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Learning curves and diagnosing generalization

A learning curve studies how training and held-out performance change as the amount of training data increases.

Imagine fitting the same model family with 100, 500, 1,000 and 5,000 examples. For each size, record both training error and validation error.

Two common patterns are informative:

  • If training and validation errors are both high and close together, the model is often underfitting. More data alone may not fix the limitation.
  • If training error is low but validation error is substantially higher, the model is overfitting. More data, stronger complexity control or a less flexible representation may help.

Learning curves are not proofs of a diagnosis, but they distinguish situations that a single final score cannot. They also answer a practical question: is collecting more data likely to help?

The comparison must use the same evaluation protocol across training sizes. Otherwise a changing split, leakage or inconsistent preprocessing can masquerade as a learning effect.