Physics in Next-token Prediction

TL;DR

This paper uncovers fundamental physical principles governing Next-token Prediction, introducing laws of information conservation and capacity that link model behavior, training, and energy use, with implications for neural language model scaling.

Contribution

It proposes the First and Second Laws of Information Capacity for NTP, integrating physics concepts into understanding model intelligence and energy efficiency.

Findings

Law of information conservation in NTP

Formulation of the First Law of Information Capacity (IC-1)

Introduction of Landauer's Principle into NTP and the Second Law (IC-2)

Abstract

We discovered the underlying physics in Next-token Prediction (NTP). We identified the law of information conservation within NTP and proposed the First Law of Information Capacity (IC-1), demonstrating that the essence of intelligence emergence in auto-regressive models is fundamentally a process of information transfer. We also introduced Landauer's Principle into NTP, formulating the Second Law of Information Capacity (IC-2), which establishes the relationship between auto-regressive model training and energy consumption. Additionally, we presented several corollaries, which hold practical significance for production practices. Finally, we demonstrate the consistency between the Law of Information Capacity and the Scaling Law for Neural Language Models, the Knowledge Capacity Scaling Laws, and the Scaling Laws for Precision.