Reproduce “Stochastic Rounding Increases Small Singular Values” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Linkai Ma, Tingzhou Yu, Petros Drineas
The paper analyzes stochastic rounding for low-precision matrices, where each entry is randomly mapped to neighboring representable values with probabilities that preserve its expectation. It proves rounding noise can raise the smallest singular value when d is at most a sufficiently small constant times n, and can increase expected tail energy under spectral-gap conditions. These are theoretical bounds, not training results.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.