To execute the training loop for a model from scratch, we instantiate the required components and begin the optimization process. For example, we initialize a linear regression model, `LinearRegressionScratch`, specifying hyperparameters such as the learning rate, `lr=0.03`. We then create the dataset using a class like `SyntheticRegressionData`, passing in ground truth parameter values. Next, an object-oriented `Trainer` is instantiated with settings such as `max_epochs=3`. Finally, training is executed by calling `trainer.fit(model, data)`, which orchestrates the iterations over the dataset to optimize the model's parameters.

Claude

The main training loop for a deep learning model executes a systematic, iterative process to optimize parameters $$\mathbf{w}$$ and $$b$$. During each epoch, the loop passes through the entire training dataset. For every iteration within an epoch, a minibatch $$\mathcal{B}$$ is processed. The model computes the loss for this minibatch and calculates the gradients of the loss with respect to each parameter using $$\mathbf{g} \leftarrow \partial_{(\mathbf{w},b)} \frac{1}{|\mathcal{B}|} \sum_{i \in \mathcal{B}} l(\mathbf{x}^{(i)}, y^{(i)}, \mathbf{w}, b)$$. Finally, the optimization algorithm updates the parameters using the rule $$(\mathbf{w}, b) \leftarrow (\mathbf{w}, b) - \eta \mathbf{g}$$. This cycle repeats until the training is complete.

Deep Learning Minibatch Training Loop

Dive into Deep Learning

When training a model such as linear regression from scratch on a synthetic dataset, the true underlying parameters are perfectly known. This provides a unique opportunity to evaluate the success of the training loop by directly comparing the ground truth weights and bias with the parameters learned by the model. While exactly recovering the true parameters is generally difficult or impossible for deep networks because unique solutions often do not exist, stochastic gradient descent typically discovers parameter configurations that yield highly accurate predictions.

Linear Regression Synthetic Data Training Evaluation

The `fit_epoch` method, typically registered within an object-oriented `Trainer` class, encapsulates the computations required for a single full pass over the training dataset. It begins by setting the model to training mode and iterating through the training dataloader to compute the loss via the `training_step` method. Within this loop, it zeroes the gradients, performs backpropagation, and updates the parameters. If a validation dataloader is provided, the method subsequently sets the model to evaluation mode and processes the validation batches within a no-gradient context to assess the model's performance.

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