Pooling (input,
         poolKind, # "max" or "average"
         {kernel dimensions}, 
         stride = {stride dimensions}, 
         autoPadding = {padding flags (boolean)},
         lowerPad = {lower padding (int)},
         upperPad = {upper padding (int)})

The pooling operations compute a new matrix by selecting the maximum (max pooling) or average value in the pooling input. In the case of average pooling, count of average does not include padded values.

N-dimensional pooling allows to create max or average pooling of any dimensions, stride or padding. The syntax is:

where:

• input - pooling input
• poolKind - "max" or "average"
• {kernel dimensions} - dimensions of the pooling window, as a BrainScript vector, e.g. (4:4).
• stride - [named, optional, default is 1] strides.
• autoPadding - [named, optional, default is true] automatic padding flags for each input dimension.
• lowerPad - [named, optional, default is 0] precise lower padding for each input dimension
• upperPad - [named, optional, default is 0] precise upper padding for each input dimension

All dimensions arrays are colon-separated. Note: If you use the deprecated NDLNetworkBuilder, these must be comma-separated and enclosed in { } instead.

Since the pooling window can have arbitrary dimensions, this allows to build various pooling configurations, for example, a "Maxout" layer (see Goodfellow et al for details):

MaxOutPool (inp, kW, kH, kC, hStride, vStride) =
    Pooling (inp, "max", (kW:kH:kC), stride=(hStride:vStride:kC), true:true:false))

There is a simplified syntax for 2D pooling:

MaxPooling(m, windowWidth, windowHeight, stepW, stepH, imageLayout="cudnn" /* or "HWC"*/ )
AveragePooling(m, windowWidth, windowHeight, stepW, stepH, imageLayout="cudnn" /* or "HWC"*/ )

with the following parameters:

• m - the input matrix.
• windowWidth - width of the pooling window
• windowHeight - height of the pooling window
• stepW - step (or stride) used in the width direction
• stepH - step (or stride) used in the height direction
• imageLayout - [named optional] the storage format of each image. This is a legacy option that you likely won't need. By default it’s HWC, which means each image is stored as [channel, width, height] in column major notation. For better performance, it is recommended to use cuDNN in which case you should set it to cudnn, which means each image is stored as [width, height, channel] in column major notation. Note that cudnn format works both on GPU and CPU.

Example (ConvReLULayer NDL macro):

# pool2
pool2W = 2
pool2H = 2
pool2hStride = 2
pool2vStride = 2
pool2 = MaxPooling (conv2, pool2W, pool2H, pool2hStride, pool2vStride, imageLayout="$imageLayout$")

Note: If you are using the deprecated NDLNetworkBuilder, the optional imageLayout parameter defaults to "HWC" instead.