Github - focal_loss_layer

Focal Loss 论文理解及公式推导 - AIUAI

基于 SoftmaxWithLossLayer 实现的 FocalLossLayer.

主要涉及四个文件：

• caffe.proto
• focal_loss_layer.hpp
• focal_loss_layer.cpp
• focal_loss_layer.cu

1. 修改 caffe.proto 文件

在 caffe_root/src/caffe.proto 中添加如下内容：

// Add the next contents to message LayerParameter
message LayerParameter {
    optional FocalLossParameter focal_loss_param = 151; // select a id.
}

// Add the next contents to your caffe.proto
// Message that stores parameter used by FocalLossLayer
message FocalLossParameter {
    // loss = -alpha * (1 - pk)^gamma * ln(pk)
    // alpha is a parameter which scale the loss
    optional float alpha = 1 [default = 0.25];
    optional float gamma = 2 [default = 2.00];
}

2. 添加 focal_loss_layer.hpp 文件

将 focal_loss_layer.hpp 文件添加到 caffe_root/include/caffe/layers/：

// focal_loss.hpp -- inplement of <<Focal Loss for Dense Object Detection>>
// modified from softmax_loss_layer.hpp
#ifndef CAFFE_FOCAL_LOSS_LAYER_HPP_
#define CAFFE_FOCAL_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 {

/**
 * @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.
 *
 * This layer should be preferred over separate
 * SoftmaxLayer + MultinomialLogisticLossLayer
 * as its gradient computation is more numerically stable.
 * At test time, this layer can be replaced simply by a SoftmaxLayer.
 *
 * @param bottom input Blob vector (length 2)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the predictions @f$ x @f$, a Blob with values in
 *      @f$ [-\infty, +\infty] @f$ indicating the predicted score for each of
 *      the @f$ K = CHW @f$ classes. This layer maps these scores to a
 *      probability distribution over classes using the softmax function
 *      @f$ \hat{p}_{nk} = \exp(x_{nk}) /
 *      \left[\sum_{k'} \exp(x_{nk'})\right] @f$ (see SoftmaxLayer).
 *   -# @f$ (N \times 1 \times 1 \times 1) @f$
 *      the labels @f$ l @f$, an integer-valued Blob with values
 *      @f$ l_n \in [0, 1, 2, ..., K - 1] @f$
 *      indicating the correct class label among the @f$ K @f$ classes
 * @param top output Blob vector (length 1)
 *   -# @f$ (1 \times 1 \times 1 \times 1) @f$
 *      the computed cross-entropy classification loss: @f$ E =
 *        \frac{-1}{N} \sum\limits_{n=1}^N \log(\hat{p}_{n,l_n})
 *      @f$, for softmax output class probabilites @f$ \hat{p} @f$
 */
 // 继承自LossLayer
template <typename Dtype>
class FocalLossLayer : public LossLayer<Dtype> {
 public:
   /**
    * @param param provides LossParameter loss_param, with options:
    *  - ignore_label (optional)
    *    Specify a label value that should be ignored when computing the loss.
    *  - normalize (optional, default true)
    *    If true, the loss is normalized by the number of (nonignored) labels
    *    present; otherwise the loss is simply summed over spatial locations.
    */
  explicit FocalLossLayer(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 "FocalLoss"; }
  virtual inline int ExactNumTopBlobs() const { return -1; }
  virtual inline int MinTopBlobs() const { return 1; }
  virtual inline int MaxTopBlobs() const { return 2; }

