Author

Peter Richtárik

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Preprint Oct 2026

SCAFFOLD under Hessian Similarity: Sharp Convergence Rates

One of the main challenges of federated learning is heterogeneous data split among the clients, leading to biased local updates called client drift. The SCAFFOLD algorithm (Karimireddy et al., 2020) corrects client drift with control variates, but its relation to the similarity of client data is not yet fully understoo...

Zhirayr Tovmasyan, Slavomír Hanzely, Egor Shulgin et al. · 0 citations

#machine learning Preprint Oct 2026

A Quadratic Lens on Muon's Polar Update: Benefits, Pitfalls, and the Role of Newton-Schulz

PolarGD, the orthogonalized update at the core of Muon, is studied on matrix quadratics, where optimizers can be analyzed in closed form, and update directions under line search are compared to remove the effect of learning-rate tuning.

Egor Shulgin, S. Laing, Antonio Orvieto et al. · 0 citations