Simple Visualization of Learned Representations

The bottleneck layer of an autoencoder stores a compressed, learned representation of input data. This design prompts a natural question: what do these learned features actually look like? How can one examine what the autoencoder has deemed important? Visualizing these learned representations offers a clear understanding of how the autoencoder processes information and whether it captures meaningful patterns.

Why Visualize Learned Features?

Visualizing the features learned by an autoencoder serves several purposes:

1. Gaining Intuition: It can help us build an intuition for what aspects of the data the autoencoder considers significant. If we feed it images of cats and dogs, does the latent space (the space where bottleneck representations live) show a clear separation or organization related to these categories?
2. Debugging and Model Assessment: If visualizations show a random scatter of points in the latent space with no discernible structure, it might indicate that the autoencoder hasn't learned effectively or that the bottleneck is too large or too small.
3. Understanding Dimensionality Reduction: When an autoencoder reduces, say, a 784-dimensional image (like a 28x28 pixel MNIST digit) to just 2 or 3 dimensions in the bottleneck, visualizing these 2D or 3D points can directly show how the data has been compressed and organized.
4. Exploring Data Structure: Sometimes, these visualizations can reveal underlying structures in the data that weren't obvious before, such as distinct clusters corresponding to different categories of input, even if the autoencoder was trained without labels (unsupervised).

Visualizing Bottleneck Activations (Latent Space)

One of the most direct ways to visualize learned features is to look at the activations in the bottleneck layer itself. If your bottleneck layer is designed to have a very low dimension, such as 2 or 3, you can plot these activations directly.

Imagine you're working with the MNIST dataset of handwritten digits. Each image is 28x28 pixels, making it 784-dimensional. If you train an autoencoder with a 2-dimensional bottleneck, you can:

1. Pass each MNIST image through the trained encoder part of your autoencoder.
2. Collect the 2D output from the bottleneck layer for each image.
3. Create a scatter plot where each point corresponds to an image, with its x and y coordinates being the two activation values from the bottleneck.

If the autoencoder has learned well, you might see that images of the same digit (e.g., all "0"s, all "1"s) tend to cluster together in this 2D latent space. This indicates that the autoencoder has learned to represent similar digits with similar compact codes.

Let's consider a scenario. Suppose we have three distinct types of data items. After passing them through an encoder that compresses them into a 2-dimensional representation, we might get a scatter plot like this:

A scatter plot showing data points from three different classes mapped to a 2-dimensional latent space. Classes A and B form distinct clusters, while Class C might be more spread out or intermingled, suggesting how the autoencoder differentiates or groups these data types.

If your bottleneck has 3 dimensions, you can create a 3D scatter plot. For bottlenecks with more than 3 dimensions, direct plotting isn't feasible. In such cases, you might employ further dimensionality reduction techniques like t-SNE (t-distributed Stochastic Neighbor Embedding) or PCA (Principal Component Analysis) specifically for visualization, to project the higher-dimensional latent space down to 2D or 3D. However, these are separate techniques, and for a basic understanding, focusing on inherently low-dimensional bottlenecks is a good starting point.

Visualizing Reconstructions from the Latent Space

Another insightful technique is to take points from the latent space and feed them only through the decoder part of the autoencoder. This shows what kind of original-like data the autoencoder associates with different regions or specific points in its learned feature space.

For instance, with our 2D latent space for MNIST digits:

1. Pick a point $(x, y)$ in the 2D plane that your latent space occupies. This point doesn't have to be one generated by an actual input image; you can choose arbitrary coordinates.
2. Treat this $(x, y)$ pair as an input to your trained decoder network.
3. The output of the decoder will be an image (e.g., 28x28 pixels). This is what the autoencoder "imagines" or reconstructs from that specific point in its learned feature space.

By sampling points in a grid across the latent space and generating reconstructions for each, you can create a manifold visualization. You might observe smooth transitions: as you move from a region encoding "1"s to a region encoding "7"s, the reconstructed images might gradually morph from looking like a "1" to looking like a "7".

This technique is particularly powerful because it highlights how the autoencoder has learned to map continuous variations in the latent space to continuous variations in the data space. It gives you a sense of the "meaning" the autoencoder has assigned to different coordinates in its compressed representation.

For example, if you trained an autoencoder on images of faces, and then sampled points along a line in the latent space, the decoded images might show a face smoothly changing an attribute, like transitioning from a smile to a neutral expression, or from looking left to looking right. This indicates that the autoencoder has captured these variations as one of its learned features.

Interpreting the Visualizations

When you look at these visualizations, here are a few things to consider:

• Clusters: Do points corresponding to similar inputs (e.g., same digit, same object category) group together? Clear clustering is a good sign that the autoencoder is learning to distinguish between different types of data.
• Separation: How well-separated are these clusters? If clusters for different categories overlap significantly, the representation might not be very discriminative for those categories.
• Continuity (for reconstructions): Do nearby points in the latent space decode to visually similar outputs? Does moving along a direction in latent space correspond to a meaningful change in the reconstructed output? This indicates a well-structured latent space.
• Empty Spaces: Are there "empty" regions in the latent space? What happens if you try to decode from these regions? Sometimes, decoders produce noisy or nonsensical outputs from areas far from where actual data was mapped.

It's important to remember that the features learned by an autoencoder are often abstract. While one axis in your 2D latent space might loosely correspond to "thickness" for digits, and another to "slant," it's rarely this straightforward. The autoencoder learns whatever features best help it reconstruct the data, and these might not always align perfectly with human-understandable attributes. However, these visualizations provide a valuable window into these learned internal representations, helping us understand and trust the representations our models build. As we move towards building our first autoencoder, we'll see how to practically generate some of these visualizations.