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The behaviour of dice loss when target and prediction are disjoint

Cross Validated Asked by BMurray on March 4, 2021

I’ve been struggling with the implication of the dice loss value generated when t (target label) and p (predicted label) are entirely disjoint. Dice score being (2pt)/(p+t), this value is zero (or very close with epsilon being involved) for all disjoint but non-empty t and p. The derivative of the dice score is (2t^2)/((p+t)^2), which means that there is still gradient when t and p are disjoint, provided that t is not empty. Does this mean that dice performs poorly from a training standpoint as a loss when t and p are disjoint or does it just mean that it isn’t informative as a metric (i.e. that dice loss returns 1 due to dice score returning 0 as its numerator is always zero when t and p are disjoint)?

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