L2 penalty

The L2 penalty, also known as ridge regression, is similar in many ways to the L1 penalty, but instead of adding a penalty based on the sum of the absolute weights, the penalty is based on the squared weights. This means that larger absolute weights are penalized more. In the context of neural networks, this is sometimes referred to as weight decay. If you examine the gradient of the regularized objective function, there is a penalty such that, at every update, there is a multiplicative penalty to the weights. As for the L1 penalty, although they could be included, biases or offsets are usually excluded from this.

From the perspective of a linear regression problem, the L2 penalty is a modification to the objective function minimized, from ∑(y_i - ?_i) to ∑(y_i - ?_i) + λΘ2.