Center Loss caffe 实现

Center Loss 
ECCV2016提出的center loss是通过将特征和特征中心的距离和softmax loss一同作为损失函数，使得类内距离更小，有点L1，L2正则化的意思。核心内容如下图所示：

接下来详细介绍center loss。如果你还是不熟悉传统的softmax loss，那么先来看看传统的softmax loss。首先区分softmax和softmax loss的区别，可以看博客：softmax，softmax-loss，BP的解释。下面公式1中log函数的输入就是softmax的结果（是概率），而Ls表示的是softmax loss的结果（是损失）。wx+b是全连接层的输出，因此log的输入就表示xi属于类别yi的概率。

那么center loss到底是什么呢？先看看center loss的公式LC。cyi表示第yi个类别的特征中心，xi表示全连接层之前的特征。后面会讲到实际使用的时候，m表示mini-batch的大小。因此这个公式就是希望一个batch中的每个样本的feature离feature 的中心的距离的平方和要越小越好，也就是类内距离要越小越好。这就是center loss。

关于LC的梯度和cyi的更新公式如下：

这个公式里面有个条件表达式如下式，这里当condition满足的时候，下面这个式子等于1，当不满足的时候，下面这个式子等于0.

因此上面关于cyi的更新的公式中，当yi（表示yi类别）和cj的类别j不一样的时候，cj是不需要更新的，只有当yi和j一样才需要更新。

作者文中用的损失L的包含softmax loss和center loss，用参数南木达（打不出这个特殊字符）控制二者的比重，如下式所示。这里的m表示mini-batch的包含的样本数量，n表示类别数。

具体的算法描述可以看下面的Algorithm1：

1. prototxt 中的使用

layer {
  name: "fc5"
  type: "InnerProduct"
  bottom: "res5_6"
  top: "fc5"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  inner_product_param {
    num_output: 512 # 提取特征层，特征维度
    weight_filler {
      type: "xavier"
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}

############## center loss ###############
layer {
  name: "center_loss"
  type: "CenterLoss"
  bottom: "fc5"
  bottom: "label"
  top: "center_loss"
  param {
    lr_mult: 1
    decay_mult: 2 
  }
  center_loss_param {
    num_output: 1000 # 类别数
    center_filler {
      type: "xavier"
    }
  }
  loss_weight: 0.008 # 权重
}


############## softmax loss ###############
# Softmax Loss 需要再接一个全连接层
layer {
  name: "fc6"
  type: "InnerProduct"
  bottom: "fc5"
  top: "fc6"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  inner_product_param {
    num_output: 1000 # 类别数
    weight_filler {
      type: "xavier"
    }
    bias_filler {
      type: "constant"
      value: 0
    }
  }
}
layer {
  name: "softmax_loss"
  type: "SoftmaxWithLoss"
  bottom: "fc6"
  bottom: "label"
  top: "softmax_loss"
}

2. caffe.proto 中的定义

message LayerParameter {
    optional CenterLossParameter center_loss_param = 149;
}


message CenterLossParameter {
  optional uint32 num_output = 1; // The number of outputs for the layer 网络层输出，与类别数一致
  optional FillerParameter center_filler = 2; // The filler for the centers 
  // The first axis to be lumped into a single inner product computation;
  // all preceding axes are retained in the output.
  // May be negative to index from the end (e.g., -1 for the last axis).
  optional int32 axis = 3 [default = 1];
}

3. center_loss_layer.hpp

#ifndef CAFFE_CENTER_LOSS_LAYER_HPP_
#define CAFFE_CENTER_LOSS_LAYER_HPP_

#include <vector>

#include "caffe/blob.hpp"
#include "caffe/layer.hpp"
#include "caffe/proto/caffe.pb.h"

#include "caffe/layers/loss_layer.hpp"

namespace caffe {

template <typename Dtype>
class CenterLossLayer : public LossLayer<Dtype> {
 public:
  explicit CenterLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);
  virtual void Reshape(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);

  virtual inline const char* type() const { return "CenterLoss"; }
  virtual inline int ExactNumBottomBlobs() const { return 2; }
  virtual inline int ExactNumTopBlobs() const { return -1; }

 protected:
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top); // 前向传播 CPU 实现
  virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top); // 前向传播 GPU 实现
  virtual void Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom); // 反向传播 CPU 实现
  virtual void Backward_gpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom);  //反向传播 GPU 实现

  int M_;
  int K_;
  int N_;

  Blob<Dtype> distance_;
  Blob<Dtype> variation_sum_;
};

