L1 and L2 Loss

L1 Loss vs L2 Loss

• Robustness: L1 > L2

  Intuitively speaking, since a L2-norm squares the error (increasing by a lot if error > 1), the model will see a much larger error than the L1-norm, so the model is much more sensitive to outliers.

• Stability: L2 > L1

  In the case of a more “outlier” point, both norms still have big change, but again the L1-norm has more changes in general.

• Solution uniqueness: Minimizing the L2 loss corresponds to calculating the arithmetic mean, which is unambiguous, while minimizing the L1 loss corresponds to calculating the median, which is ambiguous if an even number of elements are included in the median calculation, So L2 has unique solution while L1 has multiple solution

• Smooth l1 loss

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Smooth L1 loss that is less sensitive to outliers than the L2 loss used in R-CNN and SPPne.