梳理caffe代码adadelta、adagrad、adam、nesterov、rmsprop_solver（十六）

有一篇不错的blog描述梯度下降的方法。我前面有介绍solver的优化方法。

这节是新版caffe solver的5个求解方法：

adagrad_solver.cpp：

#include <vector>

#include "caffe/sgd_solvers.hpp"

namespace caffe {

#ifndef CPU_ONLY
template <typename Dtype>
void adagrad_update_gpu(int N, Dtype* g, Dtype* h, Dtype delta,
    Dtype local_rate);
#endif

template <typename Dtype>
void AdaGradSolver<Dtype>::ComputeUpdateValue(int param_id, Dtype rate) {
  CHECK(Caffe::root_solver());
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  const vector<float>& net_params_lr = this->net_->params_lr();
  Dtype delta = this->param_.delta();
  Dtype local_rate = rate * net_params_lr[param_id];
//求解公式是按照math_functions里面的函数进行实现的，新版caffe和旧版的caffe有点区别，里面函数没什么太大区别
  switch (Caffe::mode()) {
  case Caffe::CPU: {
    // compute square of gradient in update
    caffe_powx(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(), Dtype(2),
        this->update_[param_id]->mutable_cpu_data());//update[i] =cpu_diff[i] ^ 2

    // update history
    caffe_add(net_params[param_id]->count(),
        this->update_[param_id]->cpu_data(),
        this->history_[param_id]->cpu_data(),
        this->history_[param_id]->mutable_cpu_data());//history[i] = history[i] + update[i]

    // prepare update
    caffe_powx(net_params[param_id]->count(),
              this->history_[param_id]->cpu_data(), Dtype(0.5),
              this->update_[param_id]->mutable_cpu_data());//update[i]=history[i]开根号

    caffe_add_scalar(net_params[param_id]->count(),
              delta, this->update_[param_id]->mutable_cpu_data());//update[i] += delta

    caffe_div(net_params[param_id]->count(),
              net_params[param_id]->cpu_diff(),
              this->update_[param_id]->cpu_data(),
              this->update_[param_id]->mutable_cpu_data());//update[i] = cpu_diff[i] \ update[i]

    // scale and copy
//Y= alpha*X+beta*Y   cpu_diff[i]=local_rate*update[i]
    caffe_cpu_axpby(net_params[param_id]->count(), local_rate,
        this->update_[param_id]->cpu_data(), Dtype(0),
        net_params[param_id]->mutable_cpu_diff());
    break;
  }
  case Caffe::GPU: {
#ifndef CPU_ONLY
    adagrad_update_gpu(net_params[param_id]->count(),
        net_params[param_id]->mutable_gpu_diff(),
        this->history_[param_id]->mutable_gpu_data(), delta, local_rate);
#else
    NO_GPU;
#endif
    break;
  }
  default:
    LOG(FATAL) << "Unknown caffe mode: " << Caffe::mode();
  }
}

INSTANTIATE_CLASS(AdaGradSolver);
REGISTER_SOLVER_CLASS(AdaGrad);

}  // namespace caffe

adadelta_solver.cpp：

#include <vector>

#include "caffe/sgd_solvers.hpp"

namespace caffe {

template <typename Dtype>
void AdaDeltaSolver<Dtype>::AdaDeltaPreSolve() {
  // Add the extra history entries for AdaDelta after those from
  // SGDSolver::PreSolve
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  for (int i = 0; i < net_params.size(); ++i) {
        const vector<int>& shape = net_params[i]->shape();
        this->history_.push_back(
                shared_ptr<Blob<Dtype> >(new Blob<Dtype>(shape)));
  }
}

