# Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations

arXiv: https://arxiv.org/abs/2405.18392 · HTML: https://mlsanity.com/paper/2405.18392/

## Key facts

- Cited by 170 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 72 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [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)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [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)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)

## Built on by (most cited first, 30 of 170)

- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Smarter, Better, Faster, Longer: A Modern Bidirectional Encoder for Fast, Memory Efficient, and Long Context Finetuning and Inference](https://mlsanity.com/paper/2412.13663/) (2024)
- [Adam-mini: Use Fewer Learning Rates To Gain More](https://mlsanity.com/paper/2406.16793/) (2024)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [REVE: A Foundation Model for EEG -- Adapting to Any Setup with Large-Scale Pretraining on 25,000 Subjects](https://mlsanity.com/paper/2510.21585/) (2025)
- [Dynamic Chunking for End-to-End Hierarchical Sequence Modeling](https://mlsanity.com/paper/2507.07955/) (2025)
- [GigaTok: Scaling Visual Tokenizers to 3 Billion Parameters for Autoregressive Image Generation](https://mlsanity.com/paper/2504.08736/) (2025)
- [The AdEMAMix Optimizer: Better, Faster, Older](https://mlsanity.com/paper/2409.03137/) (2024)
- [Scaling Laws for Native Multimodal Models](https://mlsanity.com/paper/2504.07951/) (2025)
- [Adaptive Data Optimization: Dynamic Sample Selection with Scaling Laws](https://mlsanity.com/paper/2410.11820/) (2024)
- [Power Lines: Scaling Laws for Weight Decay and Batch Size in LLM Pre-training](https://mlsanity.com/paper/2505.13738/) (2025)
- [Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small LLMs](https://mlsanity.com/paper/2412.13337/) (2024)
- [Reconciling Kaplan and Chinchilla Scaling Laws](https://mlsanity.com/paper/2406.12907/) (2024)
- [Model Merging in Pre-training of Large Language Models](https://mlsanity.com/paper/2505.12082/) (2025)
- [Walrus: A Cross-Domain Foundation Model for Continuum Dynamics](https://mlsanity.com/paper/2511.15684/) (2025)
- [Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection](https://mlsanity.com/paper/2502.06042/) (2025)
- [Enhancing Multilingual LLM Pretraining with Model-Based Data Selection](https://mlsanity.com/paper/2502.10361/) (2025)
- [Straight to Zero: Why Linearly Decaying the Learning Rate to Zero Works Best for LLMs](https://mlsanity.com/paper/2502.15938/) (2025)
- [MuonBP: Faster Muon via Block-Periodic Orthogonalization](https://mlsanity.com/paper/2510.16981/) (2025)
- [Scaling Behavior of Discrete Diffusion Language Models](https://mlsanity.com/paper/2512.10858/) (2025)
- [The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Training](https://mlsanity.com/paper/2501.18965/) (2025)
- [Joint MoE Scaling Laws: Mixture of Experts Can Be Memory Efficient](https://mlsanity.com/paper/2502.05172/) (2025)
- [Scaling Law with Learning Rate Annealing](https://mlsanity.com/paper/2408.11029/) (2024)
- [Power Scheduler: A Batch Size and Token Number Agnostic Learning Rate Scheduler](https://mlsanity.com/paper/2408.13359/) (2024)
- [BioClinical ModernBERT: A State-of-the-Art Long-Context Encoder for Biomedical and Clinical NLP](https://mlsanity.com/paper/2506.10896/) (2025)
- [(Mis)Fitting: A Survey of Scaling Laws](https://mlsanity.com/paper/2502.18969/) (2025)
- [A Practitioner's Guide to Continual Multimodal Pretraining](https://mlsanity.com/paper/2408.14471/) (2024)
- [Scaling Laws for Pre-training Agents and World Models](https://mlsanity.com/paper/2411.04434/) (2024)

## Abstract (arXiv)

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative -- constant learning rate and cooldowns -- and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs. Our code is available at urlhttps://github.com/epfml/schedules-and-scaling/.