Caffe源码:Softmax_loss_layer.cpp

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@brief: Caffe损失层反向传播

Softmax前向传播示意图

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zi(i∈(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(zy)=ezy−m∑batchsizeiezi−m,m=max(zi)。每个样本的损失Loss=−log(f(zy)), 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Losssum=∑nj−logf(zyj),所以对每一个zy求导即：
∂Losssum∂zy=∂−logf(zy)∂zy=∂−log(ezy−m∑batchsizeiezi−m)∂zy=∂(log(∑batchsizeiezi−m)−(zy−m))∂zy=ezy−m∑batchsizeiezi−m−1=f(zy)−1。

∂Losssum∂zi=f(zi)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_ONLYSTUB_GPU(SoftmaxWithLossLayer);#endifINSTANTIATE_CLASS(SoftmaxWithLossLayer);REGISTER_LAYER_CLASS(SoftmaxWithLoss);}  // namespace caffe

http://blog.csdn.net/mounty_fsc/article/details/51379395
http://blog.csdn.net/mounty_fsc/article/details/51092906#t10

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