Caffe源码:Softmax_loss_layer.cpp

@brief: Caffe损失层反向传播

---

SoftmaxLayer是LeNet中前向传播的最后一层，也是反向传播的第一层。SoftmaxLayer作用是将网络的最后一层ip2的10个输出神经元$z_i (i\in(1,10))$通过函数$f$ 由浮点数映射到[0，1]之间的概率值,$f$ 的具体形式为$f(z_y)=\frac{e^{z_y-m}}{\sum_i^{batchsize}e^{z_i-m}}$,$m=max(z_i)$。每个样本的损失$Loss=-log(f(z_y)),$ 正确label所在的输出概率越小，损失越大。即损失由groundtruth所在的神经元产生，其中$y$为正确的label索引。因为SGD是基于一个batch_size共$n$ 个样本进行梯度更新的，所以batch_size个样本的总损失为$Loss_{sum}=\sum_j^n-logf(z_{yj})$,所以对每一个$z_y$求导即：
$\frac{\partial Loss_{sum}}{\partial z_y}=\frac{\partial -logf(z_{y})}{\partial z_y}=\frac {\partial -log(\frac{e^{z_y-m}}{\sum_i^{batchsize}e^{z_i-m}})}{\partial z_y}=\frac{\partial (log(\sum_i^{batchsize}e^{zi-m})-(z_y-m))}{\partial z_y}=\frac{e^{zy-m}}{\sum_i^{batchsize}e^{zi-m}}-1=f(z_y)-1$。

$\frac{\partial Loss_{sum}}{\partial z_i}=f(z_i)$略

#include <algorithm>
#include <cfloat>
#include <vector>

#include "caffe/layers/softmax_loss_layer.hpp"
#include "caffe/util/math_functions.hpp"

namespace caffe {

template <typename Dtype>
void SoftmaxWithLossLayer<Dtype>::LayerSetUp(
    const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
  LossLayer<Dtype>::LayerSetUp(bottom, top);
  LayerParameter softmax_param(this->layer_param_);//初始化
  softmax_param.set_type("Softmax");
  softmax_layer_ = LayerRegistry<Dtype>::CreateLayer(softmax_param);//创建softmax_layer
  softmax_bottom_vec_.clear();
  softmax_bottom_vec_.push_back(bottom[0]);//填充输出的神经元
  softmax_top_vec_.clear();
  softmax_top_vec_.push_back(&prob_);//填充预测的概率值
  softmax_layer_->SetUp(softmax_bottom_vec_, softmax_top_vec_);//一个指向softmax_layer_指针 并设置该层 softmax层的输出与输入一致

  has_ignore_label_ =//如果有设置需要忽略某个label对应的 实例/sample
    this->layer_param_.loss_param().has_ignore_label();//调用基类数据成员
  if (has_ignore_label_) {
    ignore_label_ = this->layer_param_.loss_param().ignore_label();
  }
  if (!this->layer_param_.loss_param().has_normalization() &&
      this->layer_param_.loss_param().has_normalize()) {
    normalization_ = this->layer_param_.loss_param().normalize() ?
                     LossParameter_NormalizationMode_VALID :
                     LossParameter_NormalizationMode_BATCH_SIZE;
  } else {
    normalization_ = this->layer_param_.loss_param().normalization();//默认归一化的方式为valid
  }
}

template <typename Dtype>
void SoftmaxWithLossLayer<Dtype>::Reshape(
    const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
  //this->Reshape(bottom, top);//调用的是本函数  this???????????
  LossLayer<Dtype>::Reshape(bottom, top);//top输出一个常数
  softmax_layer_->Reshape(softmax_bottom_vec_, softmax_top_vec_);//是不是重复了？  不同的在于 top没有初始化 由LossLayer的Reshape函数进行top的初始化
  softmax_axis_ =
      bottom[0]->CanonicalAxisIndex(this->layer_param_.softmax_param().axis());
  outer_num_ = bottom[0]->count(0, softmax_axis_);
  inner_num_ = bottom[0]->count(softmax_axis_ + 1);
  CHECK_EQ(outer_num_ * inner_num_, bottom[1]->count())
      << "Number of labels must match number of predictions; "
      << "e.g., if softmax axis == 1 and prediction shape is (N, C, H, W), "
      << "label count (number of labels) must be N*H*W, "
      << "with integer values in {0, 1, ..., C-1}.";
  if (top.size() >= 2) {
    // softmax output
    top[1]->ReshapeLike(*bottom[0]);
  }
}

template <typename Dtype>
Dtype SoftmaxWithLossLayer<Dtype>::get_normalizer(
    LossParameter_NormalizationMode normalization_mode, int valid_count) {
  Dtype normalizer;
  switch (normalization_mode) {
    case LossParameter_NormalizationMode_FULL:
      normalizer = Dtype(outer_num_ * inner_num_);
      break;
    case LossParameter_NormalizationMode_VALID:
      if (valid_count == -1) {
        normalizer = Dtype(outer_num_ * inner_num_);
      } else {
        normalizer = Dtype(valid_count);
      }
      break;
    case LossParameter_NormalizationMode_BATCH_SIZE:
      normalizer = Dtype(outer_num_);
      break;
    case LossParameter_NormalizationMode_NONE:
      normalizer = Dtype(1);
      break;
    default:
      LOG(FATAL) << "Unknown normalization mode: "
          << LossParameter_NormalizationMode_Name(normalization_mode);
  }
  // Some users will have no labels for some examples in order to 'turn off' a
  // particular loss in a multi-task setup. The max prevents NaNs in that case.
  return std::max(Dtype(1.0), normalizer);
}

