Developer Guide

Contents

Softmax Backward Layer

For any
x
i
1
...
i
p
from
X
R
n
1
x ... x
n
p
and for dimension
k
of size
n
k
, the softmax activation layer applies the transform defined as
The softmax function is known as the normalized exponential (see [Bishop2006] for exact definitions of softmax).
The backward softmax layer for dimension
k
of size
n
k
computes the value:
where
g
i
1
...
i
p
is the input gradient computed on the preceding layer.

Problem Statement

Given
p
-dimensional tensors of size
n
1
x
n
2
x ... x
n
p
:
  • G
    = (
    g
    i
    1
    ...
    i
    p
    ) with the gradient computed on the preceding layer
  • Y
    = (
    y
    i
    1
    ...
    i
    p
    ) with the output of the forward softmax layer
The problem is to compute the
p
-dimensional tensor
Z
= (
z
i
1
...
i
p
) of size
n
1
x
n
2
x ... x
n
p
such that:

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804