Kronecker products, low-depth circuits, and matrix rigidity
Josh Alman · 2021
For a matrix M and a positive integer r, the rank r rigidity of M is the smallest number of entries of M which one must change to make its rank at most r. There are many known applications of rigidity lower bounds to a variety of areas in complexity theory, but fewer known applications of rigidity upper bounds. In this paper, we use rigidity upper bounds to prove new upper bounds in a few different models of computation. Our results include: