Getting Started Guide

Contents

Local Response Normalization Backward Layer

For a given dimension
k
∈ {1, ...,
p
} of size
n
k
, the forward local response normalization layer normalizes the input tensor
X
R
n
1
x
n
2
x ... x
n
p
. For more details and notations, see Forward Local Response Normalization Layer .
For a dimension
k
∈ {1, ...,
p
} of size
n
k
, the backward local response normalization layer computes the value:
where:
  • g
    i
    1
    ...
    i
    p
    is the input gradient computed on the preceding layer
  • α, β, κ ∈
    R
  • n
    is a positive integer number
See [ Krizh2012 ] for an exact definition of local response normalization.

Problem Statement

Given
p
-dimensional tensors:
  • X
    R
    n
    1
    x
    n
    2
    x ... x
    n
    p
    of size
    n
    1
    x
    n
    2
    x ... x
    n
    p
  • G
    R
    n
    1
    x
    n
    2
    x ... x
    n
    p
    - the gradient computed on the preceding layer
The problem is to compute the
p
-dimensional tensor
Z
= (
z
i
1
...
i
p
) ∈
R
n
1
x
n
2
x ... x
n
p
.

Product and Performance Information

1

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Notice revision #20110804