# Questions tagged [l2-regularization]

For questions related to $L_2$ regularization (aka ridge regression or weight decay), a special case of Tikhonov regularization where the Tikhonov matrix is a multiple of the identity matrix.

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### What are the consequences when we multiply, instead of add, a penalty term?

The typical objective function in regression problems like Lasso or Ridge includes a Residual Sum of Squares (RSS) term added to a penalty term based on a norm of the coefficients. What are the ...
73 views

### How do L2 norm and Jacobian act as a regularisation term to encourage smoothness in a deformation field?

How do L2 norm and The Jacobian act as a regularisation term to encourage smoothness in a deformation field? from the VoxelMorph original paper (here) they used Jacobian as a means to smoothen the ...
618 views

### Would either $L_1$ or $L_2$ regularisation lower the MSE on the training and test data?

Consider linear regression. The mean squared error (MSE) is 120.5 for the training dataset. We've reached the minimum for the training data. Is it possible that by applying Lasso (L1 regularization) ...
40 views

### What is the effect of too harsh regularization?

While training a CNN model, I used an l1_l2 regularization (i.e. I applied both $L_1$ and $L_2$ regularization) on the final layers. While training, I saw the ...
62 views

### When is using weight regularization bad?

Regularization of weights (e.g. L1 or L2) keeps them small and standardized, which can help reduce data overfitting. From this article, regularization sounds favorable in many cases, but is it always ...
144 views

### Why does L1 regularization yield sparse features?

In contrast to L2 regularization, L1 regularization usually yields sparse feature vectors and most feature weights are zero. What's the reason for the above statement - could someone explain it ...
114 views

### Does L1/L2 Regularization help reach an optimum result faster?

I understand that L1 and L2 regularization helps to prevent overfitting. My question is then, does that mean they also help a neural network learn faster as a result? The way I'm thinking is that ...
I'm learning logistic regression and $L_2$ regularization. The cost function looks like below. $$J(w) = -\displaystyle\sum_{i=1}^{n} (y^{(i)}\log(\phi(z^{(i)})+(1-y^{(i)})\log(1-\phi(z^{(i)})))$$ And ...