}  // namespace caffe

#endif  // CAFFE_CENTER_LOSS_LAYER_HPP_

4. center_loss_layer.cpp - CPU 实现

#include <vector>

#include "caffe/filler.hpp"
#include "caffe/layers/center_loss_layer.hpp"
#include "caffe/util/math_functions.hpp"

namespace caffe {

template <typename Dtype>
void CenterLossLayer<Dtype>::LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  const int num_output = this->layer_param_.center_loss_param().num_output();  
  N_ = num_output;
  const int axis = bottom[0]->CanonicalAxisIndex(
      this->layer_param_.center_loss_param().axis());
  // Dimensions starting from "axis" are "flattened" into a single
  // length K_ vector. For example, if bottom[0]'s shape is (N, C, H, W),
  // and axis == 1, N inner products with dimension CHW are performed.
  K_ = bottom[0]->count(axis);
  // Check if we need to set up the weights
  if (this->blobs_.size() > 0) {
    LOG(INFO) << "Skipping parameter initialization";
  } else {
    this->blobs_.resize(1);
    // Intialize the weight
    vector<int> center_shape(2);
    center_shape[0] = N_;
    center_shape[1] = K_;
    this->blobs_[0].reset(new Blob<Dtype>(center_shape));
    // fill the weights
    shared_ptr<Filler<Dtype> > center_filler(GetFiller<Dtype>(
        this->layer_param_.center_loss_param().center_filler()));
    center_filler->Fill(this->blobs_[0].get());

  }  // 参数初始化
  this->param_propagate_down_.resize(this->blobs_.size(), true);
}


template <typename Dtype>
void CenterLossLayer<Dtype>::Reshape(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top) {
  CHECK_EQ(bottom[1]->channels(), 1);
  CHECK_EQ(bottom[1]->height(), 1);
  CHECK_EQ(bottom[1]->width(), 1);
  M_ = bottom[0]->num();
  // The top shape will be the bottom shape with the flattened axes dropped,
  // and replaced by a single axis with dimension num_output (N_).
  LossLayer<Dtype>::Reshape(bottom, top);
  distance_.ReshapeLike(*bottom[0]);
  variation_sum_.ReshapeLike(*this->blobs_[0]);
}


template <typename Dtype>
void CenterLossLayer<Dtype>::Forward_cpu(const vector<Blob<Dtype>*>& bottom,
    const vector<Blob<Dtype>*>& top) {
  const Dtype* bottom_data = bottom[0]->cpu_data();
  const Dtype* label = bottom[1]->cpu_data();
  const Dtype* center = this->blobs_[0]->cpu_data();
  Dtype* distance_data = distance_.mutable_cpu_data();

  // the i-th distance_data
  for (int i = 0; i < M_; i++) {
    const int label_value = static_cast<int>(label[i]);
    // D(i,:) = X(i,:) - C(y(i),:)
    caffe_sub(K_, bottom_data + i * K_, center + label_value * K_, distance_data + i * K_);
  }
  Dtype dot = caffe_cpu_dot(M_ * K_, distance_.cpu_data(), distance_.cpu_data());
  Dtype loss = dot / M_ / Dtype(2);
  top[0]->mutable_cpu_data()[0] = loss;
}


template <typename Dtype>
void CenterLossLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
    const vector<bool>& propagate_down,
    const vector<Blob<Dtype>*>& bottom) {
  // Gradient with respect to centers
  if (this->param_propagate_down_[0]) {
    const Dtype* label = bottom[1]->cpu_data();
    Dtype* center_diff = this->blobs_[0]->mutable_cpu_diff();
    Dtype* variation_sum_data = variation_sum_.mutable_cpu_data();
    const Dtype* distance_data = distance_.cpu_data();

    // \sum_{y_i==j}
    caffe_set(N_ * K_, (Dtype)0., variation_sum_.mutable_cpu_data());
    for (int n = 0; n < N_; n++) {
      int count = 0;
      for (int m = 0; m < M_; m++) {
        const int label_value = static_cast<int>(label[m]);
        if (label_value == n) {
          count++;
          caffe_sub(K_, variation_sum_data + n * K_, distance_data + m * K_, variation_sum_data + n * K_);
        }
      }
      caffe_axpy(K_, (Dtype)1./(count + (Dtype)1.), variation_sum_data + n * K_, center_diff + n * K_);
    }
  }
  // Gradient with respect to bottom data 
  if (propagate_down[0]) {
    caffe_copy(M_ * K_, distance_.cpu_data(), bottom[0]->mutable_cpu_diff());
    caffe_scal(M_ * K_, top[0]->cpu_diff()[0] / M_, bottom[0]->mutable_cpu_diff());
  }
  if (propagate_down[1]) {
    LOG(FATAL) << this->type()
               << " Layer cannot backpropagate to label inputs.";
  }
}

