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CaffeConv - 卷积层
ConvLayer 是 Caffe Vision 网络层的一种. Conv 层采用一组待学习的 filters 对...
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2018/05

CaffeConv - 卷积层

ConvLayer 是 Caffe Vision 网络层的一种.
Conv 层采用一组待学习的 filters 对输入图片进行卷积操作,每一个 filter 输出一个 feature maps.

Caffe 提供的 Vision 层一般是以 images 为输入,并输出另一种 images,或者是其它类型的数据和维度,也可以是单通道的(1 Channel)的灰度图,或三通道(3 Channel) 的 RGB 彩色图片.

Vision 层一般是对输入 images 的特定区域进行特定处理,得到特定区域对应的输出区域,如,
- Convolution Layer,
- Pooling Layer,
- Spatial Pyramid Pooling (SPP),
- Crop,
- Deconvolution Layer,
- Im2Col 等.

这里主要是卷积层 ConvLayer.

1. prototxt 中的定义

  layer {
    name: "conv1"
    type: "Convolution"
    bottom: "data"
    top: "conv1"
    # filters 的学习率和衰减率
    param { 
        lr_mult: 1 
        decay_mult: 1 
    }
    # biases 的学习率和衰减率
    param { 
        lr_mult: 2 
        decay_mult: 0 
    }
    convolution_param {
      num_output: 96     # learn 96 filters
      kernel_size: 11    # each filter is 11x11
      stride: 4          # 步长 4 pixels between each filter application
      weight_filler {
        type: "gaussian" # 初始化参数 initialize the filters from a Gaussian
        std: 0.01        # distribution with stdev 0.01 (default mean: 0)
      }
      bias_filler {
        type: "constant" # initialize the biases to zero (0)
        value: 0
      }
    }
  }

2. Caffe ConvLayer 定义

Caffe 提供了 Conv 层的 CPU 和 GPU 实现:

其输入输出 data 的维度分别为:

  • Input - N × C_i × H_i × W_i

  • Output - N × C_o × H_o × W_o

    其中,

    $${ H_o = \frac{H_i + 2 * Pad_H- Kernel_H}{Stride_H + 1} }$$

    $${ W_o = \frac{W_i + 2 * Pad_W- Kernel_W}{Stride_W + 1} }$$

3. caffe.proto 中的定义

message ConvolutionParameter {
  optional uint32 num_output = 1;  // 网络层输出数
  optional bool bias_term = 2 [default = true]; // 是否有 bias 项

  // Pad, kernel size, and stride are all given as a single value for equal
  // dimensions in all spatial dimensions, or once per spatial dimension.
  repeated uint32 pad = 3; // 补零的数量; 默认不补零,即值为 0
  repeated uint32 kernel_size = 4; // kernel 大小,如 3-3x3,1-1x1,
  repeated uint32 stride = 6; // 步长; 默认值为 1

  // Factor used to dilate the kernel, (implicitly) zero-filling the resulting holes.
  repeated uint32 dilation = 18; // The dilation; defaults to 1 用于带孔卷积(dilation)

  // For 2D convolution only, the *_h and *_w versions may also be used to
  // specify both spatial dimensions.
  optional uint32 pad_h = 9 [default = 0]; // The padding height (2D only)
  optional uint32 pad_w = 10 [default = 0]; // The padding width (2D only)
  optional uint32 kernel_h = 11; // The kernel height (2D only)
  optional uint32 kernel_w = 12; // The kernel width (2D only)
  optional uint32 stride_h = 13; // The stride height (2D only)
  optional uint32 stride_w = 14; // The stride width (2D only)

  // 将输入通道和输出通道数分组
  optional uint32 group = 5 [default = 1]; // The group size for group conv

  optional FillerParameter weight_filler = 7; // The filler for the weight
  optional FillerParameter bias_filler = 8; // The filler for the bias
  enum Engine {
    DEFAULT = 0;
    CAFFE = 1;
    CUDNN = 2;
  }
  optional Engine engine = 15 [default = DEFAULT];

