Loss Function Definition

Once a classification model produces predictions, you need a single number that tells you how often those predictions match the true labels. That number is classification accuracy. This article follows a practical route: first you watch a function that computes accuracy over a PyTorch data loader, then you predict what it should return, and only after that do you read the mechanism behind each line. The goal is not just to know the formula, but to locate the exact step where a result goes wrong when it does.

In this context, accuracy is defined as the number of correct predictions divided by the total number of examples. Written as a ratio, it looks like this: $\text{accuracy} = \frac{\text{correct predictions}}{\text{total examples}}$. The numerator counts matches between predicted and true labels. The denominator counts the examples the model was scored on.

The function is named calc_accuracy_loader. It takes a data loader, a model, a device, and an optional number of batches. The data loader yields batches, and each batch contains input examples together with their target labels. For every batch that falls within the requested number of batches, the function does four things in order. It moves the inputs and targets to the chosen device. It runs the model without tracking gradients. It reads only the logits for the last output token and takes the argument of the maximum along the final dimension to turn those logits into predicted labels. Finally, it compares the predicted labels with the target labels.

The function does not compute a separate accuracy for each batch. It keeps two running totals. After comparing one batch, it adds the number of matches to the correct counter and adds the batch size to the examples counter. The loop then moves to the next batch. When the loop ends, the function returns the ratio of the two running totals. Because the totals accumulate, the final number reflects every batch that was evaluated, not just the last one.

The num_batches argument controls how much of the loader is used. If it is left as None, the function uses every batch the loader provides. If a number is supplied, the function uses the smaller of that number and the loader's length, so requesting more batches than exist does not cause an error. Limiting the batches is a way to estimate accuracy more cheaply. The worked setting in this material uses 10 batches for that purpose. Because the denominator still counts examples, a limited run gives an estimate built from fewer examples, not a different kind of measurement.

Two other setup steps happen before any batch is scored. The function sets the device to CUDA when a GPU with Nvidia CUDA support is available and to the CPU otherwise, then moves the model to that device. It also calls model.eval() to switch the model into evaluation mode and wraps each forward pass in a no-gradient context, because no training update happens during measurement. The material also calls torch.manual_seed(123) before its accuracy calculations, so that comparing results across runs reflects the model and data rather than random variation in the setup.

Accuracy becomes useful for judgment, not just reporting, when you compare it with a baseline. In the spam classification setting, the two classes are non-spam (label 0) and spam (label 1). A random prediction would be right about 50% of the time because there are two classes. If the accuracies for the training, validation, and test splits all sit close to that level, the model is not yet performing well and needs fine-tuning. Fine-tuning means adjusting the model's parameters so that its performance improves on the specific task.

Fine-tuning cannot begin until a loss function is defined. A loss function measures the difference between the model's predictions and the true labels, and training optimizes against it. The stated objective in this setting is to maximize spam classification accuracy, which means the model should output the correct class label for each message. Accuracy is the measure you read after the fact; the loss function is what training actually pushes on. That is why a near-chance accuracy leads to a sequence of steps rather than a single fix.