pytorch中的卷积和池化计算方式详解

TensorFlow里面的padding只有两个选项也就是valid和same

pytorch里面的padding么有这两个选项，它是数字0,1,2,3等等，默认是0

所以输出的h和w的计算方式也是稍微有一点点不同的：tf中的输出大小是和原来的大小成倍数关系，不能任意的输出大小；而nn输出大小可以通过padding进行改变

nn里面的卷积操作或者是池化操作的H和W部分都是一样的计算公式：H和W的计算

class torch.nn.MaxPool2d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False):
"""
Parameters: 
  kernel_size ? the size of the window to take a max over
  stride ? the stride of the window. 默认值是kernel_size
  padding ? implicit zero padding to be added on both side,默认值是0
  dilation ? a parameter that controls the stride of elements in the window，默认值是1
  return_indices ? if True, will return the max indices along with the outputs. Useful when Unpooling later
  ceil_mode ? when True, will use ceil instead of floor to compute the output shape，向上取整和向下取整，默认是向下取整
"""

不一样的地方在于：第一点，步长stride默认值，上面默认和设定的kernel_size一样，下面默认是1；第二点，输出通道的不一样，上面的输出通道和输入通道是一样的也就是没有改变特征图的数目，下面改变特征图的数目为out_channels

class torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True):
    pass
"""
Parameters: 
  in_channels (int) ? Number of channels in the input image
  out_channels (int) ? Number of channels produced by the convolution
  kernel_size (int or tuple) ? Size of the convolving kernel
  stride (int or tuple, optional) ? Stride of the convolution. Default: 1,默认是1
  padding (int or tuple, optional) ? Zero-padding added to both sides of the input. Default: 0
  dilation (int or tuple, optional) ? Spacing between kernel elements. Default: 1
  groups (int, optional) ? Number of blocked connections from input channels to output channels. Default: 1
  bias (bool, optional) ? If True, adds a learnable bias to the output. Default: True
"""

第三点不一样是卷积有一个参数groups,将特征图分开给不同的卷积进行操作然后再整合到一起，xception就是利用这一个。

"""
At groups=1, all inputs are convolved to all outputs.
At groups=2, the operation becomes equivalent to having two conv layers side by side, each seeing half the input channels, and producing half the output channels, and both subsequently concatenated.
At groups= in_channels, each input channel is convolved with its own set of filters (of size ⌊out_channelsin_channels⌋
).
"""

pytorch AvgPool2d函数

class torch.nn.AvgPool2d(kernel_size, stride=None, padding=0, 
             ceil_mode=False, count_include_pad=True):
  pass
"""
kernel_size: the size of the window
stride: the stride of the window. Default value is :attr:`kernel_size`
padding: implicit zero padding to be added on both sides
ceil_mode: when True, will use `ceil` instead of `floor` to compute the output shape
count_include_pad: when True, will include the zero-padding in the averaging calculation
"""

shape的计算公式，在（h,w)位置处的输出值的计算。

pytorch中的F.avg_pool1d（）平均池化操作作用于一维，input 的维度是三维比如［２,２,７］。F.avg_pool1d（）中核ｓｉｚｅ是３，步长是２表示每三个数取平均，每隔两个数取一次．比如[1,3,3,4,5,6,7]安照3个数取均值，两步取一次，那么结果就是[ 2.3333 ,4 ,6 ]，也就是核是一维的，也只作用于一个维度。按照池化操作计算公式input size为[2,2,7],kernel size为3，步长为2，则输出维度计算（7-3）/2+1=3所以输出维度是[2,2,3]，这与输出结果是一致的。

pytorch中的F.avg_pool2d（），input 是维度是４维如［２，２，４，４］，表示这里批量数是２也就是两张图像，这里通道数量是２，图像是size 是４＊４的．核size是（２，２），步长是（２，２）表示被核覆盖的数取平均，横向纵向的步长都是２．那么核是二维的，所以取均值时也是覆盖二维取的。输出中第一个1.5的计算是：(1+2+1+2)/4=1.5.表示第一张图像左上角的四个像素点的均值。按照池化操作计算公式input size为[2,2,4,4],kernel size为2*2，步长为2，则输出维度计算（4-2）/2+1=2所以输出维度是[2,2,2,2]，这与输出结果是一致的。

Conv3d函数

class torch.nn.Conv3d(in_channels, out_channels, kernel_size, stride=1,
           padding=0, dilation=1, groups=1, bias=True):
  pass
"""
in_channels (int): Number of channels in the input image
out_channels (int): Number of channels produced by the convolution
kernel_size (int or tuple): Size of the convolving kernel
stride (int or tuple, optional): Stride of the convolution. Default: 1
padding (int or tuple, optional): Zero-padding added to all three sides of the input. Default: 0
dilation (int or tuple, optional): Spacing between kernel elements. Default: 1
groups (int, optional): Number of blocked connections from input channels to output channels. Default: 1
bias (bool, optional): If ``True``, adds a learnable bias to the output. Default: ``True``
Shape:
    - Input: :math:`(N, C_{in}, D_{in}, H_{in}, W_{in})`
    - Output: :math:`(N, C_{out}, D_{out}, H_{out}, W_{out})`
"""
  C_out = out_channels

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