# Scaling Laws with Vocabulary: Larger Models Deserve Larger Vocabularies

arXiv: https://arxiv.org/abs/2407.13623 · HTML: https://mlsanity.com/paper/2407.13623/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 80 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 30 of 58)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [BLOOM: A 176B-Parameter Open-Access Multilingual Language Model](https://mlsanity.com/paper/2211.05100/) (2022)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Reproducible scaling laws for contrastive language-image learning](https://mlsanity.com/paper/2212.07143/) (2022)
- [GLM: General Language Model Pretraining with Autoregressive Blank Infilling](https://mlsanity.com/paper/2103.10360/) (2021)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)

## Built on by (most cited first, 30 of 118)

- [OLMoE: Open Mixture-of-Experts Language Models](https://mlsanity.com/paper/2409.02060/) (2024)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [Addressing Representation Collapse in Vector Quantized Models with One Linear Layer](https://mlsanity.com/paper/2411.02038/) (2024)
- [Dynamic Chunking for End-to-End Hierarchical Sequence Modeling](https://mlsanity.com/paper/2507.07955/) (2025)
- [SuperBPE: Space Travel for Language Models](https://mlsanity.com/paper/2503.13423/) (2025)
- [ScaMo: Exploring the Scaling Law in Autoregressive Motion Generation Model](https://mlsanity.com/paper/2412.14559/) (2024)
- [Scaling Laws for Predicting Downstream Performance in LLMs](https://mlsanity.com/paper/2410.08527/) (2024)
- [Over-Tokenized Transformer: Vocabulary is Generally Worth Scaling](https://mlsanity.com/paper/2501.16975/) (2025)
- [How Do Large Language Monkeys Get Their Power (Laws)?](https://mlsanity.com/paper/2502.17578/) (2025)
- [Number Cookbook: Number Understanding of Language Models and How to Improve It](https://mlsanity.com/paper/2411.03766/) (2024)
- [Cut Your Losses in Large-Vocabulary Language Models](https://mlsanity.com/paper/2411.09009/) (2024)
- [Autoregressive Models in Vision: A Survey](https://mlsanity.com/paper/2411.05902/) (2024)
- [MEDA: Dynamic KV Cache Allocation for Efficient Multimodal Long-Context Inference](https://mlsanity.com/paper/2502.17599/) (2025)
- [A Hitchhiker's Guide to Scaling Law Estimation](https://mlsanity.com/paper/2410.11840/) (2024)
- [(Mis)Fitting: A Survey of Scaling Laws](https://mlsanity.com/paper/2502.18969/) (2025)
- [Scaling Laws for Gradient Descent and Sign Descent for Linear Bigram Models under Zipf's Law](https://mlsanity.com/paper/2505.19227/) (2025)
- [ATLAS: Adaptive Transfer Scaling Laws for Multilingual Pretraining, Finetuning, and Decoding the Curse of Multilinguality](https://mlsanity.com/paper/2510.22037/) (2025)
- [Scaling Embedding Layers in Language Models](https://mlsanity.com/paper/2502.01637/) (2025)
- [FR-Spec: Accelerating Large-Vocabulary Language Models via Frequency-Ranked Speculative Sampling](https://mlsanity.com/paper/2502.14856/) (2025)
- [Sailor2: Sailing in South-East Asia with Inclusive Multilingual LLMs](https://mlsanity.com/paper/2502.12982/) (2025)
- [The Rise of Small Language Models in Healthcare: A Comprehensive Survey](https://mlsanity.com/paper/2504.17119/) (2025)
- [Scaling Inference-Efficient Language Models](https://mlsanity.com/paper/2501.18107/) (2025)
- [Efficient Prediction of Pass@k Scaling in Large Language Models](https://mlsanity.com/paper/2510.05197/) (2025)
- [UNComp: Can Matrix Entropy Uncover Sparsity? -- A Compressor Design from an Uncertainty-Aware Perspective](https://mlsanity.com/paper/2410.03090/) (2024)
- [Scaling Embeddings Outperforms Scaling Experts in Language Models](https://mlsanity.com/paper/2601.21204/) (2026)
- [Intrinsic Entropy of Context Length Scaling in LLMs](https://mlsanity.com/paper/2502.01481/) (2025)
- [Tokenization is Sensitive to Language Variation](https://mlsanity.com/paper/2502.15343/) (2025)
- [Can Language Models Discover Scaling Laws?](https://mlsanity.com/paper/2507.21184/) (2025)
- [Understanding Stragglers in Large Model Training Using What-if Analysis](https://mlsanity.com/paper/2505.05713/) (2025)
- [One Tokenizer To Rule Them All: Emergent Language Plasticity via Multilingual Tokenizers](https://mlsanity.com/paper/2506.10766/) (2025)

## Abstract (arXiv)

Research on scaling large language models (LLMs) has primarily focused on model parameters and training data size, overlooking the role of vocabulary size. We investigate how vocabulary size impacts LLM scaling laws by training models ranging from 33M to 3B parameters on up to 500B characters with various vocabulary configurations. We propose three complementary approaches for predicting the compute-optimal vocabulary size: IsoFLOPs analysis, derivative estimation, and parametric fit of the loss function. Our approaches converge on the conclusion that the optimal vocabulary size depends on the compute budget, with larger models requiring larger vocabularies. Most LLMs, however, use insufficient vocabulary sizes. For example, we predict that the optimal vocabulary size of Llama2-70B should have been at least 216K, 7 times larger than its vocabulary of 32K. We validate our predictions empirically by training models with 3B parameters across different FLOPs budgets. Adopting our predicted optimal vocabulary size consistently improves downstream performance over commonly used vocabulary sizes. By increasing the vocabulary size from the conventional 32K to 43K, we improve performance on ARC-Challenge from 29.1 to 32.0 with the same 2.3e21 FLOPs. Our work highlights the importance of jointly considering tokenization and model scaling for efficient pre-training. The code and demo are available at https://github.com/sail-sg/scaling-with-vocab and https://hf.co/spaces/sail/scaling-with-vocab-demo.