caffe源码解读(11)－triplet_loss_layer.cpp

定义

TripletLossTripletLoss 的提出，是在这篇论文中——FaceNet: A Unified Embedding for Face Recognition and Clustering，论文中对TripletLossTripletLoss 的定义如下：



如上图所示，triplettriplet 是一个三元组，这个三元组是主要构成的：从训练样本中随机选取一个样本，称为 anchor(xa)anchor(xa)，然后再随机分别选取一个和anchoranchor 类别相同的样本 positive(xp)positive(xp) 以及和 anchoranchor 类别不同的样本 negative(xn)negative(xn)，因此构成了[ anchor,positive,negativeanchor,positive,negative ]三元组。TripletLossTripletLoss 的作用就是让特征表达xaxa 与xpxp 之间的距离尽可能小，让xaxa 与xnxn 的距离尽可能大。

公式

参考博文链接

同时，要让xaxa与xnxn之间的距离和xaxa与xp之间的距离有一个最小的间隔xp之间的距离有一个最小的间隔αα,公式化的表示即：

∥∥f(xai)−f(xpi)∥∥22+α<∥∥f(xai)−f(xni)∥∥22,∀(f(xai),f(xpi,f(xni))ϵτ‖f(xia)−f(xip)‖22+α<‖f(xia)−f(xin)‖22,∀(f(xia),f(xip,f(xin))ϵτ

对应的目标函数LL:这里距离用欧式距离度量，++表示[.]内的值大于0的时候，取该值为损失，小于0的时候，损失为０。

∑iN[∥∥f(xai)−f(xpi)∥∥22−∥∥f(xai)−f(xni)∥∥22+α]+∑iN[‖f(xia)−f(xip)‖22−‖f(xia)−f(xin)‖22+α]+

对目标函数LL求导：

∂L∂f(xai)=2⋅(f(xai)−f(xpi))−2⋅(f(xai)−f(xni))=2⋅(f(xni)−f(xpi))∂L∂f(xia)=2⋅(f(xia)−f(xip))−2⋅(f(xia)−f(xin))=2⋅(f(xin)−f(xip))

∂L∂f(xpi)=2⋅(f(xai)−f(xpi))⋅(−1))=2⋅(f(xpi)−f(xai))∂L∂f(xip)=2⋅(f(xia)−f(xip))⋅(−1))=2⋅(f(xip)−f(xia))

∂L∂f(xni)=−2⋅(f(xai)−f(xni))⋅(−1))=2⋅(f(xai)−f(xni))∂L∂f(xin)=−2⋅(f(xia)−f(xin))⋅(−1))=2⋅(f(xia)−f(xin))

代码

参数：

anchor−−>bottom[0]:N∗C∗1∗1anchor−−>bottom[0]:N∗C∗1∗1

positive−−>bottom[1]:N∗C∗1∗1positive−−>bottom[1]:N∗C∗1∗1

negative−−>bottom[2]:N∗C∗1∗1negative−−>bottom[2]:N∗C∗1∗1

(1)caffe.proto

层参数定义文件位于src/caffe/proto/caffe.proto

optional TripletLossParameter triplet_loss_param = 6667;

message TripletLossParameter {
//margin for negative triplet
optional float margin = 1 [default = 1.0];
}

(2)LayerSetUp

template <typename Dtype>
void TripletLossLayer<Dtype>::LayerSetUp(
const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
LossLayer<Dtype>::LayerSetUp(bottom, top);
//输入数据维度保持一致
CHECK_EQ(bottom[0]->num(), bottom[1]->num());
CHECK_EQ(bottom[1]->num(), bottom[2]->num());
CHECK_EQ(bottom[0]->channels(), bottom[1]->channels());
CHECK_EQ(bottom[1]->channels(), bottom[2]->channels());
CHECK_EQ(bottom[0]->height(), 1);
CHECK_EQ(bottom[0]->width(), 1);
CHECK_EQ(bottom[1]->height(), 1);
CHECK_EQ(bottom[1]->width(), 1);
CHECK_EQ(bottom[2]->height(), 1);
CHECK_EQ(bottom[2]->width(), 1);

diff_ap_.Reshape(bottom[0]->num(), bottom[0]->channels(), 1, 1);
diff_an_.Reshape(bottom[0]->num(), bottom[0]->channels(), 1, 1);
diff_pn_.Reshape(bottom[0]->num(), bottom[0]->channels(), 1, 1);

diff_sq_ap_.Reshape(bottom[0]->num(), bottom[0]->channels(), 1, 1);
diff_sq_an_.Reshape(bottom[0]->num(), bottom[0]->channels(), 1, 1);
dist_sq_ap_.Reshape(bottom[0]->num(), 1, 1, 1);
dist_sq_an_.Reshape(bottom[0]->num(), 1, 1, 1);
// vector of ones used to sum along channels
summer_vec_.Reshape(bottom[0]->channels(), 1, 1, 1);
for (int i = 0; i < bottom[0]->channels(); ++i)
summer_vec_.mutable_cpu_data()[i] = Dtype(1);
dist_binary_.Reshape(bottom[0]->num(), 1, 1, 1);
for (int i = 0; i < bottom[0]->num(); ++i)
dist_binary_.mutable_cpu_data()[i] = Dtype(1);
}

