Chinchilla data-optimal scaling laws: In plain English

Important: This page summarizes data scaling only, using tokens to parameters as a ratio, and as derived from large language models like GPT-3, Chinchilla, and beyond, linked to the Compute-Optimal scaling laws like Kaplan and Hoffman/Chinchilla. Please note that compute scaling laws are outside the scope of my current focus. If you would like to read more about compute-optimal scaling laws, please see the discussion by Microsoft + MIT: ‘Reconciling Kaplan and Chinchilla Scaling Laws’ 12/Jun/2024: https://arxiv.org/abs/2406.12907

Alan D. Thompson
February 2023, updated Jun/2024

Chinchilla viz

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Table of current models showing tokens:parameters ratio

Models Table

Chinchilla vs Kaplan scaling laws

Summary: For a fixed compute budget, Chinchilla showed that we need to be using 11× more data during training than that used for GPT-3 and similar models. This means that we need to source, clean, and filter to around 33TB of text data for a 1T-parameter model.

How much text data should we use when training a text-based large language model (LLM)?

Over the last three years to 2023, there have been a few discoveries, through a process of trial and error…

(Note: There is a complementary scaling law for compute built in to these findings, but this is outside the scope of my current focus.)

In May/2020, OpenAI (GPT-3 paper) tacitly announced their data scaling laws (also called the Kaplan scaling laws) for LLMs:

In plain English, GPT-3/Kaplan scaling laws said that…
300B tokens can be used to train an LLM of size 175B parameters
So, we need around 1.7 text tokens per parameter

In Sep/2022, DeepMind (Chinchilla paper) found new data scaling laws (also called the Chinchilla or Hoffman scaling laws) for ‘data optimal’ LLMs:

In plain English, Chinchilla/Hoffman scaling laws say that…
1,400B (1.4T) tokens should be used to train a data-optimal LLM of size 70B parameters
So, we need around 20 text tokens per parameter

Therefore, to make GPT-3 data optimal, and…

Keeping the original 300B tokens, GPT-3 should have been only 15B parameters (300B tokens ÷ 20).
This is around 11× smaller in terms of model size.

OR

To get to the original 175B parameters, GPT-3 should have used 3,500B (3.5T) tokens (175B parameters x 20. 3.5T tokens is about 4-6TB of data, depending on tokenization and tokens per byte).
This is around 11× larger in terms of data needed.

The data optimization scale continues for model sizes measured in trillions of parameters, and training data measured in quadrillions of text tokens or petabytes of text data. The table and explanation below originally appeared in the Jun/2022 report, The sky is bigger than we imagine.

There are a few caveats to my approximate numbers in the table above. Firstly, the ‘More books than in…’ examples are provided for text-based book data only (no pictures), and this assumes that books are about 500KB each without images²500KB ≈ 500K characters ≈ 75K words ≈ 300 pages per book. Simplified and rounded for easy figures.. We are now of course exploring training AI with multimodal data: images, music, control signals (robots, button presses), and anything else we can get our hands on. These increasing sizes are also using simplified and rounded estimates only, based on the new findings related to model scaling using more data (measured by number of tokens, which are roughly equivalent to words). 

In 2010, Google estimated that there are only 130M unique published books in existence³https://googleblog.blogspot.com/2010/08/you-can-count-number-of-books-in-world.html, so past 1T parameters (20T tokens), training data collection would naturally have to rely on alternative text-based and multimodal content. At brain-scale parameter counts of 500T (10Q tokens), the estimated book count would be over 250 times the number of books published, or more than four new books written about each living human on Earth!

Fundamentally, it should not be an incredibly onerous process to collect petabytes of high-quality and filtered multimodal data (converted to text), though that task has not yet been accomplished by any AI lab to date (Jun/2022). 

It is expected that 2023 large language models will continue to follow the Chinchilla scaling laws, though there will be new discoveries about data optimization and data use during training. For example, there is some research on whether or not data can ‘repeat’ (be seen more than once) during training, which may help alleviate the amount of data required to be sourced.

Mosaic scaling laws ≈ range with center of 190:1 (Dec/2023)

MosaicML: Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws
Training is a once-off process where an AI model is fed with a lot of data to recognize patterns and make connections. Large models use a lot of compute during training over many months, but they only have to do so once.

Inference occurs after the model has finished training, every time a user asks the AI model a question (prompt) to produce an output (response).

For inference, popular models might generate trillions and soon quadrillions of words for millions of users over the model’s lifetime (GPT-3 was generating 4.5 billion words per day back in Mar/2021, and then in Dec/2022 I estimated ChatGPT’s output @ 45 billion words per day, or around 18 trillion words since launch), using a lot of compute at all times.

Accounting for both training and inference, how does one minimize the cost required to produce and serve a high quality model?

We conduct our analysis both in terms of a compute budget and real-world costs and find that LLM researchers expecting reasonably large inference demand (~1B requests) should train models smaller and longer than Chinchilla-optimal.

With a fixed compute budget—and for no real-world users because it was locked in a lab!—Chinchilla would train a 70B model for 1.4T tokens (20:1) and also lists a 70B model for 4.26T tokens (61:1).

Mosaic’s proposal would train a popular/inference-intensive 41.6B model for 7,920B tokens (190:1).

