Category Theoretic Analysis of Photon-based Decision Making

TL;DR

This paper applies category theory to model and analyze single-photon decision making, revealing complex interdependencies and providing a foundation for advancing AI and machine learning in uncertain environments.

Contribution

It introduces a novel category theoretic framework for understanding photon-based decision processes, supported by quantitative analysis aligned with experimental results.

Findings

Category theory models complex interdependencies in photon decision making.

Octahedral and braid structures elucidate underlying mechanisms.

Quantitative metrics match experimental observations.

Abstract

Decision making is a vital function in this age of machine learning and artificial intelligence, yet its physical realization and theoretical fundamentals are still not completely understood. In our former study, we demonstrated that single-photons can be used to make decisions in uncertain, dynamically changing environments. The two-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. In this study, we present a category theoretic modeling and analysis of single-photon-based decision making, including a quantitative analysis that is in agreement with the experimental results. A category theoretic model reveals the complex interdependencies of subject matter entities in a simplified manner, even in dynamically changing environments. In particular, the octahedral and braid structures in triangulated categories provide a better understanding and quantitative metrics of the underlying mechanisms of a single-photon decision maker. This study provides both insight and a foundation for analyzing more complex and uncertain problems, to further machine learning and artificial intelligence.