# WSM: Decay-Free Learning Rate Schedule via Checkpoint Merging for LLM Pre-training

arXiv: https://arxiv.org/abs/2507.17634 · HTML: https://mlsanity.com/paper/2507.17634/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 55 of its 69 references that are in the map.
- First posted on arXiv 23 Jul 2025.

## Builds on (most cited first, 30 of 55)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Know What You Don't Know: Unanswerable Questions for SQuAD](https://mlsanity.com/paper/1806.03822/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints](https://mlsanity.com/paper/2305.13245/) (2023)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [C-Eval: A Multi-Level Multi-Discipline Chinese Evaluation Suite for Foundation Models](https://mlsanity.com/paper/2305.08322/) (2023)
- [Language Models are Multilingual Chain-of-Thought Reasoners](https://mlsanity.com/paper/2210.03057/) (2022)
- [CMMLU: Measuring massive multitask language understanding in Chinese](https://mlsanity.com/paper/2306.09212/) (2023)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Efficient Training of Language Models to Fill in the Middle](https://mlsanity.com/paper/2207.14255/) (2022)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)

## Built on by (most cited first, 23 of 23)

- [LLaDA2.0: Scaling Up Diffusion Language Models to 100B](https://mlsanity.com/paper/2512.15745/) (2025)
- [Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2606.15007/) (2026)
- [Nemotron 3 Super: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2604.12374/) (2026)
- [How Learning Rate Decay Wastes Your Best Data in Curriculum-Based LLM Pretraining](https://mlsanity.com/paper/2511.18903/) (2025)
- [Pre-training LLM without Learning Rate Decay Enhances Supervised Fine-Tuning](https://mlsanity.com/paper/2603.16127/) (2026)
- [Every Attention Matters: An Efficient Hybrid Architecture for Long-Context Reasoning](https://mlsanity.com/paper/2510.19338/) (2025)
- [MergeMix: Optimizing Mid-Training Data Mixtures via Learnable Model Merging](https://mlsanity.com/paper/2601.17858/) (2026)
- [Nucleus-Image: Sparse MoE for Image Generation](https://mlsanity.com/paper/2604.12163/) (2026)
- [Low-rank Optimization Trajectories Modeling for LLM RLVR Acceleration](https://mlsanity.com/paper/2604.11446/) (2026)
- [PCMind-2.1-Kaiyuan-2B Technical Report](https://mlsanity.com/paper/2512.07612/) (2025)
- [Extra-Merge: Tracing the Rank-1 Subspace of Model Merging in Language Model Pre-Training](https://mlsanity.com/paper/2605.26484/) (2026)
- [MaP: A Unified Framework for Reliable Evaluation of Pre-training Dynamics](https://mlsanity.com/paper/2510.09295/) (2025)
- [Optimizing Visual Generative Models via Distribution-wise Rewards](https://mlsanity.com/paper/2607.02291/) (2026)
- [Mi:dm K 2.5 Pro](https://mlsanity.com/paper/2603.18788/) (2026)
- [WSqD: A Horizon-Free Learning Rate Schedule for Large Model Training](https://mlsanity.com/paper/2607.10959/) (2026)
- [Let's Scale Step by Step: Compute-Efficient Hyperparameter Transfer for Large-Scale Mixture-of-Experts](https://mlsanity.com/paper/2608.20061/) (2026)
- [Blog: Survey of Optimizers](https://mlsanity.com/paper/2608.28557/) (2026)
- [Good Pretraining, Bad SFT: Checkpoint Quality Across the Training Stack](https://mlsanity.com/paper/2609.08966/) (2026)
- [Terminal Shrinkage Averaging Reveals a Schedule-Estimator Interaction in LLM Pretraining](https://mlsanity.com/paper/2609.25482/) (2026)
- [QAM: Quadratic-Accurate Checkpoint Merging via Sequential Consistency](https://mlsanity.com/paper/2609.35168/) (2026)
- [Trajectory Soup: Pushing the Compute-Scaling Frontier of LLM Mid-training via Diverse Trajectories](https://mlsanity.com/paper/2609.37169/) (2026)
- [Understanding the Weight Averaging Mechanism in LLM Training for Post-Training Quantization](https://mlsanity.com/paper/2610.05329/) (2026)
- [RT-J: Large-Scale Pretraining of Relational Transformers for Context-Efficient Predictions](https://mlsanity.com/paper/2610.17867/) (2026)

## Abstract (arXiv)

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.