Developer Guide

Contents

Two-Dimensional Spatial Pyramid Pooling Backward Layer

The forward two-dimensional (2D) spatial pyramid pooling layer with pyramid height
L
N
is a form of non-linear downsampling of an input tensor
X
. For more details, see Forward 2D Spatial Pyramid Pooling Layer.
The backward 2D spatial pyramid pooling layer computes the input gradient
G
R
n
1
x
n'
, where
n'
is computed on the preceding layer as explained for the forward layer. Only the elements corresponding to the values pooled from subtensors in the forward computation step are propagated to the next layer.

Problem Statement

The library provides several spatial pyramid pooling layers:
  • Spatial pyramid maximum pooling
  • Spatial pyramid average pooling
  • Spatial pyramid stochastic pooling
The following description applies to each of these layers.
Let
G
R
n
1
x
n'
be the two-dimensional tensor with the input gradient and
k
1
and
k
2
be the dimensions along which pooling kernels are applied. The backward 2D spatial pyramid pooling layer computes gradients for every pooling level from the respective input gradient and accumulates the pooling gradients to get the output gradient
Z
= (
z
i
1
...
i
p
) ∈
R
n
1
x
n
2
x ... x
n
p
of the layer:
where
is the gradient of the
l
-th pooling level.
The following figure illustrates the behavior of the backward spatial pyramid maximum pooling layer with pyramid height
L
= 2:
Spatial Pyramid Pooling Backward Layer

Product and Performance Information

1

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Notice revision #20110804