 protected:
  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);
  /**
   * @brief Computes the softmax loss error gradient w.r.t. the predictions.
   *
   * Gradients cannot be computed with respect to the label inputs (bottom[1]),
   * so this method ignores bottom[1] and requires !propagate_down[1], crashing
   * if propagate_down[1] is set.
   *
   * @param top output Blob vector (length 1), providing the error gradient with
   *      respect to the outputs
   *   -# @f$ (1 \times 1 \times 1 \times 1) @f$
   *      This Blob's diff will simply contain the loss_weight* @f$ \lambda @f$,
   *      as @f$ \lambda @f$ is the coefficient of this layer's output
   *      @f$\ell_i@f$ in the overall Net loss
   *      @f$ E = \lambda_i \ell_i + \mbox{other loss terms}@f$; hence
   *      @f$ \frac{\partial E}{\partial \ell_i} = \lambda_i @f$.
   *      (*Assuming that this top Blob is not used as a bottom (input) by any
   *      other layer of the Net.)
   * @param propagate_down see Layer::Backward.
   *      propagate_down[1] must be false as we can't compute gradients with
   *      respect to the labels.
   * @param bottom input Blob vector (length 2)
   *   -# @f$ (N \times C \times H \times W) @f$
   *      the predictions @f$ x @f$; Backward computes diff
   *      @f$ \frac{\partial E}{\partial x} @f$
   *   -# @f$ (N \times 1 \times 1 \times 1) @f$
   *      the labels -- ignored as we can't compute their error gradients
   */
  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);

  /// The internal SoftmaxLayer used to map predictions to a distribution.
  shared_ptr<Layer<Dtype> > softmax_layer_;
  /// prob stores the output probability predictions from the SoftmaxLayer.
  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_;
  /// Whether to ignore instances with a certain label.
  bool has_ignore_label_;
  /// The label indicating that an instance should be ignored.
  int ignore_label_;
  /// How to normalize the output loss.
  LossParameter_NormalizationMode normalization_;
    
  int softmax_axis_, outer_num_, inner_num_;
  /// alpha_ and gamma_ factors are for Focal Loss
  Dtype alpha_, gamma_;
};

}  // namespace caffe

#endif  // CAFFE_FOCAL_LOSS_LAYER_HPP_

3. 添加 focal_loss_layer.cpp 文件

将 focal_loss_layer.cpp 添加到 caffe_root/src/caffe/layers/中：

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

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

namespace caffe {

template <typename Dtype>
void FocalLossLayer<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();
    normalization_ = this->layer_param_.loss_param().normalization();
  }
  // get alpha and gamma
  alpha_ = this->layer_param_.focal_loss_param().alpha();
    gamma_ = this->layer_param_.focal_loss_param().gamma();
}

template <typename Dtype>
void FocalLossLayer<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()); // classify at which 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 FocalLossLayer<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 FocalLossLayer<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_);
  const Dtype* prob_data = prob_.cpu_data();
  const Dtype* label = bottom[1]->cpu_data();
  int dim = prob_.count() / outer_num_; // c * h * w
  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(p)
      const Dtype pk = prob_data[i * dim + label_value * inner_num_ + j];
      loss -= alpha_ * powf(1 - pk, gamma_) * log(std::max(pk, Dtype(FLT_MIN)));
      ++count; // count elements.
    }// 
  }// per_num
  top[0]->mutable_cpu_data()[0] = loss / get_normalizer(normalization_, count);
  if (top.size() == 2) {
    top[1]->ShareData(prob_);
  }
}

template <typename Dtype>
void FocalLossLayer<Dtype>::Backward_cpu(const vector<Blob<Dtype>*>& top,
    const vector<bool>& propagate_down, const vector<Blob<Dtype>*>& bottom) {
    // bottom[0]->cpu_data(), zk
  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();
    // if i ！= k，then diff = prob
    //caffe_copy(prob_.count(), prob_data, bottom_diff);
    const Dtype* label = bottom[1]->cpu_data();
    // const Dtype* bottom_data = bottom[0]->cpu_data();
    int dim = prob_.count() / outer_num_;
    int count = 0;
    int num_channel = bottom[0]->shape(softmax_axis_);
    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_) {
              for (int c = 0; c < bottom[0]->shape(softmax_axis_); ++c) {
                bottom_diff[i * dim + c * inner_num_ + j] = 0;
              }
        } else {
            ++count;
            int c = 0;
            const Dtype pk = std::max(prob_data[i * dim + label_value * inner_num_ + j], Dtype(FLT_MIN));
            for (c = 0; c < label_value; ++c) {
                const Dtype pj = std::max(prob_data[i * dim + c * inner_num_ + j], Dtype(FLT_MIN));
                bottom_diff[i * dim + c * inner_num_ + j] = Dtype(-1 * alpha_ * (gamma_ * pow(1 - pk, gamma_ - 1) * pk * pj * log(pk) - pow(1 - pk, gamma_) * pj)); // j != k
            } // per_channel
            bottom_diff[i * dim + label_value * inner_num_ + j] = Dtype (-1 * alpha_ * (-1 * gamma_ * powf(1 - pk, gamma_) * pk * log(pk) + powf(1 - pk, gamma_ + 1)));    // j = k
            c++;
            for ( ; c < num_channel; ++c) {
                const Dtype pj = std::max(prob_data[i * dim + c * inner_num_ + j], Dtype(FLT_MIN));
                bottom_diff[i * dim + c * inner_num_ + j] = Dtype(-1 * alpha_ * (gamma_ * pow(1 - pk, gamma_ - 1) * pk * pj * log(pk) - pow(1 - pk, gamma_) * pj)); // j != k
            } // per_channel
        }
      }// per_h_w
    }// per_num
    // 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(FocalLossLayer);
#endif

