A framework that builds tractable structured Hessian approximations by averaging over user-chosen weight-space symmetry groups, recovering Shampoo-like estimates for one choice of group.
arXiv preprint arXiv:2511.11163 , year=
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Double preconditioning (DoPr) improves downstream task performance in test-time feedback settings without consistent gains in validation loss.
Proposes equivariant optimizer updates matched to layer symmetries for embeddings, SwiGLU MLPs, and MoE routers, with reported gains in validation loss and training stability on several language model architectures.
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Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers
Proposes equivariant optimizer updates matched to layer symmetries for embeddings, SwiGLU MLPs, and MoE routers, with reported gains in validation loss and training stability on several language model architectures.