A Glimpse into Overfitting and Underfitting

When we train an autoencoder, our main goal, as we've discussed, is to get the reconstructed output as close as possible to the original input. We measure this using a loss function and try to minimize it. But, like a student who crams for an exam by memorizing specific questions and answers, a model can sometimes learn the training data too well, or not well enough. This leads to two common situations in machine learning: overfitting and underfitting. Let's take a brief look at what these mean in the context of autoencoders.

Understanding Underfitting: Not Learning Enough

Imagine you're trying to learn to draw a cat, but you only look at a very blurry picture or only spend a few seconds studying it. Your drawings afterwards probably wouldn't look much like a cat. This is similar to underfitting.

An autoencoder underfits when it's too simple to capture the important patterns in your data. It fails to learn the underlying structure, so it performs poorly not just on new, unseen data, but also on the very data it was trained on. The reconstruction error will be high for both.

What might cause an autoencoder to underfit?

• Too small a bottleneck: If the bottleneck layer is overly restrictive, trying to compress the data into an extremely small space, it might lose too much information. It's like trying to summarize a whole book in just one word.
• Model too simple: The encoder or decoder might not have enough layers or neurons to learn the complexity of the data.
• Not enough training: If you don't train the model for enough epochs, it simply hasn't had enough chances to adjust its weights and learn properly.

An underfit autoencoder won't be very good at reconstructing inputs, and the features it learns in the bottleneck layer will likely be too generic or incomplete to be useful.

In an underfitting scenario, both training and validation errors remain high, indicating the model hasn't learned the data well.

Understanding Overfitting: Learning Too Much Detail

Now, imagine the opposite. You're preparing for that exam, and instead of understanding the subject, you memorize every single punctuation mark in the textbook examples. You might ace a test that uses those exact examples, but if the questions are slightly different, you'll struggle. This is overfitting.

An autoencoder overfits when it learns the training data too specifically, including any noise or random fluctuations present in that particular dataset. It becomes so attuned to the training examples that it fails to generalize to new, unseen data. So, you'll see a very low reconstruction error on the training data, but a much higher error when you test it with data it hasn't encountered before.

Why does overfitting happen?

• Model too complex: If the autoencoder has too many layers or neurons relative to the amount or complexity of the training data, it has the capacity to memorize instead of learn general patterns.
• Bottleneck not restrictive enough: If the bottleneck isn't forcing sufficient compression, the model might just pass data through without learning meaningful compact representations.
• Training for too long: Given enough time, a complex model can start to memorize the noise in the training data.

An overfit autoencoder might give you beautiful reconstructions of your training images, but the features it extracts might be too tailored to those specific images and not very useful for broader applications.

Overfitting is characterized by a decreasing training error but an increasing validation error after a certain point.

The Goal: A Good Fit

What we're aiming for is a good fit. This is when the autoencoder learns the true underlying patterns from the training data well enough to generalize to new data. It doesn't just memorize the training set, nor is it too simple to capture the important information. Both the training error and the error on unseen data (often called validation or test error) are low and close to each other.

A well-fitted model shows both training and validation errors converging to a low value.

Why Does This Matter for Autoencoders?

Even though autoencoders are typically trained in an unsupervised manner (just trying to reconstruct the input), the quality of the learned representation in the bottleneck layer is very important.

• If your autoencoder underfits, the bottleneck representation will be too crude and won't capture much useful information about your data.
• If your autoencoder overfits, the bottleneck representation might be too specific to the noise and quirks of your training data. It won't be a good, general-purpose feature representation for other tasks or new data.

So, while we're minimizing reconstruction error, we also need to be mindful of whether our model is learning generalizable features or just memorizing.

This is just a quick introduction to these ideas. There are various techniques to help prevent overfitting and ensure your model generalizes well, such as adjusting the model's complexity, using regularization methods, or stopping training at the right time (a technique called early stopping). We won't go into these deeply now, but it's good to be aware of these common challenges as you start with autoencoders and other machine learning models. As you prepare to build your first autoencoder, keeping these potential issues in mind will help you better understand the training process and evaluate your model's performance.