(3)Forward

template <typename Dtype>
void TripletLossLayer<Dtype>::Forward_cpu(
const vector<Blob<Dtype>*>& bottom,
const vector<Blob<Dtype>*>& top) {
int count = bottom[0]->count();

//const Dtype* sampleW = bottom[3]->cpu_data();
const Dtype sampleW = Dtype(1);
caffe_sub(
count,
bottom[0]->cpu_data(),  // anchor
bottom[1]->cpu_data(),  // positive
diff_ap_.mutable_cpu_data());  // a_i-p_i
caffe_sub(
count,
bottom[0]->cpu_data(),  // anchor
bottom[2]->cpu_data(),  // negative
diff_an_.mutable_cpu_data());  // a_i-n_i
caffe_sub(
count,
bottom[1]->cpu_data(),  // positive
bottom[2]->cpu_data(),  // negative
diff_pn_.mutable_cpu_data());  // p_i-n_i
const int channels = bottom[0]->channels();
Dtype margin = this->layer_param_.triplet_loss_param().margin();//参数\alpha

Dtype loss(0.0);
for (int i = 0; i < bottom[0]->num(); ++i) {
//dist_sq_ap_=diff_ap_.cpu_data*diff_ap_.cpu_data
//即Loss表达式的前半部分
dist_sq_ap_.mutable_cpu_data()[i] = caffe_cpu_dot(channels,
diff_ap_.cpu_data() + (i*channels), diff_ap_.cpu_data() + (i*channels));
//dist_sq_an_=diff_an_.cpu_data*diff_an_.cpu_data
//即Loss表达式的后半部分
dist_sq_an_.mutable_cpu_data()[i] = caffe_cpu_dot(channels,
diff_an_.cpu_data() + (i*channels), diff_an_.cpu_data() + (i*channels));
Dtype mdist = sampleW*std::max(margin + dist_sq_ap_.cpu_data()[i] - dist_sq_an_.cpu_data()[i], Dtype(0.0));//Loss公式
loss += mdist;
if (mdist < Dtype(1e-9)) {
//dist_binary_.mutable_cpu_data()[i] = Dtype(0);
//prepare for backward pass
//对diff_ap_、diff_an_、diff_pn_进行初始化
caffe_set(channels, Dtype(0), diff_ap_.mutable_cpu_data() + (i*channels));
caffe_set(channels, Dtype(0), diff_an_.mutable_cpu_data() + (i*channels));
caffe_set(channels, Dtype(0), diff_pn_.mutable_cpu_data() + (i*channels));
}
}
loss = loss / static_cast<Dtype>(bottom[0]->num()) / Dtype(2);
top[0]->mutable_cpu_data()[0] = loss;//将loss向前传播输出至top
}

(4)Backward

template <typename Dtype>
void TripletLossLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {
//Dtype margin = this->layer_param_.contrastive_loss_param().margin();
//const Dtype* sampleW = bottom[3]->cpu_data();
const Dtype sampleW = Dtype(1);

for (int i = 0; i < 3; ++i) {//３个输入bottom都需要做反向传播
if (propagate_down[i]) {
const Dtype sign = (i < 2) ? -1 : 1;
const Dtype alpha = sign * top[0]->cpu_diff()[0] /
static_cast<Dtype>(bottom[i]->num());
int num = bottom[i]->num();
int channels = bottom[i]->channels();
for (int j = 0; j < num; ++j) {
Dtype* bout = bottom[i]->mutable_cpu_diff();
if (i == 0) {
//对输入bottom[0]anchor求导
//caffe_cpu_axpby:Y=aX+bY
//diff_pn_=alpha*sampleW*diff_pn_
caffe_cpu_axpby(
channels,
alpha*sampleW,
diff_pn_.cpu_data() + (j*channels),
Dtype(0.0),
bout + (j*channels));
}
else if (i == 1) {
//对输入bottom[１]positive求导
//diff_ap_=alpha*sampleW*diff_ap_
caffe_cpu_axpby(
channels,
alpha*sampleW,
diff_ap_.cpu_data() + (j*channels),
Dtype(0.0),
bout + (j*channels));
}
else if (i == 2) {
// 对输入bottom[2]negative求导
//diff_an_=alpha*sampleW*diff_an_
caffe_cpu_axpby(
channels,
alpha*sampleW,
diff_an_.cpu_data() + (j*channels),
Dtype(0.0),
bout + (j*channels));
}
}
}
}
}