INSTANTIATE_CLASS(FocalLossLayer);
REGISTER_LAYER_CLASS(FocalLoss);

}  // namespace caffe

4. 添加 focal_loss_layer.cu 文件

将 focal_loss_layer.cu 文件添加到路径 caffe_root/src/caffe/layers/ 中：

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

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

namespace caffe {
    template <typename Dtype>
    __global__ void FocalLossForwardGPU(const int nthreads,
                const Dtype * prob_data, const Dtype * label, Dtype* loss,
                const int num, const int dim, const int spatial_dim,
                const bool has_ignore_label_, const int ignore_label_,
                Dtype * counts, const Dtype alpha_, const Dtype gamma_) {
        CUDA_KERNEL_LOOP(index, nthreads) {
            const int n = index / spatial_dim; 
            const int s = index % spatial_dim; 
            const int label_value = static_cast<int>(label[n * spatial_dim + s]);
            if (has_ignore_label_ && label_value == ignore_label_) {
                loss[index] = 0;
                counts[index] = 0;
            } else {
                const Dtype pk = max(prob_data[n * dim + label_value * spatial_dim + s], Dtype(FLT_MIN));
                loss[index] = -1 * alpha_ * powf(1 - pk, gamma_) * log(pk);
                counts[index] = 1;
            }
        }
    }
    
    template <typename Dtype>
    void FocalLossLayer<Dtype>::Forward_gpu(
        const vector<Blob<Dtype> *> & bottom, const vector<Blob<Dtype> *> & top) {
        softmax_layer_->Forward(softmax_bottom_vec_, softmax_top_vec_);
        const Dtype * prob_data = prob_.gpu_data();
        const Dtype * label = bottom[1]->gpu_data();
        const int dim = prob_.count() / outer_num_;
        const int nthreads = outer_num_ * inner_num_;
        
        Dtype * loss_data = bottom[0]->mutable_gpu_diff();
        Dtype * counts = prob_.mutable_gpu_diff();
        FocalLossForwardGPU<Dtype><<<CAFFE_GET_BLOCKS(nthreads),
            CAFFE_CUDA_NUM_THREADS>>>(nthreads, prob_data, label, loss_data,
            outer_num_, dim, inner_num_, has_ignore_label_, ignore_label_, counts, alpha_, gamma_);
        Dtype loss;
        caffe_gpu_asum(nthreads, loss_data, &loss);
        Dtype valid_count = -1;
        if (normalization_ == LossParameter_NormalizationMode_VALID &&
            has_ignore_label_) {
            caffe_gpu_asum(nthreads, counts, & valid_count);
        }
        top[0]->mutable_cpu_data()[0] = loss / get_normalizer(normalization_,
                                                                valid_count);
        if (2 == top.size()) {
            top[1]->ShareData(prob_);
        }
    }
    
