# mx.nd.Pooling¶

## Description¶

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

*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: https://arxiv.org/pdf/1204.3968.pdf.
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:

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


## Arguments¶

Argument

Description

data

NDArray-or-Symbol.

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.

## Value¶

out The result mx.ndarray