The depth-3 model has recently gained much importance, as it has become a stepping-stone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper we take a step towards designing such hitting-sets. We define a notion of distance for multilinear depth-3 circuits (say, in n variables and k product gates) that measures how far are the partitions from a mere refinement. The 1-distance strictly subsumes the set-multilinear model, while n-distance captures general multilinear depth-3 . We design a hitting-set in time poly(ndeltalogk) for delta-distance. Further, we give an extension of our result to models where the distance is large (close to n) but it is small when restricted to certain variables. This implies the first subexponential whitebox PIT for the sum of constantly many set-multilinear depth-3 circuits.

We also explore a new model of read-once algebraic branching programs (ROABP) where the factor-matrices are invertible (called invertible-factor ROABP). We design a hitting-set in time poly(sizew2) for width-w invertible-factor ROABP. Further, we could do without the invertibility restriction when w=2. Previously, the best result for width-2 ROABP was quasi-polynomial time (Forbes-Saptharishi-Shpilka, arXiv 2013).

The common thread in all these results is the phenomenon of low-support 'rank concentration'. We exploit the structure of these models to prove rank-concentration after a 'small shift' in the variables. Our proof techniques are stronger than the results of Agrawal-Saha-Saxena (STOC 2013) and Forbes-Saptharishi-Shpilka (arXiv 2013); giving us quasi-polynomial-time hitting-sets for models where no subexponential whitebox algorithms were known before.