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Scaling law

As explained in Introduction to Generative AI, Second Edition

A scaling law is an empirical relationship describing how model performance changes as training resources, model size, data, compute, or inference-time effort increase.

A scaling law describes how model performance changes predictably as training resources increase. Common dimensions include model size, training data, and compute; larger models have often performed better on language tasks. section 2.13 section 2.7

Predictable improvement is not guaranteed for every ability. Some capabilities appear suddenly at larger sizes and do not follow established scaling patterns, making further gains difficult to forecast. More time spent reasoning during inference is another proposed route to better performance, though the overall contribution of scaling remains an open question. section 2.14 section 2.16 section 2.7

Capabilities that emerge at larger sizes

In reported evaluations, GPT-3 performed arithmetic close to random guessing at smaller sizes but answered addition, subtraction, and multiplication correctly more often at 13 billion parameters. Its performance on varied academic questions improved notably around 70 billion parameters or more. section 2.14

How Introduction to Generative AI, Second Edition covers it

How deep it goes
Explains training and inference scaling at an overview level, while noting unpredictable emergent abilities and open questions.
Examples
Uses GPT-3 arithmetic and academic-question performance, plus o1's extended reasoning at inference time.
What you can do after
Evaluate whether performance gains appear predictable across model size, data, compute, and inference effort.
How it connects
Connects scaling laws with model size, training data, compute, inference-time reasoning, and emergent abilities.

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This explainer was generated by Manning's knowledge graph from the text of Introduction to Generative AI, Second Edition. The section links point to the parts of the book it draws on.