The Problem of Overfitting

When training a neural network, the primary objective is to minimize the loss function on the training dataset. Optimization algorithms, such as gradient descent and its variants, are commonly employed for this task. However, simply achieving a very low loss on the data the model was trained on doesn't guarantee good performance in practical application. This brings us to a common challenge in developing machine learning models: overfitting.

What is Overfitting?

Overfitting occurs when a model learns the training data too well. Instead of capturing the underlying patterns and relationships in the data that generalize to new examples, the model starts memorizing the specific details and noise present only in the training set. Imagine studying for an exam by memorizing the exact answers to practice questions. You might ace the practice test, but you'd likely struggle with new questions covering the same concepts because you didn't learn the underlying principles. An overfitted model behaves similarly; it performs exceptionally well on the data it has already seen but fails to generalize to unseen data.

This leads to a situation where the model has low bias (it fits the training data closely) but high variance (its predictions change drastically with different training sets and it performs poorly on new data). The opposite problem, underfitting, occurs when the model is too simple to capture the underlying structure of the data, resulting in poor performance on both the training and validation sets (high bias). Our goal is usually to find a sweet spot between these two extremes.

Why Does Overfitting Happen?

Several factors can contribute to overfitting:

1. Model Complexity: Deep neural networks, with their potentially large number of layers and neurons, have a high capacity to learn intricate patterns. If the model's capacity is much greater than needed for the complexity of the underlying task, it can easily start fitting the noise in the training data instead of the true signal. A very deep or wide network might find complex decision boundaries that perfectly separate the training examples but are overly sensitive to minor variations.
2. Insufficient Training Data: If the amount of training data is limited or not representative of the true data distribution, the model might latch onto spurious correlations or specific examples present only in that small sample. With more diverse data, the model is encouraged to learn more general patterns that hold true across different examples.
3. Excessive Training Time: Training a model for too many epochs can also lead to overfitting. Initially, the model learns general patterns, and both training and validation performance improve. However, after a certain point, the model might begin fine-tuning itself to the noise and specific idiosyncrasies of the training set, causing the validation performance to degrade even as the training performance continues to improve.

Detecting Overfitting

The most common way to detect overfitting is by monitoring the model's performance on both the training set and a separate validation set during the training process.

• Training Performance: This is typically measured using the loss function and relevant metrics (like accuracy for classification) calculated on the data the model is being trained on.
• Validation Performance: This is measured using the same loss and metrics but calculated on a separate dataset (the validation set) that the model does not see during the gradient updates. This set acts as a proxy for unseen data.

If the model is learning well and generalizing, both the training and validation loss should decrease, and the relevant metrics should improve. However, if overfitting starts to occur, you'll typically observe:

• Training loss continues to decrease (or stays very low).
• Validation loss starts to increase after reaching a minimum point.
• Training metrics (e.g., accuracy) continue to improve or stay high.
• Validation metrics (e.g., accuracy) plateau or start to decrease.

This divergence between training and validation performance is a clear indicator of overfitting. Visualizing the training and validation loss/metrics over epochs is a standard practice.

Typical learning curves showing the training loss consistently decreasing while the validation loss begins to increase after around epoch 25, indicating the onset of overfitting.

The ultimate goal of building a machine learning model is generalization: the ability to make accurate predictions on new, previously unseen data. Overfitting is a direct obstacle to achieving good generalization. Therefore, understanding, detecting, and mitigating overfitting are essential skills for any deep learning practitioner. The subsequent sections in this chapter will introduce several techniques specifically designed to combat overfitting and improve the generalization performance of your models.