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The ReLU Function: Activating Only the Positive

The ReLU(Rectified Linear Unit) function is one of the most widely used activation functions in artificial neural networks. It performs a simple operation: it outputs the input value if it's greater than 0, otherwise it outputs 0.

In previous lessons, we explored the Sigmoid Function, which transforms all values between 0 and 1. In contrast, ReLU removes negative values, leaving only positive values.

ReLU Function Example
Input:  3  → Output: 3
Input:  0  → Output: 0
Input: -5  → Output: 0

The ReLU function decides whether a neuron in the network should be activated.

When the input is positive, it passes the value as is, retaining the information. Conversely, if the input is negative, it simplifies the computation by making it zero.


How the ReLU Function Works​

The ReLU function is defined by the following equation:

ReLU(x)=max⁡(0,x)\text{ReLU}(x) = \max(0, x)

It outputs the input value as is if it is greater than 0; otherwise, it outputs 0.

  • If the input is positive, it outputs the value as is.

  • If the input is zero or negative, it outputs 0.

ReLU Output Example Based on Input Values
Input:  5  → Output: 5
Input:  0  → Output: 0
Input: -3  → Output: 0

Advantages of the ReLU Function​

The ReLU function is among the most frequently used activation functions in deep learning.

The first advantage is that it addresses the vanishing gradient problem.

Unlike the sigmoid function, which can have gradients close to zero for large values making learning difficult, the ReLU does not encounter this issue.

The second advantage is its simplicity and speed in computation.

The ReLU function only performs the max(0, x) operation, making it faster than other activation functions like sigmoid, which require multiplications and divisions.


Limitations of the ReLU Function​

Despite its advantages, the ReLU function has some downsides. The most notable issue is the dead neuron problem.

Because the function outputs 0 for any non-positive input, some neurons can become permanently inactive during training.

To address this, variants such as Leaky ReLU or ELU are often used.

Additionally, if the input value is very large, the output can grow indefinitely, potentially destabilizing the model.

The Clipped ReLU, a variant of the ReLU function, is used to tackle this issue.


The ReLU function is one of the most widely used activation functions in deep learning due to its simplicity and fast computation, aiding faster training.

In the next lesson, we will explore the Softmax activation function.

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