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I still feel that the whole expression could be clarified quite easily be writing a \Sum_{a, b} at the front?

But that would sum everything, not just the parts which need it. You'd actually have to write this:

\sum_a(A_ia x_a) + v_i + \sum_a(x_a y_a) ( w_i + \sum_b(B_ib z_b) )

My example is actually still easier without indices. (Although you lose some information, like the fact that x & y are vectors in the indexed by a,b.) Here it's clear that Ax and x⋅y each involve a sum, which never includes v:

Ax + v + (x⋅y)(w + Bz)

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