SoftmaxWithLossLayer 用于多类别图像分类问题,即数据集共 N 个类,但每张图片只能是其中一个类,如狗或猫.
Caffe 处理分类问题中应用最普遍的 loss 层之一.

SoftmaxWithLossLayer 针对 one-of-many 的分类任务计算 multinomial logistic loss,通过 softmax 来得到每一类的概率分布,传递实值预测(real-valued predictions).

SoftmaxWithLoss 层先计算输入的经 softmax 的激活值,再计算 multinomial logistic loss,等价于 Softmax Layer(softmax 函数) + Multinomial Logistic Loss Layer(即 Cross Entropy Loss,交叉熵函数,常用于分类问题). 但具有更加数值稳定的梯度,在 test 阶段可以采用 SoftmaxLayer 来替换.

Softmax 激活函数
${p_{nk} = exp(x_{nk})/[\sum_{i}exp(x_{ni})]}$

1. 网络层参数

bottom:
输入 Blob 向量,长度为2
输入 Input1 - 预测的 x,(N×C×H×W),是值在 [-inf, +inf]区间的数据Blob,表示 K=CHW 类的各类的预测 scores. 该层采用 softmax 函数 将 scores 映射到各类别的概率分布;
输入 Input2 - 参考 Label ${l}$,(N×1×1×1),是值为 ${l_n \in [0,1,2,...,K-1]}$ 的整数值数据Blob,表示 K 类的正确的类别标签.

top:
输出 Blob 向量,长度为 1
输出 Output1 - 对 softmax 层输出类别概率 p,计算得到的 cross-entropy classification loss(交叉熵分类损失),(1×1×1×1),${E=-\frac1N \sum^N_{n=1} log(p_n, l_n)}$.

2. prototxt 定义

layer {
  name: "loss"
  type: "SoftmaxWithLoss"
  bottom: "fc7"
  bottom: "label"
  top: "loss"
  loss_param{
    ignore_label:0
  }
}

3. Caffe SoftmaxWithLossLayer 定义

3.1 头文件 softmax_loss_layer.hpp

#ifndef CAFFE_SOFTMAX_WITH_LOSS_LAYER_HPP_
#define CAFFE_SOFTMAX_WITH_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"
#include "caffe/layers/softmax_layer.hpp"

namespace caffe {

/**
* 用处:
 * @brief Computes the multinomial logistic loss for a one-of-many
 *        classification task, passing real-valued predictions through a
 *        softmax to get a probability distribution over classes.
 */
template <typename Dtype>
class SoftmaxWithLossLayer : public LossLayer<Dtype> {
 public:
   /**
   * 可选 loss 参数:
    * @param param provides LossParameter loss_param, with options:
    *  - ignore_label (optional)  // 忽略不计算的 label 
    *    Specify a label value that should be ignored when computing the loss.
    *  - normalize (optional, default true) // 归一化,默认为 true
    *    If true, the loss is normalized by the number of (nonignored) labels
    *    present; otherwise the loss is simply summed over spatial locations.
    */
  explicit SoftmaxWithLossLayer(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 "SoftmaxWithLoss"; }
  virtual inline int ExactNumTopBlobs() const { return -1; }
  virtual inline int MinTopBlobs() const { return 1; }
  virtual inline int MaxTopBlobs() const { return 2; }

 protected:
 //  重载CPU和GPU正向传播虚函数
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);
  virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom,
      const vector<Blob<Dtype>*>& top);
  //  重载CPU和GPU反向传播虚函数
  virtual void Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom);
  virtual void Backward_gpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom);

  /// Read the normalization mode parameter and compute the normalizer based
  /// on the blob size.  If normalization_mode is VALID, the count of valid
  /// outputs will be read from valid_count, unless it is -1 in which case
  /// all outputs are assumed to be valid.
  virtual Dtype get_normalizer(
      LossParameter_NormalizationMode normalization_mode, int valid_count);

