The Quantization Model of Neural Scaling

Published: 21 Sept 2023, Last Modified: 13 Jan 2024NeurIPS 2023 posterEveryoneRevisionsBibTeX
Keywords: scaling laws, emergence, language models, science of deep learning
TL;DR: Develops a model of neural scaling where smooth scaling laws average over small emergent changes in model performance on subtasks.
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 (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.
Submission Number: 9040