Low-rank factorization drops the global smoothness constant: Burer–Monteiro objectives are 2/3-generalized smooth, so step sizes adapt online
The Burer–Monteiro factorized objective for low-rank matrix minimization is shown to be generalized smooth with exponent 2/3, and adaptive gradient descent and SafeAdam built on that property match or beat Dyn-NoLips on SymNMF text and image benchmarks without tuning relative-smoothness kernel parameters.