Consider input vectors $xn$ in the equation below:

$yn=Nm=1,$anmxm

where we define coefficients anm:

anm$=$exp$\frac{xTnxm}{}N{m}^{\text{'}}=1$exp$(xTn{x}^{\text{'}})$

Show if input vectors are perpendicular to each other such that for $nmxnTxm=0.$ As a result output vectors are equal to input vectors. $(yn=xn$ for $n=1,$dots,$N$

As a result of this proof if attention mechanism inputs dont have any close relationship with each other they dont effect each other and and they appear with no change in the output$)$