Why can model weights become large and why is it necessary to reduce them with regularization?

Model weights can become large due to excessive model complexity or insufficient regularization, leading to overfitting — the model fits the training data too closely, losing its ability to generalize.

Large weights may indicate that the model is reacting too strongly to individual features, which reduces its robustness.

Regularization helps to reduce the magnitude of weights by adding a penalty for their size to the loss function (e.g., L1 or L2 regularization). This promotes a simpler and more generalizable model, improving its ability to work with new data.

Example of L2 regularization in the loss function:

loss = original_loss + lambda_ * sum(w**2 for w in weights)

where lambda_ is the regularization coefficient controlling the penalty level.