In the context of parametrized predictors, which aspect most directly influences the model's capacity to generalize to unseen data?

In a parametrized predictor, the amount of flexibility the model has—often measured by the number of free parameters or the complexity of its hypothesis class—most directly determines how well it can generalize to new data. If the model is too simple, it will underfit and miss important patterns; if it is too complex, it will overfit the training data and perform poorly on unseen examples. Regularization techniques, such as adding a penalty on large weights, effectively reduce this capacity to keep the model within a sweet spot. For instance, a linear model with 1000 features can fit almost any training set, but adding L2 regularization shrinks the weights and helps it predict new points more accurately. Thus, controlling model complexity is the key factor for good generalization.