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A note on the dynamics of extended-context disordered kinetic spin models
Jacob A Zavatone-Veth1, Cengiz Pehlevan2
1Society of Fellows and Center for Brain Science, Harvard University, Cambridge, MA, United States of America.
Journal of Physics. A, Mathematical and Theoretical
|January 26, 2026
Summary
Researchers propose disordered kinetic glass models as toy models for autoregressive sequence generation. These statistical physics models offer tunable correlations and exact solvability for studying learning dynamics in AI.
Area of Science:
- Statistical Physics
- Machine Learning
- Artificial Intelligence
Background:
- Recent advances in language modeling have spurred interest in autoregressive sequence models.
- Analytical tractability is a key challenge in understanding these complex models.
Purpose of the Study:
- To introduce and analyze extensions of disordered kinetic glass models from statistical physics.
- To propose these models as tractable "toy models" for autoregressive sequence generation.
Main Methods:
- Consider extensions of simple disordered kinetic glass models.
- Provide an expository derivation of dynamical mean field theories.
- Analyze asymptotic statistics of the proposed models.
Main Results:
- Disordered kinetic glass models exhibit tunable correlations and are easy to sample.
- These models can be solved exactly in the large state space dimension limit.
- Dynamical mean field theories accurately describe their asymptotic statistics.
Conclusions:
- Disordered kinetic glass models serve as valuable analytical tools for autoregressive sequence generation.
- These models facilitate the study of learning dynamics in sequence models.
- The proposed framework offers a bridge between statistical physics and machine learning research.
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