What is relu?

ReLU stands for Rectified Linear Unit. It is a simple mathematical function used as an activation step in artificial neural networks. The function takes a single number x and outputs the larger of 0 or x, written as f(x) = max(0, x). In other words, if the input is negative, ReLU returns 0; if the input is positive, it returns the same positive value.

Let's break it down

Think of ReLU as a gate that only lets positive signals pass through unchanged and blocks (sets to zero) any negative signals. Visually, its graph is a straight line along the x‑axis for all negative values (flat at 0) and then a 45‑degree line for positive values. Mathematically:

  • If x < 0 → f(x) = 0
  • If x ≥ 0 → f(x) = x This piece‑wise definition makes the function very easy to compute: just a comparison and, if needed, a copy of the input.

Why does it matter?

Neural networks need non‑linear functions to learn complex patterns. ReLU provides that non‑linearity while keeping the computation cheap. It also helps with the “vanishing gradient” problem that plagued older functions like sigmoid or tanh, because the gradient (derivative) for positive inputs is 1, allowing error signals to flow backward through many layers during training.

Where is it used?

ReLU is the default activation in most modern deep‑learning architectures:

  • Convolutional Neural Networks (CNNs) for image recognition
  • Fully‑connected feed‑forward networks for classification or regression
  • Some recurrent networks and transformer models (often with variations like Leaky ReLU)
  • Any deep model where speed and training stability are important

Good things about it

  • Computationally cheap: only a comparison and copy operation.
  • Sparse activation: many neurons output 0, which can make the network more efficient.
  • Helps gradient flow: gradient is 1 for positive inputs, reducing vanishing‑gradient issues.
  • Works well in practice: most state‑of‑the‑art models achieve high accuracy using ReLU.

Not-so-good things

  • Dying ReLU: if a neuron’s weights push its input to stay negative, it will output 0 forever and stop learning.
  • Unbounded output: positive values can grow without limit, which may cause exploding activations in some cases.
  • Not zero‑centered: outputs are always non‑negative, which can slow down convergence compared to functions that produce both positive and negative values.