  /// 采用 SoftmaxLayer 将预测值映射到概率分布的形式.
  shared_ptr<Layer<Dtype> > softmax_layer_;
  /// prob 保存了 SoftmaxLayer计算得到的输出概率预测值.
  Blob<Dtype> prob_;
  /// bottom vector holder used in call to the underlying SoftmaxLayer::Forward
  vector<Blob<Dtype>*> softmax_bottom_vec_;
  /// top vector holder used in call to the underlying SoftmaxLayer::Forward
  vector<Blob<Dtype>*> softmax_top_vec_;
  /// 是否有需要忽略的特定label.
  bool has_ignore_label_;
  /// 需要忽略计算的label.
  int ignore_label_;
  /// 归一化输出loss的方式.
  LossParameter_NormalizationMode normalization_;

  int softmax_axis_, outer_num_, inner_num_;
};

}  // namespace caffe

#endif  // CAFFE_SOFTMAX_WITH_LOSS_LAYER_HPP_

3.2 CPU 实现代码 softmax_loss_layer.cpp

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

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

namespace caffe {

template <typename Dtype>
// 参数设置
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_);
  softmax_param.set_type("Softmax");
  softmax_layer_ = LayerRegistry<Dtype>::CreateLayer(softmax_param);
  softmax_bottom_vec_.clear();
  softmax_bottom_vec_.push_back(bottom[0]);
  softmax_top_vec_.clear();
  softmax_top_vec_.push_back(&prob_);
  softmax_layer_->SetUp(softmax_bottom_vec_, softmax_top_vec_);

  has_ignore_label_ =
    this->layer_param_.loss_param().has_ignore_label();
  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();
  }
}

template <typename Dtype>
void SoftmaxWithLossLayer<Dtype>::Reshape(
    const vector<Blob<Dtype>*>& bottom, const vector<Blob<Dtype>*>& top) {
  LossLayer<Dtype>::Reshape(bottom, top);
  softmax_layer_->Reshape(softmax_bottom_vec_, softmax_top_vec_);
  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) {  // 归一化方法
    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);
  }
  // 避免数据不带label导致normalizer为0,出现分母为0. 
  // max 处理防止出现 NaNs. 
  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) {
  // 对 SoftmaxLayer 前向传播计算 softmax prob 值.
  softmax_layer_->Forward(softmax_bottom_vec_, softmax_top_vec_);
  const Dtype* prob_data = prob_.cpu_data();
  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++) {
    // 真实 Label 值
      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_));
      // prob_data 是由 SoftmaxLayer 计算得到的
      // 对 label 值相对应的 prob_data 预测概率值,进行 -log 操作,累加 bctch_size 个的值. 
      loss -= log(std::max(prob_data[i * dim + label_value * inner_num_ + j],
                           Dtype(FLT_MIN)));
      ++count;
    }
  }
  // loss 除以样本总数,得到单个样本的平均 loss
  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) {
  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();
    // 拷贝前向传播计算得到的 prob_data 到 偏导项 bottom_diff
    caffe_copy(prob_.count(), prob_data, bottom_diff);
    const Dtype* label = bottom[1]->cpu_data();
    int dim = prob_.count() / outer_num_;
    int count = 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]);
        // 如果是 ignore_label,则偏导数 bottom_diff 值为0
        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 {
          //偏导数计算
          bottom_diff[i * dim + label_value * inner_num_ + j] -= 1;
          ++count;
        }
      }
    }
    // Scale gradient
    Dtype loss_weight = top[0]->cpu_diff()[0] /
                        get_normalizer(normalization_, count);
    caffe_scal(prob_.count(), loss_weight, bottom_diff);
  }
}

#ifdef CPU_ONLY
STUB_GPU(SoftmaxWithLossLayer);
#endif

INSTANTIATE_CLASS(SoftmaxWithLossLayer);
REGISTER_LAYER_CLASS(SoftmaxWithLoss);

}  // namespace caffe
Last modification:October 10th, 2018 at 03:59 pm