$2\mathrm{.}6$ Using the Axiom of Completeness ${\displaystyle \underset{i=1}{\overset{n}{}}}{a}_i=F(x)-F(x^{\text{'}}),$ where $a_i$ denotes the attribution of variable

$i$ to the output $F(x)$ at input vector $x$ in comparison to output $F(x^{\text{'}})$ at baseline input $x^{\text{'}},$ one can verify

the correctness of numerical calculation of attribution $a_i$ for all $i^{\text{'}}s.$ But for this one needs to

evaluate $a_i$ for AAi, which can be daunting particularly for classification of high$-$resolution images.

However, if one is interested in evaluating and validating attributions for only a subset tilde$(x)$ of the set $x$ of

all input variables $($i$.$e$.$ specific input vectors $x$ and $x^{\text{'}}$ are different instances of $x),$ then which one of the

below expressions should one use in place of the original expression above:

a$)$ and $\{$:$x-(tilde(x))-=x^{\text{'}})-F(x^{\text{'}})$

b$)$ and $\{$:$x-(tilde(x))-=x^{\text{'}})-F(x^{\text{'}})$

c$),{\displaystyle \underset{\text{i}\text{i}\text{n}\text{t}\text{i}\text{l}\text{d}\text{e}(x)}{\overset{?}{}}}{a}_i=F(x)-F(x^{\text{'}})$

d$)$ none of the above.