What is a Binary Step Function? Should we use Binary Step Function or Heaviside Step Function? Are Binary Step functions and Heaviside Step functions the same thing? What is a Unit Step Function? Briefly, all these terms are same, let’s explain these terms.

What is an activation function in C++ AI?

An **Activation Function** ( phi() ) also called as **transfer function**, or **threshold function** that determines the activation value ( a = phi(sum) ) from a given value (sum) from the **Net Input Function**. A **Net Input Function**, here, is **the sum** is a sum of signals in their weights, and activation function is a new value of this sum with a given function or conditions. In other words, the activation function is a way to transfer the sum of all weighted signals to a new activation value of that signal. There are different activation functions, mostly Linear (Identity), bipolar and logistic (sigmoid) functions are used. The activation function and its types are explained well here.

## Is it possible to create an AI activation function in C++?

In C++ (in general in most Programming Languages) you can create your activation function. Note that sum is the result of Net Input Function which calculates the sum of all weighted signals. We will use some as a result of the input function. Here activation value of an artificial neuron (output value) can be written by the activation function as below,

By using this **sum **Net Input Function Value** **and **phi() activation functions**, let’s see some of activation functions in C++; Now Let’s see how we can use Binary Step Function as in this example formula,

## What is a Binary Step or Heaviside Step Function?

A Binary Step Function, or **Heaviside step function**, or the **unit step function**, is a step function, named after Oliver Heaviside (1850–1925), the value of which is zero for negative arguments and one for positive arguments. That means it results 0 or 1 as a Boolean. Indicator function is described as below,

This function is an example to the general class of step functions, all of which can be represented as linear combinations of translations of this one.

Thus, Binary Step Function is a Boolean function that returns bool (1 or 0), it should be as below,

1 2 3 4 5 6 |
bool phi(float sum) { return(sum>0) ; // Binary Step Function , Heaviside Step Function, Unit Step Function, } |

This activation function returns 1 (true) if sum>0 otherwise returns 0 (false)

## Is there a C++ example of an AI Binary Step or Heaviside function?

Here is a example how to use a step function.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 |
#include <iostream> #define NN 2 // number of neurons class Tneuron // neuron class { public: bool a; // activity of each neurons float w[NN+1]; // weight of links between each neurons Tneuron() { a=0; for(int i=0; i<=NN; i++) w[i]=-1; // if weight is negative there is no link } // let's define an activation function (or threshold) for the output neuron bool phi(float sum) { return(sum>0) ; // Binary Step Function , Heaviside Step Function, Unit Step Function, } }; Tneuron ne[NN+1]; // neuron objects void fire(int nn) { float sum = 0; for ( int j=0; j<=NN; j++ ) { if( ne[j].w[nn]>=0 ) sum += ne[j].a*ne[j].w[nn]; } ne[nn].a = ne[nn].activation_function(sum); } int main() { //let's define activity of two input neurons (a0, a1) and one output neuron (a2) ne[0].a = 0; ne[1].a = 1; ne[2].a = 0; //let's define weights of signals comes from two input neurons to output neuron (0 to 2 and 1 to 2) ne[0].w[2] = 0.3; ne[1].w[2] = 0.2; // Let's fire our artificial neuron activity, output will be fire(2); printf("%d\n", ne[2].a); getchar(); return 0; } |

In addition to this indicator function, other Heaviside step function types are; a piecewise function, ramp function, Dirac delta function, and integral of the Dirac delta function. More details can be found on Wikipedia.