Proposes equivariant optimizers matched to the symmetry groups of embeddings, SwiGLU projections and MoE routers, with experiments showing consistent gains over AdamW on language model pre-training.
Layer sharding for large-scale training with Muon.https://www.essential.ai/research/ infra, 2025
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Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers
Proposes equivariant optimizers matched to the symmetry groups of embeddings, SwiGLU projections and MoE routers, with experiments showing consistent gains over AdamW on language model pre-training.