Towards the reverse decomposition of unipotents

Decomposition of unipotents gives short polynomial expressions of the conjugates of elementary generators as products of elementaries. It turns out that with some minor twist the decomposition of unipotents can be read backwards, to give very short polynomial expressions of elementary generators themselves in terms of elementary conjugates of an arbitrary matrix and its inverse. For absolute elementary subgroups of classical groups this was recently observed by Raimund Preusser. I discuss various generalisations of these results for exceptional groups, specifically those of types $\mathrm E_6$ and $\mathrm E_7$, and also mention further possible generalisations and applications.