#ifndef CPU_ONLY
template <typename Dtype>
void adadelta_update_gpu(int N, Dtype* g, Dtype* h, Dtype* h2, Dtype momentum,
    Dtype delta, Dtype local_rate);
#endif

template <typename Dtype>
void AdaDeltaSolver<Dtype>::ComputeUpdateValue(int param_id, Dtype rate) {
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  const vector<float>& net_params_lr = this->net_->params_lr();
  Dtype delta = this->param_.delta();
  Dtype momentum = this->param_.momentum();
  Dtype local_rate = rate * net_params_lr[param_id];
  size_t update_history_offset = net_params.size();
  switch (Caffe::mode()) {
  case Caffe::CPU: {
    caffe_powx(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(), Dtype(2),
        this->update_[param_id]->mutable_cpu_data());//update[i] =cpu_diff[i] ^ 2

    caffe_cpu_axpby(net_params[param_id]->count(), Dtype(1) - momentum,
        this->update_[param_id]->cpu_data(), momentum,
        this->history_[param_id]->mutable_cpu_data());//history[i]=(1 - momentum)*update[i]+momentum*history[i]

    caffe_set(net_params[param_id]->count(), delta,
        this->temp_[param_id]->mutable_cpu_data());//temp=delta

    caffe_add(net_params[param_id]->count(),
        this->temp_[param_id]->cpu_data(),
        this->history_[update_history_offset + param_id]->cpu_data(),
        this->update_[param_id]->mutable_cpu_data());//update[i]=temp+history[i]

    caffe_add(net_params[param_id]->count(),
        this->temp_[param_id]->cpu_data(),
        this->history_[param_id]->cpu_data(),
        this->temp_[param_id]->mutable_cpu_data());//temp=temp+history[i]

    caffe_div(net_params[param_id]->count(),
        this->update_[param_id]->cpu_data(),
        this->temp_[param_id]->cpu_data(),
        this->update_[param_id]->mutable_cpu_data());//update[i]=update[i]/temp

 
    caffe_powx(net_params[param_id]->count(),
        this->update_[param_id]->cpu_data(), Dtype(0.5),
        this->update_[param_id]->mutable_cpu_data());//update[i]=update[i]的开根号

    caffe_mul(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(),
        this->update_[param_id]->cpu_data(),
        net_params[param_id]->mutable_cpu_diff());//cpu_diff[i]=cpu_diff[i]*update[i]

    caffe_powx(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(), Dtype(2),
        this->update_[param_id]->mutable_cpu_data());//update[i]=cpu_diff[i]^ 2

    //history[i]=(1 - momentum)*update[i]+momentum*history[i]
    caffe_cpu_axpby(net_params[param_id]->count(), Dtype(1) - momentum,
        this->update_[param_id]->cpu_data(), momentum,
        this->history_[update_history_offset + param_id]->mutable_cpu_data());

    caffe_cpu_scale(net_params[param_id]->count(), local_rate,
        net_params[param_id]->cpu_diff(),
        net_params[param_id]->mutable_cpu_diff());//cpu_diff[i]=local_rate*cpu_diff[i]
    break;
  }
  case Caffe::GPU: {
#ifndef CPU_ONLY
    adadelta_update_gpu(net_params[param_id]->count(),
        net_params[param_id]->mutable_gpu_diff(),
        this->history_[param_id]->mutable_gpu_data(),
        this->history_[update_history_offset + param_id]->mutable_gpu_data(),
        momentum, delta, local_rate);
#else
    NO_GPU;
#endif
    break;
  }
  default:
    LOG(FATAL) << "Unknown caffe mode: " << Caffe::mode();
  }
}

INSTANTIATE_CLASS(AdaDeltaSolver);
REGISTER_SOLVER_CLASS(AdaDelta);

}  // namespace caffe

adam_solver.cpp:

按照上图的实现：

#include <vector>

#include "caffe/sgd_solvers.hpp"

namespace caffe {

template <typename Dtype>
void AdamSolver<Dtype>::AdamPreSolve() {
  // Add the extra history entries for Adam after those from
  // SGDSolver::PreSolve
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  for (int i = 0; i < net_params.size(); ++i) {
    const vector<int>& shape = net_params[i]->shape();
    this->history_.push_back(
            shared_ptr<Blob<Dtype> >(new Blob<Dtype>(shape)));
  }
}

