3 papers
math.OC2026
Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback
Maria Smirnova, Alexey Kravatskiy
SignMuon compresses the Muon update to one bit per parameter by taking its elementwise sign, providing the most direct way to run a matrix-aware optimizer under an extremely low co…
cs.NE2026
ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search
Alexey Kravatskiy, Valentin Khrulkov, Ivan Oseledets
LLM-guided evolutionary computation, most notably AlphaEvolve, has been remarkably successful in discovering novel mathematical constructions by solving challenging optimization pr…
math.OC2026
Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization
Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov +3
In this article, we explore the use of various matrix norms for optimizing functions of weight matrices, a crucial problem in deep learning. Moving beyond the spectral norm that un…