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Log(loss) is convex, which means that we can use gradient descent to find weights that result in a global minimum. 0 / 1 loss is not convex due to its abrupt decision boundary at z = 0, so it is difficult to optimize.
Convex
Log(loss) is convex, which means that we can use gradient descent to find weights that result in a global minimum. 0 / 1 loss is not convex due to its abrupt decision boundary at z = 0, so it is difficult to optimize.