 $$\begin{aligned}         d({{{{\bm{x}}_\text{next}}'}}, {{{{\bm{s}}_\text{next}}'}}, {\overline{\sigma}}) &= \norm{T_{{{{{\bm{x}}_\text{next}}'}}} {{{{\bm{s}}_\text{next}}'}}- {\overline{\sigma}}{\bm{e}}}_F