A note on the dynamics of extended-context disordered kinetic spin models

TL;DR

This paper explores extended disordered kinetic spin models as toy models for autoregressive sequence generation, providing exact solutions and dynamical mean field theories to understand their asymptotic behavior and potential for studying learning dynamics.

Contribution

It introduces extended disordered kinetic spin models as analytically tractable toy models for autoregressive sequence generation, with exact solutions and dynamical mean field theories.

Findings

Models have tunable correlations and are easy to sample.

Exact solutions available for large state space dimensions.

Dynamical mean field theories describe asymptotic statistics.

Abstract

Inspired by striking advances in language modeling, there has recently been much interest in developing autogressive sequence models that are amenable to analytical study. In this short note, we consider extensions of simple disordered kinetic glass models from statistical physics. These models have tunable correlations, are easy to sample, and can be solved exactly when the state space dimension is large. In particular, we give an expository derivation of the dynamical mean field theories that describe their asymptotic statistics. We therefore propose that they constitute an interesting set of toy models for autoregressive sequence generation, in which one might study learning dynamics.