IThis article will explain what a Rectified Linear Function is in ANN. How can ReLU Activation Function Hyperbolic be used? Let us refresh our memories about activation functions and define these terms. Learning rectified linear functions will be useful when coding a C++ program with c++ software.

What is an artificial neural network (ANN) activation function?

An **Activation Function** ( phi() ) also called as **transfer function**, or **threshold function** determines the activation value ( a = phi(sum) ) from a given value (sum) from the **Net Input Function** . **Net Input Function**, here **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 another term. 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.

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 Rectified Linear Unit?

In Artificial Neural Networks, the **Rectifier Linear Unit Function** or in other terms **ReLU Activation Function** is an activation function defined as the positive part of its argument. Can be written as f(x)= max(0, x) where *x* is sum of weighted input signals to an artificial neuron. ReLU Function is also known as a Ramp Function and is analogous to Half-wave Rectification in electrical engineering.

This function called as a **Parametric ReLU function**. If Beta is 0.01 it is called **Leaky ReLU function**.

This is max-out ReLU function,

if Beta is 0 then f(x) = max(x, 0). This function will return always positive numbers. Let’s write maxout ReLU function in C programming language,

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double phi(double sum) { return ( std::max(sum, beta*sum) ); // ReLU Function } |

## Is there a simple ANN example using a Rectified Linear Unit activation function in C++?

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#include <iostream> #define NN 2 // number of neurons class Tneuron // neuron class { public: double a; // activity of each neurons double 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 double activation_function(double sum) { return ( std::max(sum, 0) ); // ReLU 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 = 0.0; ne[1].a = 1.0; 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("%10.6f\n", ne[2].a); getchar(); return 0; } |

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