MPSCNNPoolingAverageGradient(3)

NAME
MPSCNNPoolingAverageGradient

SYNOPSIS

#import <MPSCNNPooling.h>

Inherits MPSCNNPoolingGradient.

  Instance Methods
(nonnull instancetype) - initWithDevice:kernelWidth:kernelHeight:strideInPixelsX:strideInPixelsY:
(nullable instancetype) - initWithCoder:device:

  Properties
NSUInteger zeroPadSizeX
NSUInteger zeroPadSizeY

  Additional Inherited Members

Detailed Description

This depends on Metal.framework Specifies the filter for computing the gradient of the average pooling filter. The operation backpropagates a gradient vector using chain rule.

Average pooling forward pass is defined as:

out(x) = sum_{dx in Window(x)} in(s*x+dx) / N(x), where

the pooling window definition 'Window(x)' follows MPSCNNPooling specification, 'N(x)' is effective pooling window size in pixels as specified in MPSCNNPoolingAverage, 's' is the pixel stride and in() is the source input image.

Hence the partial derivative of the output value wrt. to the input value needed in the gradient backpropagation in MPSCNNPoolingGradient is:

d out(x)/d in(y) = sum_{dx in Window(x)} delta_{s*x+dx, y} / N(x), where

delta_{x,y} is the Kronecker delta symbol for which

delta_{x,y} =  {  1, when x == y
               {  0, otherwise.

In practice this means that the gradient value for the destination image at pixel 'x' is the sum over these contributions coming from all pooling windows that contribute to the average pooling computation in the forward pass, multiplied by the input gradient value in the source area of the corresponding pooling window.

Note: As average pooling is a linear operation of its inputs, the gradient does not depend at all on the original input values, but the original input image size is needed so that we know the limits where the input values seize to exist to inhibit accumulation of gradient values for those pixels. Therefore, as secondary input, any correctly sized image will produce correct results for the gradient backpropagation and hence it is recommended to use a temporary image of correct size (see MPSTemporaryImage) for the secondary source image parameter.

Method Documentation

  - (nullable instancetype) initWithCoder: (NSCoder *__nonnull) aDecoder(nonnull id< MTLDevice >) device
NSSecureCoding compatability See MPSKernel::initWithCoder.

Parameters:
    aDecoder The NSCoder subclass with your serialized MPSCNNPoolingAverageGradient
    device The MTLDevice on which to make the MPSCNNPoolingAverageGradient

Returns:
    A new MPSCNNPoolingAverageGradient object, or nil if failure.

Reimplemented from MPSCNNPoolingGradient.

  - (nonnull instancetype) initWithDevice: (nonnull id< MTLDevice >) device(NSUInteger) kernelWidth(NSUInteger) kernelHeight(NSUInteger) strideInPixelsX(NSUInteger) strideInPixelsY
Initialize a gradient average pooling filter

Parameters:
    device The device the filter will run on
    kernelWidth The width of the kernel. Can be an odd or even value.
    kernelHeight The height of the kernel. Can be an odd or even value.
    strideInPixelsX The input stride (upsampling factor) in the x dimension.
    strideInPixelsY The input stride (upsampling factor) in the y dimension.

Returns:
    A valid MPSCNNPoolingGradient object or nil, if failure.

Reimplemented from MPSCNNPoolingGradient.

Property Documentation

  - zeroPadSizeX [read], [write], [nonatomic], [assign]
How much zero padding to apply to both left and right borders of the input image for average pooling, when using

See also:
    edgeMode MPSImageEdgeModeClamp. For

    edgeMode MPSImageEdgeModeZero this property is ignored and the area outside the image is interpreted to contain zeros. The zero padding size is used to shrink the pooling window to fit inside the area bound by the source image and its padding region, but the effect is that the normalization factor of the average computation is computed also for the zeros in the padding region.

  - zeroPadSizeY [read], [write], [nonatomic], [assign]
How much zero padding to apply to both top and bottom borders of the input image for average pooling, when using

See also:
    edgeMode MPSImageEdgeModeClamp. For

    edgeMode MPSImageEdgeModeZero this property is ignored and the area outside the image is interpreted to contain zeros. The zero padding size is used to shrink the pooling window to fit inside the area bound by the source image and its padding region, but the effect is that the normalization factor of the average computation is computed also for the zeros in the padding region.

Author

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