Getting Started Guide

Contents

Local Contrast Normalization Backward Layer

For given dimensions
k
1
of size
n
k
1
,
k
2
of size
n
k
2
, and
f
different from
k
1
and
k
2
, the forward local contrast normalization layer normalizes the input
p
-dimensional tensor
X
R
n
1
x
n
2
x ... x
n
p
. For more details, see Forward Local Contrast Normalization Layer.
The library supports four-dimensional input tensors
X
R
n
1
x
n
2
x
n
3
x
n
4
.
Without loss of generality let's assume that backward local contrast normalization is applied to the last two dimensions. The backward local contrast normalization layer takes:
  • Four-dimensional tensor
    X
    R
    n
    1
    x
    n
    2
    x
    n
    3
    x
    n
    4
  • Four-dimensional tensor
    G
    R
    n
    1
    x
    n
    2
    x
    n
    3
    x
    n
    4
    with the gradient computed on the preceding layer
  • Two-dimensional tensor
    K
    R
    m
    1
    x m
    2
    that contains kernel parameters/weights of kernels, where
    m
    1
    n
    3
    ,
    m
    2
    n
    4
The layer computes the four-dimensional value tensor
Z
R
n
1
x
n
2
x
n
3
x
n
4
:

Problem Statement

The computation depends on whether the dimension
f
is set:
  • Dimension
    f
    is set; let
    n
    2
    be the sum dimension:
    Consequently:
  • Dimension
    f
    is not set:
Consequently:
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Product and Performance Information

1

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Notice revision #20110804