NAME

MPSCNNPoolingL2NormGradient

SYNOPSIS

#import <MPSCNNPooling.h>

Inherits MPSCNNPoolingGradient.

Instance Methods

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

Detailed Description

This depends on Metal.framework Specifies the filter for computing the gradient of the L2-Norm pooling filter. The operation backpropagates a gradient vector using chain rule.

L2-Norm pooling forward pass is defined as:

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

the pooling window definition 'Window(x)' follows MPSCNNPooling specification and '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} in(s*x+dx) / out(x), where

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

delta_{x,y} =  {  1, when x == y


               {  0, otherwise,

and out(x) is the L2-norm pooling value at point 'x' defined above.

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 MPSCNNPoolingL2NormGradient
device The MTLDevice on which to make the MPSCNNPoolingL2NormGradient

Returns:

A new MPSCNNPoolingL2NormGradient 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 L2-norm 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.