Balancing Early Performance Sacrifices with Long-Term Gains: Scaling Learning-Rate Warmup Duration Across Training Horizons

arXiv:2609.33041 · cs.LG · Submitted 2026-09-27 · Read on arXiv

cs.LG

Submitted: 2026-09-27

Updated: 2026-09-27

Code: https://github.com/jiaweizzhao/GaLore

Terminology

• Regret — 66× in this paper · explained in 3 episodes
• In International Conference on Learning Representations — 9× in this paper
• Scaling Laws — 6× in this paper · explained in 4 episodes
• Ablation — 5× in this paper · explained in 1 episode
• Benchmark — 4× in this paper · explained in 2 episodes
• Embeddings — 4× in this paper · explained in 2 episodes
• In International Conference on Machine Learning — 4× in this paper
• Robustness — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Annealing Effects — 1× in this paper · explained in 1 episode
• Distillation — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Transfer Learning — 1× in this paper · explained in 10 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Why Do We Need Warm-up? A Theoretical Perspective
• Scaling Optimal LR Across Token Horizons
• Learning Curves for SGD on Structured Features
• Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks
• A Dynamical Model of Neural Scaling Laws
• Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability
• Self-Stabilization: The Implicit Bias of Gradient Descent at the Edge of Stability
• DeepSeek-V3 Technical Report
• Time Transfer: On Optimal Learning Rate and Batch Size In The Infinite Data Limit
• A Loss Curvature Perspective on Training Instability in Deep Learning
• Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour
• The Llama 3 Herd of Models
• Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations
• Why Warmup the Learning Rate? Underlying Mechanisms and Improvements
• Scaling Laws for Neural Language Models
• Kimi K2: Open Agentic Intelligence
• Analyzing & Reducing the Need for Learning Rate Warmup in GPT Training
• Predictable Scale: Part I, Step Law -- Optimal Hyperparameter Scaling Law in Large Language Model Pretraining
• Muon is Scalable for LLM Training
• On the Variance of the Adaptive Learning Rate and Beyond

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