At its most basic, Mosaic is attempting to minimize the cost of serving a model. While we can be certain that OpenAI trained, optimized, and deployed the original ChatGPT (gpt-3.5-turbo) 20B model as efficiently as possible to serve more than 200 million people (most of them free users), the world was not yet accustomed to AI copilots, let alone paying for AI inference.

Consider the major frontier models, and the pricing for inference of one million tokens. This is around 750,000 words, which is about how much we speak every 46 days (2007), or most of the seven Harry Potter books (2017):

Pricing per 1M tokens as of Dec/2023. CMU Gemini paper, p3, Table 2.

Evolutions of the original Kaplan (GPT-3) and Chinchilla scaling laws are expected and welcomed. I’m interested to see how this significant increase in training data—an unspoken conclusion of the Mosaic paper—will develop in the real world.

Read the paper: https://arxiv.org/abs/2401.00448

The largest datasets are listed in my Datasets Table: https://lifearchitect.ai/datasets-table/

DeepSeek scaling laws ≈ range with center of 30:1 (Jan/2024)

We attempted to fit the scaling curve on various datasets and found that the data quality significantly influences the optimal model/data scaling up allocation strategy. The higher the data quality, the more the increased compute budget should be allocated to model scaling. This implies that high-quality data can drive the training of larger models given the same data scale. The differences in the optimal model/data scaling-up allocation strategy may also serve as an indirect approach to assess the quality of data.

Read the paper: https://arxiv.org/abs/2401.02954

Tsinghua scaling laws = 192:1 (Apr/2024)

Tsinghua University: MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies

[Our] scaling law indicates a much higher data size / model size ratio compared with Chinchilla Optimal… we notice that [Chinchilla’s] scaling experiment was conducted in a not very recent configuration.

Specifically, the data size should be 192 times larger than the model size on average, as opposed to 20 times in Hoffmann et al. (2022).

Read the paper: https://arxiv.org/abs/2404.06395

Epoch replication of Chinchilla = 26:1 (Apr/2024)

Epoch AI: Chinchilla Scaling: A replication attempt

Optimal scaling. We find a range consistent with the 20 tokens per parameter rule of thumb. Indeed, our point estimates imply that 25.6 tokens per parameters is optimal.

Read the paper: https://www.arxiv.org/abs/2404.10102

Llama 3 scaling law = 1,875:1 (Apr/2024)

Andrej Karpathy (former OpenAI, Tesla, Stanford) commented on the Llama 3 8B model, trained with 15T tokens:

Meta mentions that even at this point [1,875:1], the model doesn’t seem to be “converging” in a standard sense. In other words, the LLMs we work with all the time are significantly undertrained by a factor of maybe 100-1000X or more, nowhere near their point of convergence. (18/Apr/2024)

Read the paper: https://arxiv.org/abs/2407.21783

2024 update

View all model tokens:parameters ratios on the Models Table: https://lifearchitect.ai/models-table/

Based on the papers above—particularly 2024 work by Mosaic and Tsinghua—in plain English, and possibly oversimplified:

For the best performance, and at 2024 median model sizes and training budgets, if a large language model used to read 20M books during training, then it should instead read more than 190M books (or 40M books five times!).

Working, assume a 100B parameter model:
Chinchilla: 20M books × 75K words = 1.5T words or 2T tokens
Mosaic/Tsinghua: 190M books × 75K words = 14.25T words or 19T tokens

DeepMind models to Gemini

Videos on scaling and Chinchilla models

Dr Alan D. Thompson is an AI expert and consultant, advising Fortune 500s and governments on post-2020 large language models. His work on artificial intelligence has been featured at NYU, with Microsoft AI and Google AI teams, at the University of Oxford’s 2021 debate on AI Ethics, and in the Leta AI (GPT-3) experiments viewed more than 4.5 million times. A contributor to the fields of human intelligence and peak performance, he has held positions as chairman for Mensa International, consultant to GE and Warner Bros, and memberships with the IEEE and IET. Technical highlights.

• 1
  Kindle ≈ 6M books (estimate) https://justpublishingadvice.com/how-many-kindle-ebooks-are-there
  Yale ≈ 15M items https://yaledailynews.com/blog/2018/04/06/stange-love-your-library
  Google Books ≈ 25M books https://archive.ph/rMbE2
  US Library of Congress ≈ 51M cataloged books https://www.loc.gov/about/general-information/#year-at-a-glance
  British Library ≈ 170M items https://www.bl.uk/about-us/our-story/facts-and-figures-of-the-british-library
  US public libraries ≈ 732M books, note that this definitely includes (many) duplicates https://nces.ed.gov/programs/digest/d17/tables/dt17_701.60.asp
  Bibles ≈ 5B copies https://www.guinnessworldrecords.com/world-records/best-selling-book-of-non-fiction
  Earth to Moon ≈ 384,400km≈ 38,440,000,000cm, each book spine 2.4cm thick ≈ 16B books
  Human population ≈ 8B (Jun/2022)
• 2
  500KB ≈ 500K characters ≈ 75K words ≈ 300 pages per book. Simplified and rounded for easy figures.
• 3
  https://googleblog.blogspot.com/2010/08/you-can-count-number-of-books-in-world.html