path: root/include/caffe/loss_layers.hpp

#ifndef CAFFE_LOSS_LAYERS_HPP_
#define CAFFE_LOSS_LAYERS_HPP_

#include <string>
#include <utility>
#include <vector>

#include "caffe/blob.hpp"
#include "caffe/common.hpp"
#include "caffe/layer.hpp"
#include "caffe/neuron_layers.hpp"
#include "caffe/proto/caffe.pb.h"

namespace caffe {

const float kLOG_THRESHOLD = 1e-20;

/**
 * @brief Computes the classification accuracy for a one-of-many
 *        classification task.
 */
template <typename Dtype>
class AccuracyLayer : public Layer<Dtype> {
 public:
  /**
   * @param param provides AccuracyParameter accuracy_param,
   *     with AccuracyLayer options:
   *   - top_k (\b optional, default 1).
   *     Sets the maximum rank @f$ k @f$ at which a prediction is considered
   *     correct.  For example, if @f$ k = 5 @f$, a prediction is counted
   *     correct if the correct label is among the top 5 predicted labels.
   */
  explicit AccuracyLayer(const LayerParameter& param)
      : Layer<Dtype>(param) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_ACCURACY;
  }

  virtual inline int ExactNumBottomBlobs() const { return 2; }
  virtual inline int ExactNumTopBlobs() const { return 1; }

 protected:
  /**
   * @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. Each @f$ x_n @f$ is mapped to a predicted
   *      label @f$ \hat{l}_n @f$ given by its maximal index:
   *      @f$ \hat{l}_n = \arg\max\limits_k x_{nk} @f$
   *   -# @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 accuracy: @f$
   *        \frac{1}{N} \sum\limits_{n=1}^N \delta\{ \hat{l}_n = l_n \}
   *      @f$, where @f$
   *      \delta\{\mathrm{condition}\} = \left\{
   *         \begin{array}{lr}
   *            1 & \mbox{if condition} \\
   *            0 & \mbox{otherwise}
   *         \end{array} \right.
   *      @f$
   */
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);


  /// @brief Not implemented -- AccuracyLayer cannot be used as a loss.
  virtual void Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom) {
    for (int i = 0; i < propagate_down.size(); ++i) {
      if (propagate_down[i]) { NOT_IMPLEMENTED; }
    }
  }

  int top_k_;
};

/**
 * @brief An interface for Layer%s that take two Blob%s as input -- usually
 *        (1) predictions and (2) ground-truth labels -- and output a
 *        singleton Blob representing the loss.
 *
 * LossLayers are typically only capable of backpropagating to their first input
 * -- the predictions.
 */
template <typename Dtype>
class LossLayer : public Layer<Dtype> {
 public:
  explicit LossLayer(const LayerParameter& param)
     : Layer<Dtype>(param) {}
  virtual void LayerSetUp(
      const vector<Blob<Dtype>*>& bottom, vector<Blob<Dtype>*>* top);

  virtual inline int ExactNumBottomBlobs() const { return 2; }

  /**
   * @brief For convenience and backwards compatibility, instruct the Net to
   *        automatically allocate a single top Blob for LossLayers, into which
   *        they output their singleton loss, (even if the user didn't specify
   *        one in the prototxt, etc.).
   */
  virtual inline bool AutoTopBlobs() const { return true; }
  virtual inline int ExactNumTopBlobs() const { return 1; }
  /**
   * We usually cannot backpropagate to the labels; ignore force_backward for
   * these inputs.
   */
  virtual inline bool AllowForceBackward(const int bottom_index) const {
    return bottom_index != 1;
  }
};

