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Why would we add regularization loss to the gradient itself in an SVM?

But then you need to find the gradient of this new loss; since gradients are additive, this is the same as the gradient of the unpenalized loss plus the gradient of the l2 term, the latter of which is … Note that it makes sense: when updating the weights, you will subtract some multiple of the gradient, so are moving the weights opposite their current location, i.e. toward the origin, as you expect regularization …
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