What's the triplet loss back propagation gradient formula?

Question

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?

Answer 1

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.