Normalize-Then-Precondition: A Hierarchical Approach to Marginal Scale and Interaction Geometry for LLM Training
cs.LG, cs.AI
Submitted: 2026-09-29
Updated: 2026-09-29
Code: https://github.com/zx-gong/NormPre
Project page: http://skylion007.github.io/OpenWebTextCorpus
Sources
- The Sharpness Disparity Principle in Transformers for Accelerating Language Model Pre-Training
- Muon is Scalable for LLM Training
- Mano: Restriking Manifold Optimization for LLM Training
- RMNP: Row-Momentum Normalized Preconditioning for Scalable Matrix-Based Optimization
- On the Width Scaling of Neural Optimizers Under Matrix Operator Norms I: Row/Column Normalization and Hyperparameter Transfer
- SWAN: SGD with Normalization and Whitening Enables Stateless LLM Training
- MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration
- Training Deep Learning Models with Norm-Constrained LMOs
- Old Optimizer, New Norm: An Anthology
- LLaMA: Open and Efficient Foundation Language Models
- Qwen3 Technical Report
- The Pile: An 800GB Dataset of Diverse Text for Language Modeling
- A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale
- NorMuon: Making Muon more efficient and scalable
- AdaMuon: Adaptive Muon Optimizer
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