weight decay 和正则化caffe

正则化是为了防止过拟合,因为正则化能降低权重

caffe默认L2正则化

代码讲解的地址:http://alanse7en.github.io/caffedai-ma-jie-xi-4/

重要的一个回答:https://stats.stackexchange.com/questions/29130/difference-between-neural-net-weight-decay-and-learning-rate

按照这个答主的说法,正则化损失函数,正则化之后的损失函数如下:

这个损失函数求偏导就变成了:加号前面是原始损失函数求偏导,加号后面就变成了 *w,这样梯度更新就变了下式:

$w_{i} \leftarrow w_{i} - η \frac{\partial E}{\partial w_{i}} - η λ w_{i} .$

L2正则化的梯度更新公式,与没有加regulization正则化相比,每个参数更新的时候多剪了正则化的值,相当于让每个参数多剪了weight_decay*w原本的值

根据caffe中的代码也可以推断出L1正则化的公式:

把替换成*w的绝对值

所以求偏导的时候就变成了,当w大于0为,当w小于0为-

void SGDSolver<Dtype>::Regularize(int param_id) {
  const vector<shared_ptr<Blob<Dtype> > >& net_params = this->net_->params();
  const vector<float>& net_params_weight_decay =
      this->net_->params_weight_decay();
  Dtype weight_decay = this->param_.weight_decay();
  string regularization_type = this->param_.regularization_type();
  Dtype local_decay = weight_decay * net_params_weight_decay[param_id];
  switch (Caffe::mode()) {
  case Caffe::CPU: {
    if (local_decay) {
      if (regularization_type == "L2") {
        // add weight decay
        caffe_axpy(net_params[param_id]->count(),
            local_decay,
            net_params[param_id]->cpu_data(),
            net_params[param_id]->mutable_cpu_diff());
      } else if (regularization_type == "L1") {
        caffe_cpu_sign(net_params[param_id]->count(),
            net_params[param_id]->cpu_data(),
            temp_[param_id]->mutable_cpu_data());
        caffe_axpy(net_params[param_id]->count(),
            local_decay,
            temp_[param_id]->cpu_data(),
            net_params[param_id]->mutable_cpu_diff());
      } else {
        LOG(FATAL) << "Unknown regularization type: " << regularization_type;
      }    
    }    
    break;
  }

caffe_axpy的实现在util下的math_functions.cpp里,实现的功能是y = a*x + y,也就是相当于把梯度更新值和weight_decay*w加起来了

caffe_sign的实现在util下的math_functions.hpp里,通过一个宏定义生成了caffe_cpu_sign这个函数,函数实现的功能是当value>0返回1,<0返回-1

weight decay 和正则化caffe

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