#ifndef CPU_ONLY
template <typename Dtype>
void adam_update_gpu(int N, Dtype* g, Dtype* m, Dtype* v, Dtype beta1,
    Dtype beta2, Dtype eps_hat, Dtype corrected_local_rate);
#endif

template <typename Dtype>
void AdamSolver<Dtype>::ComputeUpdateValue(int param_id, Dtype rate) {
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  const vector<float>& net_params_lr = this->net_->params_lr();
  Dtype local_rate = rate * net_params_lr[param_id];
  const Dtype beta1 = this->param_.momentum();
  const Dtype beta2 = this->param_.momentum2();

  // we create aliases for convenience
  size_t update_history_offset = net_params.size();
  Blob<Dtype>* val_m = this->history_[param_id].get();
  Blob<Dtype>* val_v = this->history_[param_id + update_history_offset].get();
  Blob<Dtype>* val_t = this->temp_[param_id].get();

  const int t = this->iter_ + 1;
  const Dtype correction = std::sqrt(Dtype(1) - pow(beta2, t))
      (Dtype(1.) - pow(beta1, t));//correction=()^0.5 *();
  const int N = net_params[param_id]->count();
  const Dtype eps_hat = this->param_.delta();

  switch (Caffe::mode()) {
    case Caffe::CPU: {
    // update m <- \beta_1 m_{t-1} + (1-\beta_1)g_t
    caffe_cpu_axpby(N, Dtype(1)-beta1,
        net_params[param_id]->cpu_diff(), beta1,
        val_m->mutable_cpu_data());

    // update v <- \beta_2 m_{t-1} + (1-\beta_2)g_t^2
    caffe_mul(N,
        net_params[param_id]->cpu_diff(),
        net_params[param_id]->cpu_diff(),
    val_t->mutable_cpu_data());
    caffe_cpu_axpby(N, Dtype(1)-beta2,
        val_t->cpu_data(), beta2,
        val_v->mutable_cpu_data());

    // set update
    //t=v^0.5
    caffe_powx(N,
        val_v->cpu_data(), Dtype(0.5),
        val_t->mutable_cpu_data());
    //t=t+eps
    caffe_add_scalar(N, eps_hat, val_t->mutable_cpu_data());
    //  t=m/t
    caffe_div(N,
        val_m->cpu_data(),
        val_t->cpu_data(),
        val_t->mutable_cpu_data());
    //cpu_diff[i]=local_rate*correction*t
    caffe_cpu_scale(N, local_rate*correction,
        val_t->cpu_data(),
        net_params[param_id]->mutable_cpu_diff());
    break;
  }
  case Caffe::GPU: {
#ifndef CPU_ONLY
    adam_update_gpu(N, net_params[param_id]->mutable_gpu_diff(),
        val_m->mutable_gpu_data(), val_v->mutable_gpu_data(), beta1, beta2,
        eps_hat, local_rate*correction);
#else
    NO_GPU;
#endif
    break;
  }
  default:
    LOG(FATAL) << "Unknown caffe mode: " << Caffe::mode();
  }
}

INSTANTIATE_CLASS(AdamSolver);
REGISTER_SOLVER_CLASS(Adam);

}  // namespace caffe

nesterov_solver.cpp：

这个求解方法可以参考知乎上的图解：here

实现:

#include <vector>

#include "caffe/sgd_solvers.hpp"

namespace caffe {

#ifndef CPU_ONLY
template <typename Dtype>
void nesterov_update_gpu(int N, Dtype* g, Dtype* h, Dtype momentum,
    Dtype local_rate);
#endif

template <typename Dtype>
void NesterovSolver<Dtype>::ComputeUpdateValue(int param_id, Dtype rate) {
  CHECK(Caffe::root_solver());
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  const vector<float>& net_params_lr = this->net_->params_lr();
  Dtype momentum = this->param_.momentum();
  Dtype local_rate = rate * net_params_lr[param_id];
  switch (Caffe::mode()) {
  case Caffe::CPU: {
    // save history momentum for stepping back
    //如果梯度求解时出现迭代倒退时需要将当前动量保存下来，一起不是很理解动量，其实
    就是每次梯度下降的时候往前迭代需要一定的动量(按照物理理解)
    caffe_copy(net_params[param_id]->count(),
        this->history_[param_id]->cpu_data(),
        this->update_[param_id]->mutable_cpu_data());