/**
 * @brief Computes the Euclidean (L2) loss @f$
 *          E = \frac{1}{2N} \sum\limits_{n=1}^N \left| \left| \hat{y}_n - y_n
 *        \right| \right|_2^2 @f$ for real-valued regression tasks.
 *
 * @param bottom input Blob vector (length 2)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the predictions @f$ \hat{y} \in [-\infty, +\infty]@f$
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the targets @f$ y \in [-\infty, +\infty]@f$
 * @param top output Blob vector (length 1)
 *   -# @f$ (1 \times 1 \times 1 \times 1) @f$
 *      the computed Euclidean loss: @f$ E =
 *          \frac{1}{2n} \sum\limits_{n=1}^N \left| \left| \hat{y}_n - y_n
 *        \right| \right|_2^2 @f$
 *
 * This can be used for least-squares regression tasks.  An InnerProductLayer
 * input to a EuclideanLossLayer exactly formulates a linear least squares
 * regression problem. With non-zero weight decay the problem becomes one of
 * ridge regression -- see src/caffe/test/test_sgd_solver.cpp for a concrete
 * example wherein we check that the gradients computed for a Net with exactly
 * this structure match hand-computed gradient formulas for ridge regression.
 *
 * (Note: Caffe, and SGD in general, is certainly \b not the best way to solve
 * linear least squares problems! We use it only as an instructive example.)
 */
template <typename Dtype>
class EuclideanLossLayer : public LossLayer<Dtype> {
 public:
  explicit EuclideanLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param), diff_() {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_EUCLIDEAN_LOSS;
  }

  /**
   * Unlike most loss layers, in the EuclideanLossLayer we can backpropagate
   * to both inputs -- override to return true and always allow force_backward.
   */
  virtual inline bool AllowForceBackward(const int bottom_index) const {
    return true;
  }

 protected:
  /// @copydoc EuclideanLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);
  virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  /**
   * @brief Computes the Euclidean error gradient w.r.t. the inputs.
   *
   * Unlike other children of LossLayer, EuclideanLossLayer \b can compute
   * gradients with respect to the label inputs bottom[1] (but still only will
   * if propagate_down[1] is set, due to being produced by learnable parameters
   * or if force_backward is set). In fact, this layer is "commutative" -- the
   * result is the same regardless of the order of the two bottoms.
   *
   * @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$.
   *      (*Assuming that this top Blob is not used as a bottom (input) by any
   *      other layer of the Net.)
   * @param propagate_down see Layer::Backward.
   * @param bottom input Blob vector (length 2)
   *   -# @f$ (N \times C \times H \times W) @f$
   *      the predictions @f$\hat{y}@f$; Backward fills their diff with
   *      gradients @f$
   *        \frac{\partial E}{\partial \hat{y}} =
   *            \frac{1}{n} \sum\limits_{n=1}^N (\hat{y}_n - y_n)
   *      @f$ if propagate_down[0]
   *   -# @f$ (N \times C \times H \times W) @f$
   *      the targets @f$y@f$; Backward fills their diff with gradients
   *      @f$ \frac{\partial E}{\partial y} =
   *          \frac{1}{n} \sum\limits_{n=1}^N (y_n - \hat{y}_n)
   *      @f$ if propagate_down[1]
   */
  virtual void Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom);
  virtual void Backward_gpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom);

  Blob<Dtype> diff_;
};

