Intrinsic Muon provides closed-form linear maximization oracles on multiple Riemannian matrix manifolds for unitarily invariant norms, with convergence rates depending only on manifold dimension or rank.
Manifold constrained steepest descent
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Manifold constraints via the new MACRO optimizer independently bound activation scales and enforce rotational equilibrium in LLM pre-training, subsuming RMS normalization and decoupled weight decay while delivering competitive performance with convergence guarantees.
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Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
Intrinsic Muon provides closed-form linear maximization oracles on multiple Riemannian matrix manifolds for unitarily invariant norms, with convergence rates depending only on manifold dimension or rank.