转caffe scale layer

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Scale Layer是输入进行缩放和平移，常常出现在BatchNorm归一化后，Caffe中常用BatchNorm+Scale实现归一化操作（等同Pytorch中BatchNorm）

首先我们先看一下 ScaleParameter

message ScaleParameter {
	  // The first axis of bottom[0] (the first input Blob) along which to apply
	  // bottom[1] (the second input Blob).  May be negative to index from the end
	  // (e.g., -1 for the last axis).
	  // 根据 bottom[0] 指定 bottom[1] 的形状
	  // For example, if bottom[0] is 4D with shape 100x3x40x60, the output
	  // top[0] will have the same shape, and bottom[1] may have any of the
	  // following shapes (for the given value of axis):
	  //    (axis == 0 == -4) 100; 100x3; 100x3x40; 100x3x40x60
	  //    (axis == 1 == -3)          3;     3x40;     3x40x60
	  //    (axis == 2 == -2)                   40;       40x60
	  //    (axis == 3 == -1)                                60
	  // Furthermore, bottom[1] may have the empty shape (regardless of the value of
	  // "axis") -- a scalar multiplier.
	  // 例如，如果 bottom[0] 的 shape 为 100x3x40x60，则 top[0] 输出相同的 shape；
	  // bottom[1] 可以包含上面 shapes 中的任一种(对于给定 axis 值). 
	  // 而且，bottom[1] 可以是 empty shape 的，没有任何的 axis 值，只是一个标量的乘子.
	  optional int32 axis = 1 [default = 1];
  // (num_axes is ignored unless just one bottom is given and the scale is
  // a learned parameter of the layer.  Otherwise, num_axes is determined by the
  // number of axes by the second bottom.)
  // (忽略 num_axes 参数，除非只给定一个 bottom 及 scale 是网络层的一个学习到的参数. 
  // 否则，num_axes 是由第二个 bottom 的数量来决定的.)
  // The number of axes of the input (bottom[0]) covered by the scale
  // parameter, or -1 to cover all axes of bottom[0] starting from `axis`.
  // Set num_axes := 0, to multiply with a zero-axis Blob: a scalar.
  // bottom[0] 的 num_axes 是由 scale 参数覆盖的；
  optional int32 num_axes = 2 [default = 1];

  // (filler is ignored unless just one bottom is given and the scale is
  // a learned parameter of the layer.)
  // (忽略 filler 参数，除非只给定一个 bottom 及 scale 是网络层的一个学习到的参数.
  // The initialization for the learned scale parameter.
  // scale 参数学习的初始化
  // Default is the unit (1) initialization, resulting in the ScaleLayer
  // initially performing the identity operation.
  // 默认是单位初始化，使 Scale 层初始进行单位操作.
  optional FillerParameter filler = 3;

  // Whether to also learn a bias (equivalent to a ScaleLayer+BiasLayer, but
  // may be more efficient).  Initialized with bias_filler (defaults to 0).
  // 是否学习 bias，等价于 ScaleLayer+BiasLayer，只不过效率更高
  // 采用 bias_filler 进行初始化. 默认为 0.
  optional bool bias_term = 4 [default = false];
  optional FillerParameter bias_filler = 5;

}
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Scale layer 在prototxt里面的书写：

layer {
 	 name: "scale_conv1"
     type: "Scale"
	 bottom: "conv1"
     top: "conv1"
 scale_param {
    bias_term: true

}
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例如在MobileNet中：

layer {
	  name: "conv6_4/scale"
	  type: "Scale"
	  bottom: "conv6_4/bn"
	  top: "conv6_4/bn"
	  param {
	    lr_mult: 1
	    decay_mult: 0
	  }
	  param {
	    lr_mult: 1
	    decay_mult: 0
	  }
	  scale_param {
	    bias_term: true
	  }
}
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