/**
 * @brief Computes the hinge loss for a one-of-many classification task.
 *
 * @param bottom input Blob vector (length 2)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the predictions @f$ t @f$, a Blob with values in
 *      @f$ [-\infty, +\infty] @f$ indicating the predicted score for each of
 *      the @f$ K = CHW @f$ classes. In an SVM, @f$ t @f$ is the result of
 *      taking the inner product @f$ X^T W @f$ of the D-dimensional features
 *      @f$ X \in \mathcal{R}^{D \times N} @f$ and the learned hyperplane
 *      parameters @f$ W \in \mathcal{R}^{D \times K} @f$, so a Net with just
 *      an InnerProductLayer (with num_output = D) providing predictions to a
 *      HingeLossLayer and no other learnable parameters or losses is
 *      equivalent to an SVM.
 *   -# @f$ (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 hinge loss: @f$ E =
 *        \frac{1}{N} \sum\limits_{n=1}^N \sum\limits_{k=1}^K
 *        [\max(0, 1 - \delta\{l_n = k\} t_{nk})] ^ p
 *      @f$, for the @f$ L^p @f$ norm
 *      (defaults to @f$ p = 1 @f$, the L1 norm; L2 norm, as in L2-SVM,
 *      is also available), and @f$
 *      \delta\{\mathrm{condition}\} = \left\{
 *         \begin{array}{lr}
 *            1 & \mbox{if condition} \\
 *           -1 & \mbox{otherwise}
 *         \end{array} \right.
 *      @f$
 *
 * In an SVM, @f$ t \in \mathcal{R}^{N \times K} @f$ is the result of taking
 * the inner product @f$ X^T W @f$ of the features
 * @f$ X \in \mathcal{R}^{D \times N} @f$
 * and the learned hyperplane parameters
 * @f$ W \in \mathcal{R}^{D \times K} @f$. So, a Net with just an
 * InnerProductLayer (with num_output = @f$k@f$) providing predictions to a
 * HingeLossLayer is equivalent to an SVM (assuming it has no other learned
 * outside the InnerProductLayer and no other losses outside the
 * HingeLossLayer).
 */
template <typename Dtype>
class HingeLossLayer : public LossLayer<Dtype> {
 public:
  explicit HingeLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param) {}

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_HINGE_LOSS;
  }

 protected:
  /// @copydoc HingeLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  /**
   * @brief Computes the hinge 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$t@f$; Backward computes diff
   *      @f$ \frac{\partial E}{\partial t} @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, vector<Blob<Dtype>*>* bottom);
};

/**
 * @brief A generalization of MultinomialLogisticLossLayer that takes an
 *        "information gain" (infogain) matrix specifying the "value" of all label
 *        pairs.
 *
 * Equivalent to the MultinomialLogisticLossLayer if the infogain matrix is the
 * identity.
 *
 * @param bottom input Blob vector (length 2-3)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the predictions @f$ \hat{p} @f$, a Blob with values in
 *      @f$ [0, 1] @f$ indicating the predicted probability of each of the
 *      @f$ K = CHW @f$ classes.  Each prediction vector @f$ \hat{p}_n @f$
 *      should sum to 1 as in a probability distribution: @f$
 *      \forall n \sum\limits_{k=1}^K \hat{p}_{nk} = 1 @f$.
 *   -# @f$ (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
 *   -# @f$ (1 \times 1 \times K \times K) @f$
 *      (\b optional) the infogain matrix @f$ H @f$.  This must be provided as
 *      the third bottom blob input if not provided as the infogain_mat in the
 *      InfogainLossParameter. If @f$ H = I @f$, this layer is equivalent to the
 *      MultinomialLogisticLossLayer.
 * @param top output Blob vector (length 1)
 *   -# @f$ (1 \times 1 \times 1 \times 1) @f$
 *      the computed infogain multinomial logistic loss: @f$ E =
 *        \frac{-1}{N} \sum\limits_{n=1}^N H_{l_n} \log(\hat{p}_n) =
 *        \frac{-1}{N} \sum\limits_{n=1}^N \sum\limits_{k=1}^{K} H_{l_n,k}
 *        \log(\hat{p}_{n,k})
 *      @f$, where @f$ H_{l_n} @f$ denotes row @f$l_n@f$ of @f$H@f$.
 */
template <typename Dtype>
class InfogainLossLayer : public LossLayer<Dtype> {
 public:
  explicit InfogainLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param), infogain_() {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  // InfogainLossLayer takes 2-3 bottom Blobs; if there are 3 the third should
  // be the infogain matrix.  (Otherwise the infogain matrix is loaded from a
  // file specified by LayerParameter.)
  virtual inline int ExactNumBottomBlobs() const { return -1; }
  virtual inline int MinBottomBlobs() const { return 2; }
  virtual inline int MaxBottomBlobs() const { return 3; }

