When can we say that overfitting occurred to our machine learning model?

I When the model fails to train after several hours of runtime.
II When the gap between the training and test errors is too large, no matter the absolute level of one of the two error numbers.
III When the model cannot obtain a sufficiently low error value on the training set.
IV When the model performs well on the training set but fails miserably on the test set.

Question

When can we say that overfitting occurred to our machine learning model?

I	When the model fails to train after several hours of runtime.
II	When the gap between the training and test errors is too large, no matter the absolute level of one of the two error numbers.
III	When the model cannot obtain a sufficiently low error value on the training set.
IV	When the model performs well on the training set but fails miserably on the test set.

BlackTom AI · Accepted Answer

Here is a step-by-step examination of each option in the context of overfitting in machine learning.
Option I: 'When the model fails to train after several hours of runtime.' This describes a training-time issue such as resource constraints, convergence problems, or a bug, not a symptom of overfitting. Overfitting is about the model's behavior on unseen data, not about failing to complete training.
Option II: 'When the gap between the training and test errors is too large, no matter the absolute level of one of the two error numbers.' A very large generalization gap can signal overfitting, because the model captures noise in the training data and fails to generalize. However, saying 'no matter the absolute level' introduces ambiguity: if both errors are very high, the model is also underfitting; the gap alone isn’t a universal indicator in all contexts. Still, a consistently large gap with relatively low training error is a common red flag for overfitting.
Option III: 'When the model cannot obtain a sufficiently low error value on the training set.' If the training error remains high, the model is likely underfitting rather than overfitting. Overfitting is characterized by good training performance but poor generalization, not by poor training performance.
Option IV: 'When the model performs well on the training set but fails miserably on the test set.' This is the classic textbook symptom of overfitting: the model has learned patterns specific to the training data that do not generalize to unseen data, resulting in strong training performance but weak test performance.

In summary, Option I describes a training process issue, Option II could indicate overfitting but depends on the absolute error levels and context, Option III indicates underfitting, and Option IV aligns with the standard overfitting symptom of high training accuracy paired with poor test accuracy. The most precise and widely recognized overfitting signal among these choices is Option IV.

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