Year: 2024
Type: preprint
Abstract: Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws may result from general properties of natural learning tasks. We develop a mathematical model intended to describe natural datasets using percolation theory. Two distinct criticality regimes emerge, each yielding optimal power-law neural scaling laws. These regimes, corresponding to power-law-distributed discrete subtasks and a dominant data manifold, can be associated with previously proposed theories of neural scaling, thereby grounding and unifying prior works. We test the theory by training regression models on toy datasets derived from percolation theory simulations. We suggest directions for quantitatively predicting language model scaling.
Source: arXiv (Cornell University)
Author: Brill, Ari
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405300917