### Summary

ReLU, short for Rectified Linear Unit, is a simple yet influential mathematical function used in artificial neural networks. It helps the model learn complex patterns in the data by introducing non-linearities into the network. The function calculates the output of a neuron by turning any negative input into zero and lets positive input pass unchanged.

### ELI5

Imagine you’re counting apples in a basket. Instead of subtracting from your count for every rotten apple found (negative input), you decide to ignore those and just continue counting the good ones (positive input). You don’t count backwards, you just keep adding or stay at the same count. ReLU works exactly this way when processing data in a neural network: negative data becomes zero and positive data remains unchanged.

### In-depth explanation

ReLU is a type of activation function used in artificial neural networks. Activation functions are mathematical equations that determine the output of a neural network. They map the resulting values into a suitable form that fits within the intended boundary.

The mathematical expression for the ReLU function is `f(x) = max(0, x)`

. This means that for any input `x`

, if the `x`

is greater than zero, the output will be `x`

. Otherwise, the output will be zero.

ReLU introduces non-linearity into the neural network, enabling it to learn and perform more complex tasks. By neglecting the negative inputs and considering only the positive ones, ReLU provides the network the capability to solve non-linear problems.

Compared to other activation functions like the sigmoid or Tanh, ReLU holds several advantages: it’s computationally efficient since it involves simpler mathematical operations, accelerates the convergence of stochastic gradient descent compared to sigmoid/tanh. It also mitigates the vanishing gradient problem, where the gradients of the loss function become too small to contribute significantly to the learning process.

However, ReLU isn’t without its caveats. It’s subject to the dying ReLU problem, where some neurons can become inactive and stop contributing to the learning process if they get stuck in the state where their output is zero.

Despite these, ReLU remains a popular choice for an activation function due to its simplicity and efficiency. It’s extensively used in convolutional neural networks and deep learning models.

Backpropagation and gradient descent, two critical mechanisms in neural network learning, use the derivatives of activation functions, such as ReLU. The derivative of the ReLU function is either 0 for negative inputs or 1 for positive inputs. This simple derivative makes backpropagation computationally efficient when using ReLU.

Python representation of ReLU: `relu = lambda x : max(0, x)`

### Related terms

Activation Function, Neural Network, Backpropagation, Gradient Descent, Sigmoid Function, Tanh Function, Convolutional Neural Network (CNN),, Deep Learning, Vanishing Gradient Problem, Dying ReLU Problem