caffe SigmoidCrossEntropyLossLayer 理论代码学习

交叉熵损失函数

交叉熵损失函数的简单介绍的链接
下面我们就介绍一下caffe里面实现交叉熵的流程：
首先：下面这个式子就是交叉熵的损失表达式

E=−1n∑n=1n[pnlogp^n+(1−pn)log(1−p^n)]

SigmoidCrossEntropyLossLayer的输入bottom[0]，bottom[1]，其中bottom[0]是输入的预测的结果，bottom[1]是标签值。bottom的维度都是 (N×C×H×W) ，bottom的表示符号是x， x∈[−∞,+∞] ， p^n=σ(xn)∈[0,1] ，bottom[1]是 p∈[0,1] ，输出的loss维度是 (1×1×1×1) 。

σ(xn)=11+exn

反向传播的导数：

∂E∂xn=∂E∂p^n∂p^n∂xn=−1N(pn1p^n−1−pn1−p^n)(p^n(1−p^n))=1N(p^n−pn)

其中caffe里面计算loss的代码看起来有点跟表达式不相像可以参考：
代码：

  Dtype loss = 0;
  for (int i = 0; i < count; ++i) {
    loss -= input_data[i] * (target[i] - (input_data[i] >= 0)) -
        log(1 + exp(input_data[i] - 2 * input_data[i] * (input_data[i] >= 0)));
  }
  top[0]->mutable_cpu_data()[0] = loss / num;

caffe loss理解

图片引用自链接：

介绍完理论和注意的内容，接下来就贴代码和一些注释：

SigmoidCrossEntropyLossLayer的定义
template <typename Dtype>
class SigmoidCrossEntropyLossLayer : public LossLayer {
 public:
  explicit SigmoidCrossEntropyLossLayer(const LayerParameter& param)
      : LossLayer(param),
          sigmoid_layer_(new SigmoidLayer(param)),
          sigmoid_output_(new Blob()) {}
  virtual void LayerSetUp(const vector*>& bottom,
      const vector*>& top);
  virtual void Reshape(const vector*>& bottom,
      const vector*>& top);
  virtual inline const char* type() const { return "SigmoidCrossEntropyLoss"; }
 protected:
  virtual void Forward_cpu(const vector*>& bottom,
      const vector*>& top);
  virtual void Backward_cpu(const vector*>& top,
      const vector<bool>& propagate_down, const vector*>& bottom);
  virtual void Backward_gpu(const vector*>& top,
      const vector<bool>& propagate_down, const vector*>& bottom);

  /// The internal SigmoidLayer used to map predictions to probabilities.
  shared_ptr > sigmoid_layer_;//用于生成生成sigmoid结果
  /// sigmoid_output stores the output of the SigmoidLayer.
  shared_ptr > sigmoid_output_;//指向sigmoid的输出
  /// bottom vector holder to call the underlying SigmoidLayer::Forward
  vector*> sigmoid_bottom_vec_;//sigmoid的输入
  /// top vector holder to call the underlying SigmoidLayer::Forward
  vector*> sigmoid_top_vec_; //sigmoid的输出
};

SigmoidCrossEntropyLossLayer类的成员函数实现
template <typename Dtype>
void SigmoidCrossEntropyLossLayer::LayerSetUp(
    const vector*>& bottom, const vector*>& top) {
  LossLayer::LayerSetUp(bottom, top);
  sigmoid_bottom_vec_.clear();
  sigmoid_bottom_vec_.push_back(bottom[0]);
  sigmoid_top_vec_.clear();
  sigmoid_top_vec_.push_back(sigmoid_output_.get());
  sigmoid_layer_->SetUp(sigmoid_bottom_vec_, sigmoid_top_vec_);
}

template <typename Dtype>
void SigmoidCrossEntropyLossLayer::Reshape(
    const vector*>& bottom, const vector*>& top) {
  LossLayer::Reshape(bottom, top);
  CHECK_EQ(bottom[0]->count(), bottom[1]->count()) <<
      "SIGMOID_CROSS_ENTROPY_LOSS layer inputs must have the same count.";
  sigmoid_layer_->Reshape(sigmoid_bottom_vec_, sigmoid_top_vec_);
}

template <typename Dtype>
void SigmoidCrossEntropyLossLayer::Forward_cpu(
    const vector*>& bottom, const vector*>& top) {
  // The forward pass computes the sigmoid outputs.
  sigmoid_bottom_vec_[0] = bottom[0];
  sigmoid_layer_->Forward(sigmoid_bottom_vec_, sigmoid_top_vec_);
  // Compute the loss (negative log likelihood)
  const int count = bottom[0]->count();
  const int num = bottom[0]->num();
  // Stable version of loss computation from input data
  const Dtype* input_data = bottom[0]->cpu_data();
  const Dtype* target = bottom[1]->cpu_data();
  Dtype loss = 0;
  for (int i = 0; i < count; ++i) {
    loss -= input_data[i] * (target[i] - (input_data[i] >= 0)) -
        log(1 + exp(input_data[i] - 2 * input_data[i] * (input_data[i] >= 0)));
  }
  top[0]->mutable_cpu_data()[0] = loss / num;
}

template <typename Dtype>
void SigmoidCrossEntropyLossLayer::Backward_cpu(
    const vector*>& top, const vector<bool>& propagate_down,
    const vector*>& bottom) {
  if (propagate_down[1]) {
    LOG(FATAL) << this->type()
               << " Layer cannot backpropagate to label inputs.";
  }
  if (propagate_down[0]) {
    // First, compute the diff
    const int count = bottom[0]->count();
    const int num = bottom[0]->num();
    const Dtype* sigmoid_output_data = sigmoid_output_->cpu_data();
    const Dtype* target = bottom[1]->cpu_data();
    Dtype* bottom_diff = bottom[0]->mutable_cpu_diff();
    caffe_sub(count, sigmoid_output_data, target, bottom_diff);
    // Scale down gradient
    const Dtype loss_weight = top[0]->cpu_diff()[0];
    caffe_scal(count, loss_weight / num, bottom_diff);
  }
}