    template <typename Dtype>
    __global__ void FocalLossBackwardGPU(const int nthreads, const Dtype * prob_data,
                const Dtype * label, Dtype * bottom_diff, const int num, const int dim,
                const int spatial_dim, const bool has_ignore_label_,
                const int ignore_label_, Dtype * counts, const Dtype alpha_, const Dtype gamma_) {
        const int channels = dim / spatial_dim;
        CUDA_KERNEL_LOOP(index, nthreads) {
            const int n = index / spatial_dim;
            const int s = index % spatial_dim;
            const int label_value = static_cast<int>(label[n * spatial_dim + s]);
            if (has_ignore_label_ && label_value == ignore_label_) {
                for (int c = 0; c < channels; ++c) {
                    bottom_diff[n * dim + c * spatial_dim + s] = 0;
                }
                counts[index] = 0;
            } else {
                int c = 0;
                const Dtype pk = max(prob_data[n * dim + label_value * spatial_dim + s], Dtype(FLT_MIN));
                for (c = 0; c < label_value; ++c) {
                    const Dtype pj = max(prob_data[n * dim + c * spatial_dim + s], Dtype(FLT_MIN));
                    bottom_diff[n * dim + c * spatial_dim + s] = Dtype(
                        -1 * alpha_ * (gamma_ * pow(1 - pk, gamma_ - 1) * pk * pj * log(pk) - pow(1 - pk, gamma_) * pj));
                }
                bottom_diff[n * dim + c * spatial_dim + s] = Dtype(
                    -1 * alpha_ * (-1 * gamma_ * pow(1 - pk, gamma_) * pk * log(pk) + pow(1 - pk, gamma_ + 1)));
                c++;
                for ( ; c < channels; ++c) {
                    const Dtype pj = max(prob_data[n * dim + c * spatial_dim + s], Dtype(FLT_MIN));
                    bottom_diff[n * dim + c * spatial_dim + s] = Dtype(
                        -1 * alpha_ * (gamma_ * pow(1 - pk, gamma_ - 1) * pk * pj * log(pk) - pow(1 - pk, gamma_) * pj));
                }
                counts[index] = 1;
            }
        }
    }
    
    template <typename Dtype>
    void FocalLossLayer<Dtype>::Backward_gpu(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_gpu_diff();
            const Dtype* prob_data = prob_.gpu_data();
            const Dtype* top_data = top[0]->gpu_data();
            const Dtype* label = bottom[1]->gpu_data();
            const int dim = prob_.count() / outer_num_;
            const int nthreads = outer_num_ * inner_num_;
            // Since this memory is nerver used for anything else,
            // we use to to avoid allocating new GPU memory 
            Dtype* counts = prob_.mutable_gpu_diff();
            // NOLINT_NEXT_LINE(whitespace/operators)
            FocalLossBackwardGPU<Dtype><<<CAFFE_GET_BLOCKS(nthreads),
                CAFFE_CUDA_NUM_THREADS>>>(nthreads, prob_data, label, bottom_diff,
                outer_num_, dim, inner_num_, has_ignore_label_, ignore_label_, counts,
                alpha_, gamma_);
            Dtype valid_count = -1;
            // Only launch another CUDA kernel if we actually need the count of valid
            // outputs.
            if (normalization_ == LossParameter_NormalizationMode_VALID &&
                has_ignore_label_) {
                caffe_gpu_asum(nthreads, counts, & valid_count);
            }
            const Dtype loss_weight = top[0]->cpu_diff()[0] / 
                                    get_normalizer(normalization_, valid_count);
            caffe_gpu_scal(prob_.count(), loss_weight, bottom_diff);
        }
    }
    
    INSTANTIATE_LAYER_GPU_FUNCS(FocalLossLayer);
} // namespace caffe

5. FocalLossLayer 用法

在 caffe 编译完成后，FocalLossLayer 在 prototxt文件中的用法为：

layer {
    name: "focal_loss"
    type: "FocalLoss"
    bottom: "conv_cls"
    bottom: "label"
    top: "loss"
    include {
        phase: TRAIN
    }
    loss_param {
        ignore_label: 255
    }
    focal_loss_param {
        alpha: 0.25
        gamma: 2.00
    }
}