The most widely used technique for solving large-scale semidefinite programs (SDPs) in practice is the non-convex Burer-Monteiro method, which explicitly maintains a low-rank SDP solution for memory efficiency. There has been much recent interest in obtaining a better theoretical understanding of the Burer-Monteiro method. When the rank r of the SDP solution is above the Barvinok-Pataki bound (where a globally optimal solution of rank at most r is guaranteed to exist), a recent line of work esta…