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Why is it important/beneficial for an activation function to be zero-meaned?

The first part of this answer is regarding your concrete question and the second part summarizes things on activation functions in general because I believe that there are more important factors than ...
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Should the range of target values match the range of activation function used in the output layer?

Yes, you should use an activation function that match the range of your ground truth labels, or the other way around, i.e. apply a normalization function to the labels to match your activation ...
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Should the range of target values match the range of activation function used in the output layer?

If you have already trained your model to predict either -1 or 1, and now your target variable is either 0 or 1, if -1 predicted by your model is the same as 0 in your target variable, then there are ...
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