template <typename Dtype>
void SoftmaxWithLossLayer<Dtype>::Forward_cpu(
    const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
  // The forward pass computes the softmax prob values.
  softmax_layer_->Forward(softmax_bottom_vec_, softmax_top_vec_);//通过SoftmaxLayer映射成概率
  /*const Dtype* data_pointer = softmax_top_vec_[0]->cpu_data();
  for (int i = 0; i < 10; i++)
      std::cout << *(data_pointer++) << " ";*/
  const Dtype* prob_data = prob_.cpu_data();//prob_指针已经被压倒vector<Blob<Dtype>*> softmax_top_vec_中
 /* const Dtype* data_pointerto_prob = prob_data;
  for (int i = 0; i < 10; i++)
      std::cout << *(data_pointerto_prob++) << " ";*///they are the same
  const Dtype* label = bottom[1]->cpu_data();
  int dim = prob_.count() / outer_num_;
  int count = 0;
  Dtype loss = 0;
  for (int i = 0; i < outer_num_; ++i) {
    for (int j = 0; j < inner_num_; j++) {
      const int label_value = static_cast<int>(label[i * inner_num_ + j]);
      if (has_ignore_label_ && label_value == ignore_label_) {
        continue;
      }
      DCHECK_GE(label_value, 0);
      DCHECK_LT(label_value, prob_.shape(softmax_axis_));
      loss -= log(std::max(prob_data[i * dim + label_value * inner_num_ + j],
                           Dtype(FLT_MIN)));//计算一个batch_size的所有样本的损失函数
      ++count;
    }
  }
  top[0]->mutable_cpu_data()[0] = loss / get_normalizer(normalization_, count);
  if (top.size() == 2) {
    top[1]->ShareData(prob_);
  }
}

template <typename Dtype>
void SoftmaxWithLossLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
    const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {//bottom[0]为NxKx1x1 N为批量数 K为总类别数目 bottom[1]为Nx1x1x1 为真实标签 输出top为计算得到的交叉熵分类损失E 1x1x1x1
    //输出loss的值
    std::cout << "Loss is: " << *(top[0]->mutable_cpu_data()) << std::endl;
  if (propagate_down[1]) {
    LOG(FATAL) << this->type()
               << " Layer cannot backpropagate to label inputs.";
  }
  if (propagate_down[0]) {
    Dtype* bottom_diff = bottom[0]->mutable_cpu_diff();
    const Dtype* prob_data = prob_.cpu_data();
    caffe_copy(prob_.count(), prob_data, bottom_diff);//将一个batch_size的概率值拷贝到bottom_diff
    const Dtype* label = bottom[1]->cpu_data();//拿到batch的所有label指针
    //print all labels from one batch 
    //for (int i = 0; i < bottom[1]->count(); i++)
    //  std::cout << *(label++) << " ";//这个有问题啊   因为你把label的指针向后移了当然后面的label_value有错
    int dim = prob_.count() / outer_num_;
    int count = 0;
    for (int i = 0; i < outer_num_; ++i) {//对batch中的每一张图片
      for (int j = 0; j < inner_num_; ++j) {//????????????
        const int label_value = static_cast<int>(label[i * inner_num_ + j]);//groundtruth
        //std::cout << label_value;
        if (has_ignore_label_ && label_value == ignore_label_) {
          for (int c = 0; c < bottom[0]->shape(softmax_axis_); ++c) {
            bottom_diff[i * dim + c * inner_num_ + j] = 0;
          }
        } else {
          bottom_diff[i * dim + label_value * inner_num_ + j] -= 1;//根据推导的公式，SoftmaxlossLayer层的梯度只在label所在的神经元更新，其余神经元的梯度即原输入。
          ++count;//batch中第i个样本对应正确label的值 理想的label对应的概率值为1,其它为0 实际上优化达不到1 所以最小化损失使得概率值尽可能的大
        }
      }
    }
    // Scale gradient
    //std::cout << *(top[0]->cpu_diff()) << " " << top[0]->cpu_diff()[0]; 
    Dtype loss_weight = top[0]->cpu_diff()[0] /
                        get_normalizer(normalization_, count);
    std::cout << "Original value of bottom_diff[0] is: " << bottom_diff[0] << " " << std::endl;
    caffe_scal(prob_.count(), loss_weight, bottom_diff);//bottom_diff=loss_weight*bottom_diff,prob_.count()为bottom_diff的元素个数
    std::cout <<"loss_weight is: "<<loss_weight<< "After operating on X=alpah*X, the result of bottom_diff[0] is: " << bottom_diff[0] << std::endl;
  }
}

#ifdef CPU_ONLY
STUB_GPU(SoftmaxWithLossLayer);
#endif

INSTANTIATE_CLASS(SoftmaxWithLossLayer);
REGISTER_LAYER_CLASS(SoftmaxWithLoss);

}  // namespace caffe

http://blog.youkuaiyun.com/mounty_fsc/article/details/51379395
http://blog.youkuaiyun.com/mounty_fsc/article/details/51092906#t10