caffe中BatchNorm层和Scale层实现批量归一化（batch-normalization）注意事项

caffe中实现批量归一化（batch-normalization）需要借助两个层：BatchNorm 和 Scale
BatchNorm实现的是归一化
Scale实现的是平移和缩放
在实现的时候要注意的是由于Scale需要实现平移功能，所以要把bias_term项设为true
另外，实现BatchNorm的时候需要注意一下参数use_global_stats，在训练的时候设为false，在测试的时候设为true
use_global_stats = false 时采用滑动平均计算新的均值和方差
use_global_stats = true 时会强制使用模型中存储的BatchNorm层均值与方差参数
具体训练实现过程为（conv-batchnorm-scale-relu）:

layer {
  bottom: "data"
  top: "conv1_1"
  name: "conv1_1"
  type: "Convolution"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  convolution_param {
    weight_filler {
      type: "xavier"
    }
    bias_filler {
      type: "constant"
    }
    num_output: 64
    pad: 1
    kernel_size: 3
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "bn_conv1_1"
  type: "BatchNorm"
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
  batch_norm_param {
    use_global_stats: false
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "scale_conv1_1"
  type: "Scale"
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  scale_param {
    bias_term: true
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "relu1_1"
  type: "ReLU"
}

具体测试实现过程为（conv-batchnorm-scale-relu）(把use_global_stats由false设为true):

layer {
  bottom: "data"
  top: "conv1_1"
  name: "conv1_1"
  type: "Convolution"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  convolution_param {
    weight_filler {
      type: "xavier"
    }
    bias_filler {
      type: "constant"
    }
    num_output: 64
    pad: 1
    kernel_size: 3
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "bn_conv1_1"
  type: "BatchNorm"
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
  batch_norm_param {
    use_global_stats: true
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "scale_conv1_1"
  type: "Scale"
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  scale_param {
    bias_term: true
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "relu1_1"
  type: "ReLU"
}

其实也没必要这么麻烦，因为在BathNorm层的源码中设定了如果use_global_stats缺省，那么在训练时为false，测试时为true，源代码为（caffe/src/caffe/layers/batch_norm_layer.cpp）第14行：

use_global_stats_ = this->phase_ == TEST;

在测试时为1，训练时为0，这样的话我们在代码里就不用设定use_global_stats的值了，这样上面的代码我们可以简化为（训练和测试时都一样）：

layer {
  bottom: "data"
  top: "conv1_1"
  name: "conv1_1"
  type: "Convolution"
  param {
    lr_mult: 1
    decay_mult: 1
  }
  param {
    lr_mult: 2
    decay_mult: 0
  }
  convolution_param {
    weight_filler {
      type: "xavier"
    }
    bias_filler {
      type: "constant"
    }
    num_output: 64
    pad: 1
    kernel_size: 3
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "bn_conv1_1"
  type: "BatchNorm"
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
  param {
    lr_mult: 0
    decay_mult: 0
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "scale_conv1_1"
  type: "Scale"
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  param {
    lr_mult: 0.1
    decay_mult: 0
  }
  scale_param {
    bias_term: true
  }
}
layer {
  bottom: "conv1_1"
  top: "conv1_1"
  name: "relu1_1"
  type: "ReLU"
}

另外可以看到BatchNorm层学习率都设为0，具体原因或者需不需要设为0验证了再回来补充