Theano conv2d的border_mode

文档是这么写的:

    border_mode: str, int or tuple of two int    Either of the following:        ``'valid'``: apply filter wherever it completely overlaps with the    input. Generates output of shape: input shape - filter shape + 1    ``'full'``: apply filter wherever it partly overlaps with the input.    Generates output of shape: input shape + filter shape - 1    ``'half'``: pad input with a symmetric border of ``filter rows // 2``    rows and ``filter columns // 2`` columns, then perform a valid    convolution. For filters with an odd number of rows and columns, this    leads to the output shape being equal to the input shape.    ``int``: pad input with a symmetric border of zeros of the given    width, then perform a valid convolution.    ``(int1, int2)``: pad input with a symmetric border of ``int1`` rows    and ``int2`` columns, then perform a valid convolution.

首先, 这几种模式对应的padding都是zero-padding.

• int, (int1, int2): 它们最容易理解的: 手动指定行和列方向上的padding数量.
• valid: 其实就是不padding, 即\(border\_mode = (0, 0)\)
  
• full: 它的padding为:\(border\_mode=(k_h-1, k_w-1)\), 其中\(k\)为kernel的行数(高)与列数(宽). 若\(k_h=k_w=3\), conv操作会全方位覆盖所有的\((3, 3)\), \((3, 1)\), \((2,1)\), \((1, 1)\)区域. 这也是它叫full的原因.
  
• half: \(border\_mode = (\frac {(k-1)}{2}, \frac{k-1}{2})\). 注意, \(k\)一般都是奇数. full模式的padding得到的conv输出比输入要大, 而half的输出形状与输入相同. 也有叫same的.
  

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• 原始图片来源: https://github.com/vdumoulin/conv_arithmetic
• Reference: http://deeplearning.net/software/theano_versions/dev/tutorial/conv_arithmetic.html