Infinite Time Turing Machines and their Applications

TL;DR

This paper introduces Infinite Time Turing Machines to analyze deep learning, revealing limitations of current models and proposing the Universal State Machine for scalable, interpretable AI.

Contribution

It establishes a theoretical foundation using ITTMs and proposes the USM paradigm to improve scalability and interpretability in AI systems.

Findings

Reveals fundamental limitations in current deep learning architectures.

Introduces the Universal State Machine as a new computational paradigm.

Lays groundwork for scalable, generalizable AI systems.

Abstract

This work establishes a rigorous theoretical foundation for analyzing deep learning systems by leveraging Infinite Time Turing Machines (ITTMs), which extend classical computation into transfinite ordinal steps. Using ITTMs, we reinterpret modern architectures like Transformers, revealing fundamental limitations in scalability, efficiency, and interpretability. Building on these insights, we propose the Universal State Machine (USM), a novel computational paradigm designed from first principles. The USM employs a dynamic, queryable computation graph that evolves in real time, enabling modular, interpretable, and resource-efficient computation. This framework not only overcomes the inefficiencies and rigidity of current models but also lays the groundwork for scalable, generalizable artificial intelligence systems.