#ifdef CPU_ONLY
STUB_GPU(CenterLossLayer);
#endif

INSTANTIATE_CLASS(CenterLossLayer);
REGISTER_LAYER_CLASS(CenterLoss);

}  // namespace caffe

5. center_Loss_layer.cu - GPU 实现

#include <vector>

#include "caffe/filler.hpp"
#include "caffe/layers/center_loss_layer.hpp"
#include "caffe/util/math_functions.hpp"

namespace caffe {

template <typename Dtype>
__global__ void Compute_distance_data_gpu(int nthreads, const int K, const Dtype* bottom,
          const Dtype* label, const Dtype* center, Dtype* distance) {
  CUDA_KERNEL_LOOP(index, nthreads) {
    int m = index / K;
    int k = index % K;
    const int label_value = static_cast<int>(label[m]);
    // distance(i) = x(i) - c_{y(i)}
    distance[index] = bottom[index] - center[label_value * K + k];
  }
}

template <typename Dtype>
__global__ void Compute_center_diff_gpu(int nthreads, const int M, const int K, 
        const Dtype* label, const Dtype* distance, Dtype* variation_sum, 
        Dtype* center_diff) {
  CUDA_KERNEL_LOOP(index, nthreads) {
    int count = 0;
    for (int m = 0; m < M; m++) {
      const int label_value = static_cast<int>(label[m]);
      if (label_value == index) {
        count++;
        for (int k = 0; k < K; k++) {
          variation_sum[index * K + k] -= distance[m * K + k];
        }
      }
    }
    for (int k = 0; k < K; k++) {
      center_diff[index * K + k] = variation_sum[index * K + k] /(count + (Dtype)1.);
    }
  }
}


template <typename Dtype>
void CenterLossLayer<Dtype>::Forward_gpu(const vector<Blob<Dtype>*>& bottom,
    const vector<Blob<Dtype>*>& top) {
  int nthreads = M_ * K_;
  Compute_distance_data_gpu<Dtype><<<CAFFE_GET_BLOCKS(nthreads),
      CAFFE_CUDA_NUM_THREADS>>>(nthreads, K_, bottom[0]->gpu_data(), bottom[1]->gpu_data(),
                                this->blobs_[0]->gpu_data(), distance_.mutable_gpu_data());
  Dtype dot;
  caffe_gpu_dot(M_ * K_, distance_.gpu_data(), distance_.gpu_data(), &dot);
  Dtype loss = dot / M_ / Dtype(2);
  top[0]->mutable_cpu_data()[0] = loss;
}

template <typename Dtype>
void CenterLossLayer<Dtype>::Backward_gpu(const vector<Blob<Dtype>*>& top,
    const vector<bool>& propagate_down,
    const vector<Blob<Dtype>*>& bottom) {
  int nthreads = N_;
  caffe_gpu_set(N_ * K_, (Dtype)0., variation_sum_.mutable_cpu_data());
  Compute_center_diff_gpu<Dtype><<<CAFFE_GET_BLOCKS(nthreads),
      CAFFE_CUDA_NUM_THREADS>>>(nthreads, M_, K_, bottom[1]->gpu_data(), distance_.gpu_data(), 
                                variation_sum_.mutable_cpu_data(), this->blobs_[0]->mutable_gpu_diff());

  if (propagate_down[0]) {
    caffe_gpu_scale(M_ * K_, top[0]->cpu_diff()[0] / M_, 
                             distance_.gpu_data(), bottom[0]->mutable_gpu_diff());
  }
  if (propagate_down[1]) {
    LOG(FATAL) << this->type()
               << " Layer cannot backpropagate to label inputs.";
  }
}

INSTANTIATE_LAYER_GPU_FUNCS(CenterLossLayer);

}  // namespace caffe

6. 基于 Center Loss 的训练

• 数据准备

  与基于 Softmax Loss 的分类问题的数据格式一致，即：

  img1 label1
  img2 label2
  img3 label3
  ...

  • 1
  • 2
  • 3
  • 4

  其中，label 从 0 开始.

  根据数据集 labels 的总数设置 CenterLossLayer 的 num_output.

• 网络训练

  类似于分类问题的训练，进行网络训练即可.