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Help in understanding unipolar transmission function

The question arises that I am stuck using the following formula for a unipolar transfer function:

f(net)=     1
         __________
               -net
         1 + e

The example has the following:

out =        1
        ____________  = 0.977
               -3.75
        1 + e

How do we reach 0.977?

What is e?

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4 answers


e = 2.71828 ... is the base of natural logarithms . It is a mathematical constant that appears in many different equations like & pi. You will see this all the time when doing exponents and logarithms.



Plug it into your equation and you get 0.977.

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In fact, the other answers are correct just provide the value of e and confirm the underlying computation. This type of sigmoid function is so large for neural networks that some additional insight might be welcomed.

Essentially an exponential function (e to the power of x) has a very characteristic curve:

  • Mostly flat at zero (very slightly above zero, in fact), from - infinity to about -2
  • gradual sharp turn towards the vertical, between -2 and +4
  • quasi "vertical", with values ​​over 150 and more and more huge, from +5 to infinity

As a result, exponential curves are very useful for creating "S-shaped" functions ; BTW, "S" is sigma in Greek that endows the etymology with "sigmoid". Such functions are often structured according to the formula shown in the question:



 1/(1 + e^-x)

where x is a variable. Typically, such functions also include constants aimed at stretching the range (the entry zone where changes in x are significant) and / or when the curve changes in that middle zone.
The result of such functions is that up to a certain value of the input the function is quasi-constant, then for a certain range of inputs the function provides an increase in the output signal and, finally, passes the upper value of the range, the function is quasi-constant. In addition, in more detail, such sigmoids have an inflection point that corresponds to the reverse change in the rate of change of the axis, and which also marks the area of ​​the curve on both sides, where the changes are slowest, relative.

In turn, such S-shaped curves (1) are very useful for normalizing the output of neural neural networks, or, moreover, for normalizing different numerical values ​​in processes of different nature. Intuitively, this corresponds to the “ sweet spot ” or “ sweet range ” of the underlying neuron or device.

(1) Or also possibly "stepped" profiles, i.e. curves with a predominantly constant high value, a decreasing value within the middle range and a low mostly constant value thereafter.

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e Euler's number == 2.718281828 ....

If you raise e to the -3.75 level, add it to it and take it back, you get exactly 0.977022630 ....

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'e' is the base for the natural logarithm function, the value of which is equivalent to the sum of an infinite series 1 / n! for n from 0 to infinity. It is available in the C standard library or in the java Math package as the exp () function.

If you rate 1 / (1 + exp (-3.75)) you get 0.977

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