Smooth l1 loss

$$\ell (x,y)=L=\{l_1,...,l_N{\}}^T$$

With

$$l_n=\{\begin{array}{ll}0.5(x_n-y_n{)}^2/beta,& \text{if }|x_n-y_n|<beta\\ |x_n-y_n|-0.5\ast beta,& \text{otherwise }\end{array}$$

If reduction is not none, then:

$$\ell (x,y)=\{\begin{array}{ll}\mathrm{mean}(L),& \text{if reduction}=\text{`mean';}\\ \mathrm{sum}(L),& \text{if reduction}=\text{`sum'.}\end{array}$$

等有机会 plot 一下。