No, that's not how backprop works. There will be no discontinuity in a backpropagated gradient.
I did not say there will be a discontinuity in the gradient; I said that the modified loss function will not have a mathematically well-defined derivative because of the discontinuity in the function.
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I did not say there will be a discontinuity in the gradient; I said that the modified loss function will not have a mathematically well-defined derivative because of the discontinuity in the function.