Forward passes and loss

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Beginner explanation

A forward pass runs inputs through the network to get a prediction. A loss function measures how wrong that prediction is according to a chosen rule. The rule should match the task, because different errors can have different consequences.

Intermediate explanation

Mean squared error averages squared numeric prediction errors. Classification often uses cross-entropy with probabilities or logits handled by a suitable implementation. Training loss guides optimization; evaluation metrics describe behavior that matters to users.

Advanced explanation

Empirical risk is the average loss over observed training examples, often combined with a regularization penalty. Minimizing it does not guarantee minimum real-world error. A loss is a surrogate objective and can misrepresent asymmetric operational costs.

PUT IT IN CONTEXT

A worked example

Predictions [4, 7] for true values [2, 8] produce squared errors 4 and 1. Mean squared error is (4 + 1)/2 = 2.5. A single larger miss can dominate because the errors are squared.

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Practice the idea

For predictions [3, 5] and targets [1, 5], compute mean squared error and mean absolute error.

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Reveal the answer guide

The errors are 2 and 0. MSE = (4 + 0)/2 = 2; MAE = (2 + 0)/2 = 1. Both summarize the same predictions differently.

Go further: advanced challenge

Give a case where the model with lower average loss still creates more harmful errors. Propose a complementary evaluation metric.

An open-ended discussion task. Explain your assumptions and evidence; there may be more than one defensible answer.

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