Consider the training dataset D $=\{($x$1,$ y$1),...,($xn$,$ yn$)\}$ with n samples where xi in Rd$1,$ yi in R for

all i in $[$n$].$ Let H in Rd$2\backslash$times d$1$ be a fixed matrix, and let s : Rd$2->$ Rd$2$ be the softmax function, that ezi

is ith output s$($z$)$i :$=$ Pd$2$ ezi $.$ A sample xi from input dataset, goes through the transformations i$=1$

depicted in Figure $1.$ And our prediction y$$i $=$ z$$i $\backslash$theta $.$ As a result, for a single sample $($xi$,$ yi$),$ we can construct a regression loss function as: