Encoder Hidden Layers and Data Compression

We've established that the encoder's primary mission is to take the input data and condense it. This crucial task of compression largely unfolds within the encoder's hidden layers.

What Are Hidden Layers in an Encoder?

In a neural network, layers are essentially stages of computation. The input layer is the entry point for our data. The bottleneck layer, which we'll explore in detail soon, holds the most compressed version of this data. Between the input and the bottleneck, we typically find one or more hidden layers.

They are termed "hidden" because their outputs are intermediate steps; they are not the final, directly observed output of the autoencoder. Within an encoder, these hidden layers are specifically designed to progressively reduce the dimensionality of the data. Dimensionality simply refers to the number of features or values used to describe each data point. For example, an image made of 28x28 pixels has $28 \times 28 = 784$ dimensions if we flatten it out.

The Squeeze: How Hidden Layers Compress Information

The principal method by which hidden layers achieve compression is by having fewer neurons (also called units) than the layer that precedes them. You can think of this as data passing through a narrowing channel or a series of funnels, where each stage has less capacity than the one before. This structure forces the network to be selective about what information it passes along.

Consider an example with image data that has 784 features:

• The input layer would have 784 neurons, one for each input feature.
• A first hidden layer in the encoder might then have, for instance, 256 neurons.
• A subsequent, second hidden layer could further reduce this to 128 neurons. This tapering continues until the data reaches the bottleneck layer, which has the fewest neurons and thus holds the most compressed representation of the input.

This architecture compels the network to learn how to retain the most significant aspects of the input. Since it cannot preserve every detail due to the decreasing number of neurons, it must identify and encode the underlying patterns or most informative features to allow for later reconstruction.

Each neuron in a hidden layer receives inputs from neurons in the previous layer. It then computes a value (typically a weighted sum of its inputs, passed through an activation function) and sends its output to the next layer. Because there are fewer neurons in subsequent layers, the information is necessarily combined and condensed.

Here's a diagram illustrating this flow:

Data flows through the encoder's hidden layers. Each layer typically reduces the number of dimensions, effectively compressing the information as it moves towards the bottleneck.

Why Fewer Neurons Mean Compression

When a hidden layer has fewer neurons than the layer that fed into it, it simply does not have the capacity to pass along all the information it received in the same level of detail. It is forced to create a more compact summary. Through the training process (which we'll cover in Chapter 3), the network learns to make these summaries as rich and useful as possible, so the decoder can later attempt to reconstruct the original input accurately.

For instance, if an early hidden layer processes pixel data from an image, it might learn to combine these pixels to identify basic elements like edges or simple textures. A subsequent, smaller hidden layer might then take these edge and texture features as input and learn to represent more complex components of an object. Each step involves summarizing and abstracting information, which is the core of how compression works in this setting.

The Role of Activation Functions

As we've mentioned, neurons in these hidden layers also apply an activation function to their computed outputs. We'll look more closely at specific activation functions like $ReLU$ (Rectified Linear Unit) later in this chapter. For now, it's important to know that these functions introduce non-linearities into the network. This is a significant point. Without non-linearity, a deep neural network (one with multiple layers) would effectively behave like a single, much simpler linear layer. This would severely limit its ability to learn complex relationships in the data and, consequently, its power to compress data meaningfully. $ReLU$ is a popular choice for encoder hidden layers due to its simplicity and effectiveness in many scenarios.

Leading to the Bottleneck

This journey of data through progressively smaller hidden layers continues until the data reaches the bottleneck layer. The output from the encoder's final hidden layer serves as the direct input to this bottleneck layer. In essence, these hidden layers perform the demanding work of transforming the initial high-dimensional input data into the low-dimensional, compressed representation that the bottleneck will store.

Understanding how these encoder hidden layers systematically reduce data dimensionality is a foundational piece in grasping how autoencoders achieve compression and learn valuable features from data. Next, we will examine the bottleneck layer itself, which is the very core of this compressed representation.