Contents
Why do we penalize large weights?
Large weights in a neural network are a sign of a more complex network that has overfit the training data. Penalizing a network based on the size of the network weights during training can reduce overfitting. An L1 or L2 vector norm penalty can be added to the optimization of the network to encourage smaller weights.
What does L2 regularization penalize?
L2 regularization forces weights toward zero but it does not make them exactly zero. L2 regularization acts like a force that removes a small percentage of weights at each iteration. Therefore, weights will never be equal to zero.
Why does L2 normalization cause weight decay?
This term is the reason why L2 regularization is often referred to as weight decay since it makes the weights smaller. Hence you can see why regularization works, it makes the weights of the network smaller.
What will happen if you use a very large value of the Hyperparameter λ?
If your lambda value is too high, your model will be simple, but you run the risk of underfitting your data. Your model won’t learn enough about the training data to make useful predictions. If your lambda value is too low, your model will be more complex, and you run the risk of overfitting your data.
How to penalize a model based on the size of the weights?
There are two parts to penalizing the model based on the size of the weights. The first is the calculation of the size of the weights, and the second is the amount of attention that the optimization process should pay to the penalty.
How can machine learning reduce the size of weights?
We can achieve this by penalizing the size of weights by adding to the cost function each of the weights squared, multiplied by some regularization paramater. Now, the Machine Learning algorithm will aim to reduce the size of the weights whilst retaining the accuracy on the training set.
What happens when weight regularization is too weak?
If the penalty is too strong, the model will underestimate the weights and underfit the problem. If the penalty is too weak, the model will be allowed to overfit the training data. The vector norm of the weights is often calculated per-layer, rather than across the entire network.