    """
    inputs = inputs.float()  # (B, C)
    targets = targets.float()  # (B, C)
    p = torch.sigmoid(inputs)  # (B, C)
    ce_loss = F.binary_cross_entropy_with_logits(inputs, targets, reduction="none") # (B, C)
    p_t = p * targets + (1 - p) * (1 - targets)
    loss = ce_loss * ((1 - p_t) ** gamma)  # (B, C)

    if alpha >= 0:
        alpha_t = alpha * targets + (1 - alpha) * (1 - targets) # # (B, C)
        loss = alpha_t * loss # (B, C)

    if reduction == "mean":
        loss = loss.mean()
    elif reduction == "sum":
        loss = loss.sum()

    return loss