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_INFOGAIN_LOSS;
  }

 protected:
  /// @copydoc InfogainLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  /**
   * @brief Computes the infogain 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. (The same applies to the infogain matrix, if
   * provided as bottom[2] rather than in the layer_param.)
   *
   * @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$.
   *      (*Assuming that this top Blob is not used as a bottom (input) by any
   *      other layer of the Net.)
   * @param propagate_down see Layer::Backward.
   *      propagate_down[1] must be false as we can't compute gradients with
   *      respect to the labels (similarly for propagate_down[2] and the
   *      infogain matrix, if provided as bottom[2])
   * @param bottom input Blob vector (length 2-3)
   *   -# @f$ (N \times C \times H \times W) @f$
   *      the predictions @f$ \hat{p} @f$; Backward computes diff
   *      @f$ \frac{\partial E}{\partial \hat{p}} @f$
   *   -# @f$ (N \times 1 \times 1 \times 1) @f$
   *      the labels -- ignored as we can't compute their error gradients
   *   -# @f$ (1 \times 1 \times K \times K) @f$
   *      (\b optional) the information gain matrix -- ignored as its error
   *      gradient computation is not implemented.
   */
  virtual void Backward_cpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom);

  Blob<Dtype> infogain_;
};

/**
 * @brief Computes the multinomial logistic loss for a one-of-many
 *        classification task, directly taking a predicted probability
 *        distribution as input.
 *
 * When predictions are not already a probability distribution, you should
 * instead use the SoftmaxWithLossLayer, which maps predictions to a
 * distribution using the SoftmaxLayer, before computing the multinomial
 * logistic loss. The SoftmaxWithLossLayer should be preferred over separate
 * SoftmaxLayer + MultinomialLogisticLossLayer
 * as its gradient computation is more numerically stable.
 *
 * @param bottom input Blob vector (length 2)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the predictions @f$ \hat{p} @f$, a Blob with values in
 *      @f$ [0, 1] @f$ indicating the predicted probability of each of the
 *      @f$ K = CHW @f$ classes.  Each prediction vector @f$ \hat{p}_n @f$
 *      should sum to 1 as in a probability distribution: @f$
 *      \forall n \sum\limits_{k=1}^K \hat{p}_{nk} = 1 @f$.
 *   -# @f$ (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 multinomial logistic loss: @f$ E =
 *        \frac{-1}{N} \sum\limits_{n=1}^N \log(\hat{p}_{n,l_n})
 *      @f$
 */
template <typename Dtype>
class MultinomialLogisticLossLayer : public LossLayer<Dtype> {
 public:
  explicit MultinomialLogisticLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_MULTINOMIAL_LOGISTIC_LOSS;
  }

 protected:
  /// @copydoc MultinomialLogisticLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  /**
   * @brief Computes the multinomial logistic 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$ \hat{p} @f$; Backward computes diff
   *      @f$ \frac{\partial E}{\partial \hat{p}} @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, vector<Blob<Dtype>*>* bottom);
};

/**
 * @brief Computes the cross-entropy (logistic) loss @f$
 *          E = \frac{-1}{n} \sum\limits_{n=1}^N \left[
 *                  p_n \log \hat{p}_n +
 *                  (1 - p_n) \log(1 - \hat{p}_n)
 *              \right]
 *        @f$, often used for predicting targets interpreted as probabilities.
 *
 * This layer is implemented rather than separate
 * SigmoidLayer + CrossEntropyLayer
 * as its gradient computation is more numerically stable.
 * At test time, this layer can be replaced simply by a SigmoidLayer.
 *
 * @param bottom input Blob vector (length 2)
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the scores @f$ x \in [-\infty, +\infty]@f$,
 *      which this layer maps to probability predictions
 *      @f$ \hat{p}_n = \sigma(x_n) \in [0, 1] @f$
 *      using the sigmoid function @f$ \sigma(.) @f$ (see SigmoidLayer).
 *   -# @f$ (N \times C \times H \times W) @f$
 *      the targets @f$ y \in [0, 1] @f$
 * @param top output Blob vector (length 1)
 *   -# @f$ (1 \times 1 \times 1 \times 1) @f$
 *      the computed cross-entropy loss: @f$
 *          E = \frac{-1}{n} \sum\limits_{n=1}^N \left[
 *                  p_n \log \hat{p}_n + (1 - p_n) \log(1 - \hat{p}_n)
 *              \right]
 *      @f$
 */
template <typename Dtype>
class SigmoidCrossEntropyLossLayer : public LossLayer<Dtype> {
 public:
  explicit SigmoidCrossEntropyLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param),
          sigmoid_layer_(new SigmoidLayer<Dtype>(param)),
          sigmoid_output_(new Blob<Dtype>()) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_SIGMOID_CROSS_ENTROPY_LOSS;
  }

