Activation Functions

Activation functions are a critical component of any neural network. They are functions applied to the output of a neuron (the weighted sum of its inputs) to determine its final output or 'activation'. Their primary purpose is to introduce non-linearity into the network. Without a non-linear activation function, a multi-layer neural network would behave just like a single-layer perceptron, because summing linear functions just results in another linear function. This would limit the network to learning only linear relationships in the data. By introducing non-linearity, activation functions allow neural networks to learn incredibly complex patterns and act as universal function approximators. There are several common types of activation functions. The Sigmoid function, which outputs values between 0 and 1, was popular in the past but is less used in hidden layers today due to the 'vanishing gradient' problem. The Hyperbolic Tangent (Tanh) function is similar to sigmoid but outputs values between -1 and 1, which is often preferred as its output is zero-centered. The most popular activation function for hidden layers in modern deep learning is the Rectified Linear Unit (ReLU). It's a simple function that outputs the input directly if it's positive, and zero otherwise (f(x) = max(0, x)). ReLU is computationally efficient and helps mitigate the vanishing gradient problem, leading to faster training. Choosing the right activation function is an important part of designing a neural network architecture.