Regularization

Definition

Regularization is a method for discouraging overfitting.

Simple form:

training objective + constraint or penalty

The goal is to guide the model toward solutions that work better on unseen data.

Regularization pushes learning away from overly specific fits.

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Why Regularization Is Needed

A model may find a solution that fits training data very well but generalizes poorly.

Regularization changes what kind of solution is preferred.

Example:

not just low training loss
also simpler or more stable behavior

Regularization changes the model's preference among possible solutions.

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Regularization As Constraint

Regularization can act like a constraint on the model.

Examples:

penalize large weights
drop some activations during training
stop training before overfitting
limit model complexity

Different methods constrain different parts of learning.

A regularizer narrows the kinds of solutions the model is encouraged to choose.

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Regularization Is Not Always More Better

Too little regularization may allow overfitting.

Too much regularization may cause underfitting.

weak regularization -> unstable or overly specific fit
strong regularization -> model cannot learn enough

The amount matters.

Regularization must be strong enough to help, but not so strong that it blocks learning.

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Common Regularization Methods

Examples include:

L1 regularization
L2 regularization
dropout
early stopping
data augmentation
weight decay

Each method shapes learning differently.

The next topics focus on several common ones.

Regularization is a family of methods, not one single technique.

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Final Summary

• Regularization discourages overfitting.
• It adds constraints or penalties to learning.
• It changes which solutions the model prefers.
• Too much regularization can cause underfitting.
• L1, L2, dropout, and early stopping are common examples.