Common Activation Functions in Encoders

An activation function is applied in the encoder part of an autoencoder, after each layer performs its calculations (multiplying inputs by weights and adding biases). Think of an activation function as a simple gatekeeper for each neuron. It decides what information should be passed forward to the next layer. Without these functions, no matter how many layers we stack, our network would only be able to learn simple, linear relationships. Activation functions introduce non-linearity, allowing the encoder to learn much more complex patterns and representations from the input data.

One of the most common and effective activation functions used in the hidden layers of encoders is the Rectified Linear Unit, or ReLU.

ReLU (Rectified Linear Unit)

The ReLU function is remarkably straightforward. If the input to the function is positive, it outputs the input value directly. If the input is zero or negative, it outputs zero.

Mathematically, ReLU is defined as:

$$f(x) = \max(0, x)$$

Where $x$ is the input to the neuron.

Let's visualize this:

The ReLU function outputs the input directly if it's positive, and zero otherwise.

So, why is ReLU so popular in encoders?

1. Simplicity and Efficiency: It's computationally very cheap. The operations (a maximum comparison and then either passing a value or zero) are fast, which speeds up the training process.
2. Reduces Vanishing Gradient Problem: In deeper networks, some other activation functions (like sigmoid or tanh, which we'll touch upon later for decoders) can suffer from a "vanishing gradient" problem. This means the learning signal becomes too small as it propagates backward through many layers, making it hard for earlier layers to learn. ReLU helps mitigate this for positive inputs because its derivative (the rate of change) is constant (either 0 or 1). This allows the learning signal to flow better.
3. Sparsity: Because ReLU outputs zero for any negative input, it can lead to some neurons in a layer being "inactive" (outputting zero). This is called sparsity. Sparse representations can be more efficient and can help the network learn more distinct features, as not all neurons are firing all the time for every input.

When building an encoder, you'll typically apply the ReLU activation function to the output of each hidden layer. For instance, if a hidden layer in your encoder calculates a value $h_1$ for a neuron, the actual output passed to the next layer would be $ReLU(h_1)$. This process repeats for all neurons in the layer and for subsequent hidden layers in the encoder, each step helping to transform the data into a more compressed and abstract representation.

While ReLU is a go-to choice for hidden layers in encoders, it's important to know that other activation functions exist. For example, variations like "Leaky ReLU" or "Parametric ReLU (PReLU)" were developed to address the "dying ReLU" problem (where neurons can get stuck outputting zero if their inputs are always negative). However, for an introduction, understanding ReLU provides a solid foundation as it's widely effective and commonly used. The choice of activation function can influence how well and how quickly your autoencoder learns to compress data.