pooling(data=None, kernel=None, stride=None, pad=None, pool_type='max', pooling_convention='valid', global_pool=False, cudnn_off=False, p_value=None, count_include_pad=None, layout=None, **kwargs)

Performs pooling on the input.

The shapes for 1-D pooling are

  • data and out: (batch_size, channel, width) (NCW layout) or (batch_size, width, channel) (NWC layout),

The shapes for 2-D pooling are

  • data and out: (batch_size, channel, height, width) (NCHW layout) or (batch_size, height, width, channel) (NHWC layout),

    out_height = f(height, kernel[0], pad[0], stride[0]) out_width = f(width, kernel[1], pad[1], stride[1])

The definition of f depends on pooling_convention, which has two options:

  • valid (default):

    f(x, k, p, s) = floor((x+2*p-k)/s)+1
  • full, which is compatible with Caffe:

    f(x, k, p, s) = ceil((x+2*p-k)/s)+1

When global_pool is set to be true, then global pooling is performed. It will reset kernel=(height, width) and set the appropiate padding to 0.

Three pooling options are supported by pool_type:

  • avg: average pooling

  • max: max pooling

  • sum: sum pooling

  • lp: Lp pooling

For 3-D pooling, an additional depth dimension is added before height. Namely the input data and output will have shape (batch_size, channel, depth, height, width) (NCDHW layout) or (batch_size, depth, height, width, channel) (NDHWC layout).

Notes on Lp pooling:

Lp pooling was first introduced by this paper: L-1 pooling is simply sum pooling, while L-inf pooling is simply max pooling. We can see that Lp pooling stands between those two, in practice the most common value for p is 2.

For each window X, the mathematical expression for Lp pooling is:

\(f(X) = \sqrt[p]{\sum_{x}^{X} x^p}\)

  • data (NDArray) – Input data to the pooling operator.

  • kernel (Shape(tuple), optional, default=[]) – Pooling kernel size: (y, x) or (d, y, x)

  • pool_type ({'avg', 'lp', 'max', 'sum'},optional, default='max') – Pooling type to be applied.

  • global_pool (boolean, optional, default=0) – Ignore kernel size, do global pooling based on current input feature map.

  • cudnn_off (boolean, optional, default=0) – Turn off cudnn pooling and use MXNet pooling operator.

  • pooling_convention ({'full', 'same', 'valid'},optional, default='valid') – Pooling convention to be applied.

  • stride (Shape(tuple), optional, default=[]) – Stride: for pooling (y, x) or (d, y, x). Defaults to 1 for each dimension.

  • pad (Shape(tuple), optional, default=[]) – Pad for pooling: (y, x) or (d, y, x). Defaults to no padding.

  • p_value (int or None, optional, default='None') – Value of p for Lp pooling, can be 1 or 2, required for Lp Pooling.

  • count_include_pad (boolean or None, optional, default=None) – Only used for AvgPool, specify whether to count padding elements for averagecalculation. For example, with a 5*5 kernel on a 3*3 corner of a image,the sum of the 9 valid elements will be divided by 25 if this is set to true,or it will be divided by 9 if this is set to false. Defaults to true.

  • layout ({None, 'NCDHW', 'NCHW', 'NCW', 'NDHWC', 'NHWC', 'NWC'},optional, default='None') – Set layout for input and output. Empty for default layout: NCW for 1d, NCHW for 2d and NCDHW for 3d.


out – The output of this function.

Return type

NDArray or list of NDArrays