Once you initiate the training process, often by calling a function like fit in Keras or managing a training loop in PyTorch, the framework begins the iterative process of adjusting model weights based on the training data. However, training a neural network isn't a task you can simply start and walk away from. It's essential to observe how the training is progressing to understand if the model is learning effectively, learning too slowly, or perhaps learning the training data too well at the expense of generalizing to new data (overfitting).

Why Monitor?

Monitoring training provides critical insights into the learning dynamics. By tracking key indicators over time (typically across training epochs), you can diagnose problems, make informed decisions about when to stop training, and gather clues for how to improve the model or the training setup. The two primary types of indicators you'll monitor are loss and performance metrics.

Tracking Loss: Training vs. Validation

The loss function quantifies how far the model's predictions are from the actual target values during training. Lower loss generally indicates a better-performing model on the data being evaluated. It's standard practice to monitor two types of loss:

Training Loss: Calculated on the batch of data used for gradient computation and weight updates in the current training step. A decreasing training loss shows the model is learning to fit the training data.
Validation Loss: Calculated on a separate validation dataset that the model does not train on. This provides an estimate of how well the model generalizes to unseen data. Comparing training loss and validation loss is fundamental for diagnosing overfitting.

Tracking Performance Metrics: Beyond Loss

While loss guides the optimization process, it might not always be the most intuitive measure of performance. For instance, knowing the cross-entropy loss is 0.1 doesn't immediately tell you how many classifications were correct. Therefore, we also track performance metrics relevant to the task.

Training Metrics: Calculated on the training data, similar to training loss. Common examples include accuracy for classification tasks or Mean Absolute Error (MAE) for regression.
Validation Metrics: Calculated on the validation dataset. These metrics (e.g., validation accuracy) provide a more realistic assessment of the model's performance on unseen data during training.

Most deep learning frameworks make it easy to specify which metrics to track alongside the loss function when you configure or compile the model.

How Frameworks Report Progress

During training, frameworks like Keras or libraries like PyTorch Lightning typically print the loss and metric values at the end of each epoch. You might see output like this:

Epoch 1/20
1500/1500 [==============================] - 5s 3ms/step - loss: 0.4521 - accuracy: 0.8534 - val_loss: 0.2105 - val_accuracy: 0.9312
Epoch 2/20
1500/1500 [==============================] - 4s 3ms/step - loss: 0.1855 - accuracy: 0.9432 - val_loss: 0.1520 - val_accuracy: 0.9558
...
Epoch 20/20
1500/1500 [==============================] - 4s 3ms/step - loss: 0.0412 - accuracy: 0.9870 - val_loss: 0.0950 - val_accuracy: 0.9715

This output shows the epoch number, progress within the epoch, time taken, training loss, training accuracy, validation loss, and validation accuracy.

Furthermore, the training function often returns a history object (the name might vary slightly depending on the framework). This object stores the loss and metric values recorded for each epoch, allowing you to analyze and visualize the training trends after the process completes.

# Example using Keras history object (conceptual)
# history = model.fit(train_data, train_labels, epochs=20, validation_data=(val_data, val_labels))

# Accessing logged data
# training_loss = history.history['loss']
# validation_loss = history.history['val_loss']
# training_accuracy = history.history['accuracy']
# validation_accuracy = history.history['val_accuracy']

# You can then use libraries like Matplotlib or Plotly to plot these values

Interpreting Training Curves

Plotting the training and validation loss/metrics against epochs is the most effective way to understand training dynamics. Here are common patterns:

Healthy Convergence

Ideally, both training and validation loss decrease steadily and converge, while training and validation metrics increase and converge. This indicates the model is learning well and generalizing effectively.

Training and validation loss decrease and plateau together.

Training and validation accuracy increase and plateau together.

Overfitting

A common problem where the model learns the training data too specifically, including its noise and idiosyncrasies. This results in poor performance on new, unseen data. Overfitting is typically identified when:

Training loss continues to decrease.
Validation loss begins to increase after some point.
Training metrics might continue to improve.
Validation metrics plateau or start to decrease.

Training loss keeps decreasing while validation loss starts to increase, indicating overfitting.

Underfitting

This occurs when the model is too simple to capture the underlying patterns in the data, or it hasn't been trained for enough epochs. Signs include:

Both training and validation loss remain high or plateau quickly at a high value.
Both training and validation metrics are low and fail to improve significantly.

Both training and validation loss plateau at a high value, suggesting the model cannot adequately learn the data patterns.

Other Issues

Noisy Curves: Very jagged or unstable loss/metric curves might suggest the learning rate is too high, causing the optimization process to overshoot minima.
Slow Convergence: If the loss decreases very slowly, the learning rate might be too low, or the optimization algorithm might be stuck.

The Role of the Validation Set

It's essential to monitor performance on a validation set separate from both the training set and the final test set. The validation set provides an unbiased estimate of how the model is generalizing during training. It helps detect overfitting early and informs decisions like when to stop training (a technique called Early Stopping, discussed later). The final test set should only be used after training is complete and model selection/tuning (based on the validation set) is finished, to get a final, unbiased evaluation of the chosen model's performance.

In the upcoming practical exercise where you train a classifier on the MNIST dataset, pay close attention to these curves (loss, accuracy, val_loss, val_accuracy). Observing these trends is a fundamental skill in applied deep learning. Understanding these patterns is the first step towards addressing potential issues, which often involves techniques like regularization or hyperparameter tuning, topics we will cover shortly.