Regularization

A flexible model can fit training-specific patterns that do not help on unseen data. Regularization changes the fitting process to discourage some of that behavior. One approach adds a penalty based on the model's weights to the prediction loss. An L2 penalty uses a sum of squared weights and encourages shrinkage. An L1 penalty uses absolute values and, in methods such as Lasso, can produce exact zero coefficients. These penalties are mathematical definitions, so their values can be calculated for a given weight vector. For weights minus two and one, the unscaled L1 penalty is three, while the sum-of-squares L2 penalty is five. The total objective may be written as prediction error plus lambda times the penalty. Lambda determines how much influence that penalty has; it does not erase the prediction-error term. Dropout takes a different approach by randomly zeroing activations during training rather than permanently deleting neurons. Early stopping limits training based on a monitored criterion, often validation performance. Data augmentation can also help constrain what patterns a model learns by supplying relevant variations. None of these methods guarantees better performance in every task. Too much regularization can prevent a model from fitting useful structure. Compare training and validation behavior, choose settings with appropriate validation data, and reserve a separate test set for final evaluation when possible. L2 penalties should also not be treated as universally identical to optimizer weight decay: the Decoupled Weight Decay paper explains important differences for adaptive optimizers.