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The Quantization Model of Neural Scaling

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arxiv 2303.13506 v3 pith:WJIAKUMX submitted 2023-03-23 cs.LG cond-mat.dis-nn

Eric J. Michaud , Ziming Liu , Uzay Girit , Max Tegmark This is my paper
classification cs.LGcond-mat.dis-nn
keywords modelscalingpowerquantalanguagequantizationdecomposefrequency
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abstract

We propose the Quantization Model of neural scaling laws, explaining both the observed power law dropoff of loss with model and data size, and also the sudden emergence of new capabilities with scale. We derive this model from what we call the Quantization Hypothesis, where network knowledge and skills are "quantized" into discrete chunks ($\textbf{quanta}$). We show that when quanta are learned in order of decreasing use frequency, then a power law in use frequencies explains observed power law scaling of loss. We validate this prediction on toy datasets, then study how scaling curves decompose for large language models. Using language model gradients, we automatically decompose model behavior into a diverse set of skills (quanta). We tentatively find that the frequency at which these quanta are used in the training distribution roughly follows a power law corresponding with the empirical scaling exponent for language models, a prediction of our theory.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 8 citations worldwide. Full citation record

  1. From Zipf's Law to Neural Scaling through Heaps' Law and Hilberg's Hypothesis

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    Zipf's law, via differential Heaps and Hilberg laws, forces a power-law lower bound on the excess cross entropy of any entropy-bounded foundation model.

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    Under fixed-distribution neural scaling laws, the capability gap between state-of-the-art and low-compute AI models shrinks over time toward zero.

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    Across 2,500 class-balanced MNIST subsets and 10 model architectures, test-error Z-scores correlate strongly across models (mean R2=0.82 excluding GNB), supporting dataset quality as an intrinsic property.

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