Back

Explore Courses Blog Tutorials Interview Questions
0 votes
1 view
in Machine Learning by (11.4k points)

In the output layer of a neural network, it is typical to use the softmax function to approximate a probability distribution:

enter image description here

This is expensive to compute because of the exponents. Why not simply perform a Z transform so that all outputs are positive, and then normalize just by dividing all outputs by the sum of all outputs?

1 Answer

0 votes
by (33.1k points)

Softmax as compared to standard normalization, it performs exponential normalization, that means its output directly depends upon the uniform distribution of input. While the output of normal distribution does not get affected until the ratio proportion is the same.

The formula for Softmax function:

image

The formula for standard deviation:

     image

Example for softmax function:

>>> softmax([1,2]) # blurry image of a ferret

[0.26894142, 0.73105858]) # it is a cat perhaps !?

 

>>> softmax([10,20]) # crisp image of a cat 

[0.0000453978687, 0.999954602]) # it is definitely a CAT !

Example for standard normalization:

>>> std_norm([1,2]) # blurry image of a ferret 

[0.3333333333333333, 0.6666666666666666] # it is a cat perhaps

>>> std_norm([10,20]) # crisp image of a cat 

[0.3333333333333333, 0.6666666666666666] # it is a cat perhaps !?

In the above example, softmax predicts more accurately when the image resolution is higher, but the standard normalization function predicted the same probability in lower and higher resolution of the image. That’s why Softmax is most commonly used in neural network.

Welcome to Intellipaat Community. Get your technical queries answered by top developers!

28.4k questions

29.7k answers

500 comments

94.1k users

Browse Categories

...