三重损失反向传播梯度公式是什么? [英] What's the triplet loss back propagation gradient formula?

问题描述

我正在尝试使用 caffe 来实现

渐变 w.r.t 锚"输入 (fa):

梯度 w.r.t 正"输入 (fp):

梯度 w.r.t 负"输入 (fn):

<小时>

原来的计算(我出于感情原因离开这里……)

请参阅评论 更正最后一项.

I am trying to use caffe to implement triplet loss described in Schroff, Kalenichenko and Philbin "FaceNet: A Unified Embedding for Face Recognition and Clustering", 2015.

I am new to this so how to calculate the gradient in back propagation?

解决方案

I assume you define the loss layer as

layer {
  name: "tripletLoss"
  type: "TripletLoss"
  bottom: "anchor"
  bottom: "positive"
  bottom: "negative"
  ...
}

Now you need to compute a gradient w.r.t each of the "bottom"s.

The loss is given by:

The gradient w.r.t the "anchor" input (fa):

The gradient w.r.t the "positive" input (fp):

The gradient w.r.t the "negative" input (fn):

---

The original calculation (I leave here for sentimental reasons...)

Please see comment correcting the last term.

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