Algorithm 7 Weighted Softmax Loss with Edge Penalty

Require: $y,\widehat{y}$ Initialize $grad$ and $hess$ as zero matrices of the same shape as $\widehat{y}$ Define class pair weights Set $extra\_penalty\leftarrow 1.2$ for $i=0$ to $len\left(y\right)-1$ do     for $j=0$ to $columns\left(\widehat{y}\right)-1$ do         $weight\leftarrow$ weight for the pair $(min(y\left[i\right],j),max(y\left[i\right],j\left)\right)$         $prob\leftarrow \widehat{y}[i,j]$         $penalty\leftarrow extra\_penalty$ if $y\left[i\right]$ or j is an edge class, else 1         $grad[i,j]\leftarrow penalty\times weight\times (prob-(y\left[i\right]==j\left)\right)$         $hess[i,j]\leftarrow penalty\times weight\times prob\times (1-prob)+0.02$     end for end forreturn  $grad,hess$