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.
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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.
Fisher-information-guided margin refinement reorganizes the Voronoi tessellation of an LLM's latent space to raise median token margins by 28% with no benchmark degradation, though gains concentrate on high-frequency structural tokens.
Pion is an optimizer that preserves the singular values of weight matrices in LLM training by applying orthogonal equivalence transformations.
Muon+ adds one normalization step after polar orthogonalization in the Muon optimizer, yielding lower training and validation perplexity and faster pre-training across 60M-7B models.
citing papers explorer
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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.
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Demystifying Manifold Constraints in LLM Pre-training
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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Geometric Properties of the Voronoi Tessellation in Latent Semantic Manifolds of Large Language Models
Fisher-information-guided margin refinement reorganizes the Voronoi tessellation of an LLM's latent space to raise median token margins by 28% with no benchmark degradation, though gains concentrate on high-frequency structural tokens.
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Pion: A Spectrum-Preserving Optimizer via Orthogonal Equivalence Transformation
Pion is an optimizer that preserves the singular values of weight matrices in LLM training by applying orthogonal equivalence transformations.
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MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training
Muon+ adds one normalization step after polar orthogonalization in the Muon optimizer, yielding lower training and validation perplexity and faster pre-training across 60M-7B models.
- Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers