plots of cost function by number of iterations

Why does L2 regularization smooth the loss surface? went over my head.


1 Answer 1


You can think of minimising the MSE as finding an interpolating surface between the $(x_i, y_i)$ pairs. Regularisation is introduced to reduce the contribution of highly noisy single $ y_i $. From that perspective we'd expect the cost surface to become smoother, as we're biasing it be smoother!

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    $\begingroup$ "we're biasing it be smoother"... how? I thought we're biasing weights to be smaller. very confused. $\endgroup$ Commented Feb 19, 2018 at 17:22
  • $\begingroup$ smaller weights lead to a smoother function. How does it lead to a smoother cost function too? $\endgroup$ Commented Feb 19, 2018 at 17:28
  • $\begingroup$ Could you make your question more specific please? $\endgroup$
    – Tom Kealy
    Commented Oct 2, 2021 at 10:51

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