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 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 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.

Massive scale, both in terms of data availability and computation, enables significant breakthroughs in key application areas of deep learning such as natural language processing (NLP) and computer vision. There is emerging evidence that scale may be a key ingredient in scientific deep learning, but the importance of physical priors in scientific domains makes the strategies and benefits of scaling uncertain. Here, we investigate neural scaling behavior in large chemical models by varying model and dataset sizes over many orders of magnitude, studying models with over one billion parameters, pre-trained on datasets of up to ten million datapoints. We consider large language models for generative chemistry and graph neural networks for machine-learned interatomic potentials. To enable large-scale scientific deep learning studies under resource constraints, we develop the Training Performance Estimation (TPE) framework to reduce the costs of scalable hyperparameter optimization by up to 90%.