  // The axis to interpret as "channels" when performing convolution.
  // Preceding dimensions are treated as independent inputs;
  // succeeding dimensions are treated as "spatial".
  // With (N, C, H, W) inputs, and axis == 1 (the default), we perform
  // N independent 2D convolutions, sliding C-channel (or (C/g)-channels, for
  // groups g>1) filters across the spatial axes (H, W) of the input.
  // With (N, C, D, H, W) inputs, and axis == 1, we perform
  // N independent 3D convolutions, sliding (C/g)-channels
  // filters across the spatial axes (D, H, W) of the input.
  optional int32 axis = 16 [default = 1];

  // Whether to force use of the general ND convolution, even if a specific
  // implementation for blobs of the appropriate number of spatial dimensions
  // is available. (Currently, there is only a 2D-specific convolution
  // implementation; for input blobs with num_axes != 2, this option is
  // ignored and the ND implementation will be used.)
  optional bool force_nd_im2col = 17 [default = false];
}

4. ConvLayer 涉及的参数说明

Conv 层在 Caffe 定义中涉及的参数:convolution_param.

  • num_output(C_o) - filters 数
  • kernel_size - 指定的每个 filter 的 height 和 width,也可以定义为 kernel_hkernel_w
  • weight_filler - 权重初始化

    • type: 'constant' value: 0 默认值
    • type: "gaussian"
    • type: "positive_unitball"
    • type: "uniform"
    • type: "msra"
    • type: "bilinear"
  • bias_term - 可选参数(默认True),指定是否学习 bias,在 filter 输出上添加额外的 biases.
  • pad - 补零,可选参数(默认为 0),也可以是 pad_hpad_w.
  • stride - 步长,可选参数(默认为 1),也可以是 stride_hstride_w.
  • group - 分组,可选参数(默认为 1),如果 group>1,则限制每个 filter 的连续性,分组到输入的一个子集subset 中. 即:
    输入和输出通道被分为 group 个组,第 i 个输出通道组仅与第 i 个输入通道组相连接.

4.1 group 参数

根据 Caffe 官方给出的说明:

group (g) [default 1]: If g > 1, we restrict the connectivity of each filter to a subset of the input. Specifically, the input and output channels are separated into g groups, and the i-th output group channels will be only connected to the i-th input group channels.

group - 分组,可选参数(默认为 1),如果 group>1,则限制每个 filter 的连续性,分组到输入的一个子集subset 中. 即:

输入和输出通道被分为 group 个组,第 i 个输出通道组仅与第 i 个输入通道组相连接.

例如:

假设卷积层输入数据大小为 128×32×100×100,图像数据尺寸为 100×100,通道数为 32,假设卷积 filters 为 1024 ×3 ×3,
在 group 默认为 1 时,即为常见的全连接的卷积层.
当 group 大于 1 时,如 group=2,则卷积层输入 32 通道会被分组为 2 个 16 通道,而输出的 1024 个通道会被分组为 2 个 512 通道. 第一个 512 通道仅与对应的第一个 16 通道进行卷积操作,而第二个 512 通道仅与对应的第二个 16 通道进行卷积操作.

在极端情况下,如,输入输出通道数相同,如都为 32 个通道,group 值也为 32,则,每个输出卷积核 fliter 仅与其对应的输入通道进行卷积操作.

group conv

ResNext与Xception——对模型的新思考

ResNeXt - Aggregated Residual Transformations for Deep Neural Networks 论文有关于 Group Convolution 的介绍.

论文阅读理解 - ResNeXt - Aggregated Residual Transformations for DNN

4.2 dilation 参数

[论文阅读理解 - Dilated Convolution]

5. gif 图示

Github - conv_arithmetic 给出的动图展示效果很不错.

以下图中,蓝色 maps 是输入,青色 maps 是输出.

Blue maps are inputs, and cyan maps are outputs.
  • No padding, no strides

  • Arbitrary padding, no strides

  • Half padding, no strides

  • Full padding, no strides

  • No padding, strides

  • Padding, strides

  • Padding, strides (odd)

  • Dilated convolution - No padding, no stride, dilation

Last modification:October 10th, 2018 at 04:00 pm

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