Effective Learning Rate Governs Loss Dynamics in Language Model Pretraining
cs.LG, stat.ML
Submitted: 2026-08-25
Updated: 2026-08-25
Code: https://github.com/KellerJordan/modded-nanogpthttps:
Project page: http://skylion007.github.io
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Optimal Learning Rate Schedules under Functional Scaling Laws: Power Decay and Warmup-Stable-Decay
- Efficient Hyperparameter Tuning via Trajectory Invariance Principle
- Muon is Scalable for LLM Training
- RoBERTa: A Robustly Optimized BERT Pretraining Approach
- Weight Norm Control
- LLaMA: Open and Efficient Foundation Language Models
- L2 Regularization versus Batch and Weight Normalization
- GradPower: Powering Gradients for Faster Language Model Pre-Training
- Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimization
- Hyperball May Not Be a Free Lunch
- Controlled LLM Training on Spectral Sphere
- Qwen3 Technical Report
- On the Nonlinearity of Learning Rate Scaling for LLM Training
- Kimi Linear: An Expressive, Efficient Attention Architecture
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