Training a neural network isn't a one-shot calculation. Instead, it's an iterative process where the network gradually learns from the training data. This iterative refinement happens within what's commonly called the training loop. Understanding this loop's structure is fundamental to grasping how models learn.

At its core, the training loop repeatedly performs a sequence of steps designed to adjust the network's parameters, the weights $W$ and biases $b$ , so that its predictions get closer to the actual target values over time. Think of it as a systematic way of showing the network examples, evaluating its performance, and telling it how to adjust itself to do better next time.

The typical training loop involves iterating over the dataset multiple times. Each complete pass over the entire training dataset is called an epoch. Within each epoch, the data is usually processed in smaller chunks called batches or mini-batches.

Here's a breakdown of the essential steps executed within a single iteration of the training loop, typically operating on one batch of data:

Fetch a Batch: Select a small subset (batch) of the training data (inputs $X_{batch}$ and corresponding target outputs $Y_{batch}$ ). Using batches rather than the entire dataset at once makes the computation more manageable, especially for large datasets, and often leads to faster convergence and better generalization due to the stochastic nature of the updates.
Forward Propagation: Feed the input data ( $X_{batch}$ ) through the network, layer by layer, applying linear transformations (using current $W$ and $b$ ) and activation functions to generate predictions ( $\hat{Y}_{batch}$ ). This is the process detailed in Chapter 3.
Calculate Loss: Compute the discrepancy between the network's predictions ( $\hat{Y}_{batch}$ ) and the actual target values ( $Y_{batch}$ ). This uses a chosen loss function, $L$ , such as Mean Squared Error (MSE) for regression or Cross-Entropy Loss for classification, as discussed in Chapter 4. The loss quantifies how wrong the network's predictions are for the current batch.
Backward Propagation (Backprop): Calculate the gradients of the loss function with respect to each parameter in the network (e.g., $\frac{\partial L}{\partial W}$ and $\frac{\partial L}{\partial b}$ for all weights and biases). This process, also covered in Chapter 4, uses the chain rule to determine how much each parameter contributed to the overall loss. These gradients indicate the direction of steepest ascent of the loss function.
Update Parameters: Adjust the network's weights and biases to minimize the loss. This is typically done using an optimization algorithm like Gradient Descent or its variants (e.g., Adam, RMSprop). The parameters are updated in the direction opposite to their gradients, scaled by a learning rate ( $\eta$ ): $W = W - \eta \frac{\partial L}{\partial W}$ $b = b - \eta \frac{\partial L}{\partial b}$ This step nudges the parameters in a direction that should reduce the loss on the next iteration.

These five steps constitute one training iteration or step. The loop repeats these steps for all batches within an epoch, and then repeats the entire process for multiple epochs.

The overall structure can be visualized as follows:

A typical neural network training loop structure, iterating through epochs and processing data in batches. Each batch goes through forward propagation, loss calculation, backpropagation, and parameter updates.

During training, it's essential to monitor the network's performance, usually by tracking the loss and accuracy (for classification tasks) on both the training set and a separate validation set after each epoch or even after a certain number of iterations. This helps in diagnosing issues like overfitting or underfitting and deciding when to stop training (as discussed further in Chapter 6).

While deep learning frameworks like TensorFlow and PyTorch provide high-level abstractions that often hide the explicit loop structure from the user, understanding this fundamental flow is important for debugging, customizing training procedures, and interpreting model behavior. The next sections will guide you through implementing these steps to build and train your first network.