# Language models scale reliably with over-training and on downstream tasks

arXiv: https://arxiv.org/abs/2403.08540 · HTML: https://mlsanity.com/paper/2403.08540/

## Key facts

- Cited by 113 papers in the map (data through 14 Oct 2026).
- Builds on 105 of its 128 references that are in the map.
- First posted on arXiv 13 Mar 2024.

## Builds on (most cited first, 30 of 105)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (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)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [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)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (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)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)

## Built on by (most cited first, 30 of 113)

- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [Scaling Laws and Compute-Optimal Training Beyond Fixed Training Durations](https://mlsanity.com/paper/2405.18392/) (2024)
- [Rho-1: Not All Tokens Are What You Need](https://mlsanity.com/paper/2404.07965/) (2024)
- [Observational Scaling Laws and the Predictability of Language Model Performance](https://mlsanity.com/paper/2405.10938/) (2024)
- [Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies](https://mlsanity.com/paper/2407.13623/) (2024)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [Understanding Emergent Abilities of Language Models from the Loss Perspective](https://mlsanity.com/paper/2403.15796/) (2024)
- [CWM: An Open-Weights LLM for Research on Code Generation with World Models](https://mlsanity.com/paper/2510.02387/) (2025)
- [Resolving Discrepancies in Compute-Optimal Scaling of Language Models](https://mlsanity.com/paper/2406.19146/) (2024)
- [Perplexed by Perplexity: Perplexity-Based Data Pruning With Small Reference Models](https://mlsanity.com/paper/2405.20541/) (2024)
- [Scaling Laws for Data Filtering -- Data Curation cannot be Compute Agnostic](https://mlsanity.com/paper/2404.07177/) (2024)
- [Distillation Scaling Laws](https://mlsanity.com/paper/2502.08606/) (2025)
- [Archon: An Architecture Search Framework for Inference-Time Techniques](https://mlsanity.com/paper/2409.15254/) (2024)
- [Scaling Retrieval-Based Language Models with a Trillion-Token Datastore](https://mlsanity.com/paper/2407.12854/) (2024)
- [Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for Mixture-of-Experts Language Models](https://mlsanity.com/paper/2501.12370/) (2025)
- [Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models](https://mlsanity.com/paper/2507.17702/) (2025)
- [The Larger the Better? Improved LLM Code-Generation via Budget Reallocation](https://mlsanity.com/paper/2404.00725/) (2024)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Power Lines: Scaling Laws for Weight Decay and Batch Size in LLM Pre-training](https://mlsanity.com/paper/2505.13738/) (2025)
- [Establishing Task Scaling Laws via Compute-Efficient Model Ladders](https://mlsanity.com/paper/2412.04403/) (2024)
- [Training on the Test Task Confounds Evaluation and Emergence](https://mlsanity.com/paper/2407.07890/) (2024)
- [Energy-Based Transformers are Scalable Learners and Thinkers](https://mlsanity.com/paper/2507.02092/) (2025)
- [Not All LLM Reasoners Are Created Equal](https://mlsanity.com/paper/2410.01748/) (2024)
- [Scaling Laws Are Unreliable for Downstream Tasks: A Reality Check](https://mlsanity.com/paper/2507.00885/) (2025)
- [Streaming DiLoCo with overlapping communication: Towards a Distributed Free Lunch](https://mlsanity.com/paper/2501.18512/) (2025)
- [A Hitchhiker's Guide to Scaling Law Estimation](https://mlsanity.com/paper/2410.11840/) (2024)
- [Communication-Efficient Language Model Training Scales Reliably and Robustly: Scaling Laws for DiLoCo](https://mlsanity.com/paper/2503.09799/) (2025)
- [Signal and Noise: A Framework for Reducing Uncertainty in Language Model Evaluation](https://mlsanity.com/paper/2508.13144/) (2025)
- [Scaling Laws Across Model Architectures: A Comparative Analysis of Dense and MoE Models in Large Language Models](https://mlsanity.com/paper/2410.05661/) (2024)

## Abstract (arXiv)

Scaling laws are useful guides for derisking expensive training runs, as they predict performance of large models using cheaper, small-scale experiments. However, there remain gaps between current scaling studies and how language models are ultimately trained and evaluated. For instance, scaling is usually studied in the compute-optimal training regime (i.e., "Chinchilla optimal" regime). In contrast, models are often over-trained to reduce inference costs. Moreover, scaling laws mostly predict loss on next-token prediction, but models are usually compared on downstream task performance. To address both shortcomings, we create a testbed of 104 models with 0.011B to 6.9B parameters trained with various numbers of tokens on three data distributions. First, we fit scaling laws that extrapolate in both the amount of over-training and the number of model parameters. This enables us to predict the validation loss of a 1.4B parameter, 900B token run (i.e., 32× over-trained) and a 6.9B parameter, 138B token run (i.e., a compute-optimal run)unicodex2014each from experiments that take 300× less compute. Second, we relate the perplexity of a language model to its downstream task performance by proposing a power law. We use this law to predict top-1 error averaged over downstream tasks for the two aforementioned models, using experiments that take 20× less compute. Our experiments are available at https://github.com/mlfoundations/scaling.