 protected:
  /// @copydoc SigmoidCrossEntropyLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);
  virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  /**
   * @brief Computes the sigmoid cross-entropy loss error gradient w.r.t. the
   *        predictions.
   *
   * Gradients cannot be computed with respect to the target 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$.
   *      (*Assuming that this top Blob is not used as a bottom (input) by any
   *      other layer of the Net.)
   * @param propagate_down see Layer::Backward.
   *      propagate_down[1] must be false as gradient computation with respect
   *      to the targets is not implemented.
   * @param bottom input Blob vector (length 2)
   *   -# @f$ (N \times C \times H \times W) @f$
   *      the predictions @f$x@f$; Backward computes diff
   *      @f$ \frac{\partial E}{\partial x} =
   *          \frac{1}{n} \sum\limits_{n=1}^N (\hat{p}_n - p_n)
   *      @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, vector<Blob<Dtype>*>* bottom);
  virtual void Backward_gpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom);

  /// The internal SigmoidLayer used to map predictions to probabilities.
  shared_ptr<SigmoidLayer<Dtype> > sigmoid_layer_;
  /// sigmoid_output stores the output of the SigmoidLayer.
  shared_ptr<Blob<Dtype> > sigmoid_output_;
  /// bottom vector holder to call the underlying SigmoidLayer::Forward
  vector<Blob<Dtype>*> sigmoid_bottom_vec_;
  /// top vector holder to call the underlying SigmoidLayer::Forward
  vector<Blob<Dtype>*> sigmoid_top_vec_;
};

// Forward declare SoftmaxLayer for use in SoftmaxWithLossLayer.
template <typename Dtype> class SoftmaxLayer;

/**
 * @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$
 */
template <typename Dtype>
class SoftmaxWithLossLayer : public LossLayer<Dtype> {
 public:
  explicit SoftmaxWithLossLayer(const LayerParameter& param)
      : LossLayer<Dtype>(param),
        softmax_layer_(new SoftmaxLayer<Dtype>(param)) {}
  virtual void LayerSetUp(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);

  virtual inline LayerParameter_LayerType type() const {
    return LayerParameter_LayerType_SOFTMAX_LOSS;
  }
  virtual inline int ExactNumBottomBlobs() const { return -1; }
  virtual inline int MinBottomBlobs() const { return 2; }
  virtual inline int MaxBottomBlobs() const { return 3; }
  virtual inline int ExactNumTopBlobs() const { return -1; }
  virtual inline int MinTopBlobs() const { return 1; }
  virtual inline int MaxTopBlobs() const { return 2; }

 protected:
  /// @copydoc SoftmaxWithLossLayer
  virtual void Forward_cpu(const vector<Blob<Dtype>*>& bottom,
      vector<Blob<Dtype>*>* top);
  virtual void Forward_gpu(const vector<Blob<Dtype>*>& bottom,
      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, vector<Blob<Dtype>*>* bottom);
  virtual void Backward_gpu(const vector<Blob<Dtype>*>& top,
      const vector<bool>& propagate_down, vector<Blob<Dtype>*>* bottom);

  /// The internal SoftmaxLayer used to map predictions to a distribution.
  shared_ptr<SoftmaxLayer<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_;
};

}  // namespace caffe

#endif  // CAFFE_LOSS_LAYERS_HPP_