Say, there are two neural network layers with weights $W_1$ and $W_2$. These two layers are part of a larger network but their inputs are completely independent of each other and their outputs could be joined somehow and propagated jointly in subsequent layers.
So, a vanilla L2 term discourages the weight matrices from learning too big values. But if I calculate the Frobenius norm of $W_1$ and $W_2$, subtract one from the other and add that as a regularization term, what would that mean? Mathematically,
$L(\centerdot) + \lambda (||W_1||_F - ||W_2||_F) $ where $\lambda$ is some rate parameter.
What would this sort of regularization do to the learning? Can we say this term would encourage $W_1$ and $W_2$ to be 'similar'? How would it affect the outputs of these layers?