    // update history
    //这个算法也不是很复杂，所以代码比较简单点
    //history=local_rate*diff+momentum*history
    caffe_cpu_axpby(net_params[param_id]->count(), local_rate,
              net_params[param_id]->cpu_diff(), momentum,
              this->history_[param_id]->mutable_cpu_data());

    // compute update: step back then over step
    //update=(1+ momentum)*history-momentum*update
    caffe_cpu_axpby(net_params[param_id]->count(), Dtype(1) + momentum,
        this->history_[param_id]->cpu_data(), -momentum,
        this->update_[param_id]->mutable_cpu_data());

    // copy
    caffe_copy(net_params[param_id]->count(),
        this->update_[param_id]->cpu_data(),
        net_params[param_id]->mutable_cpu_diff());
    break;
  }
  case Caffe::GPU: {
#ifndef CPU_ONLY
    nesterov_update_gpu(net_params[param_id]->count(),
        net_params[param_id]->mutable_gpu_diff(),
        this->history_[param_id]->mutable_gpu_data(),
        momentum, local_rate);
#else
    NO_GPU;
#endif
    break;
  }
  default:
    LOG(FATAL) << "Unknown caffe mode: " << Caffe::mode();
  }
}

INSTANTIATE_CLASS(NesterovSolver);
REGISTER_SOLVER_CLASS(Nesterov);

}  // namespace caffe

rmsprop_solver.cpp:

这里有一个官网的介绍:here

rmsprop的算法推导：here

实现：

#include <vector>

#include "caffe/sgd_solvers.hpp"

namespace caffe {

#ifndef CPU_ONLY
template <typename Dtype>
void rmsprop_update_gpu(int N, Dtype* g, Dtype* h, Dtype rms_decay,
    Dtype delta, Dtype local_rate);
#endif

template <typename Dtype>
void RMSPropSolver<Dtype>::ComputeUpdateValue(int param_id, Dtype rate) {
  const vector<Blob<Dtype>*>& net_params = this->net_->learnable_params();
  const vector<float>& net_params_lr = this->net_->params_lr();

  // get the learning rate
  Dtype delta = this->param_.delta();
  Dtype rms_decay = this->param_.rms_decay();
  Dtype local_rate = rate * net_params_lr[param_id];

  switch (Caffe::mode()) {
  case Caffe::CPU:
    // compute square of gradient in update
    //update=diff^2
    caffe_powx(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(), Dtype(2),
        this->update_[param_id]->mutable_cpu_data());

    // update history
    //history=(1-rms_decay)*update+rms_decay*history
    caffe_cpu_axpby(net_params[param_id] -> count(),
        Dtype(1-rms_decay), this->update_[param_id]->cpu_data(),
        rms_decay, this->history_[param_id]-> mutable_cpu_data());

    // prepare update
    //update=history^0.5
    caffe_powx(net_params[param_id]->count(),
        this->history_[param_id]->cpu_data(), Dtype(0.5),
        this->update_[param_id]->mutable_cpu_data());
    //update=delta*update
    caffe_add_scalar(net_params[param_id]->count(),
        delta, this->update_[param_id]->mutable_cpu_data());
    // update=diff/update
    caffe_div(net_params[param_id]->count(),
        net_params[param_id]->cpu_diff(), this->update_[param_id]->cpu_data(),
        this->update_[param_id]->mutable_cpu_data());

    // scale and copy
    //diff=local_rate*update
    caffe_cpu_axpby(net_params[param_id]->count(), local_rate,
        this->update_[param_id]->cpu_data(), Dtype(0),
        net_params[param_id]->mutable_cpu_diff());
    break;
  case Caffe::GPU:
#ifndef CPU_ONLY
    rmsprop_update_gpu(net_params[param_id]->count(),
        net_params[param_id]->mutable_gpu_diff(),
        this->history_[param_id]->mutable_gpu_data(),
        rms_decay, delta, local_rate);
#else
    NO_GPU;
#endif
    break;
  default:
    LOG(FATAL) << "Unknown caffe mode: " << Caffe::mode();
  }
}

INSTANTIATE_CLASS(RMSPropSolver);
REGISTER_SOLVER_CLASS(RMSProp);

}  // namespace caffe