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Three datasets, three different jobs

The training examples determine the gradients that change weights. The validation examples help you compare settings or decide when to stop. The test examples provide an independent check of the final frozen model, as long as you have not used their outcomes to choose it.

All three supplied splits are generated from separate fixed random streams. They sample the same synthetic XOR task with an 8% chance of a label flip per example. They are small samples, so their observed noise and accuracy differ. Adding points changes only the training set. A held-out result here says nothing by itself about photos, language, medical decisions, or any other real-world task.

Follow the actual learning computation

Each neuron multiplies inputs by weights and adds a bias. Hidden layers use tanh, which smoothly maps a score between −1 and 1 and introduces nonlinearity. The final neuron uses sigmoid to produce a number between 0 and 1. We predict class 1 when that value is at least 0.5.

Training minimizes mean cross-entropy, plus an optional weight penalty. Backpropagation calculates sensitivities; gradient descent updates all parameters simultaneously. One epoch here is one full-batch update using every training example. Validation and test data never enter those updates. The network trace uses the current learned weights and the selected example; its animation does not change parameters.

Two useful measurements can disagree

Accuracy counts how many predictions cross the 0.5 threshold on the correct side. Cross-entropy also considers how much probability the model assigned to the observed label. A confidently wrong prediction can greatly increase loss without changing the number of mistakes. Compare both measures, and inspect individual errors.

The confusion matrix separates the two kinds of mistakes: observed 0 predicted as 1, and observed 1 predicted as 0. In another task those errors might have different consequences. In this project, neither class represents a real person or a consequential decision.

Honest reporting is part of the model

Saved candidates keep their settings, training additions, weights, and validation results. The same validation set is reused, so extensive experimentation can also overfit your choices to validation. The first untouched test evaluation is a useful final check, not a guarantee.

If you resume training after seeing the test, the project preserves that history and labels later test evaluations as practice. A model card should state the intended use, the data, the selection process, the results, and the limitations. Completion requires a trained, frozen model and text in each card section; it does not automatically grade the writing or certify the model’s quality.