Decision making is a vital function in the era of artificial intelligence; however, its physical realizations and their theoretical fundamentals are not yet known. In our former study [Sci. Rep. 5, 513253 (2015)], we demonstrated that single photons can be used to make decisions in uncertain, dynamically changing environments. The multi-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. Herein, we present the category theoretic foundation of the single-photon-based decision making, including quantitative analysis that agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure in triangulated categories provides a clear understanding of the underlying mechanisms of the single-photon decision maker. This is the first demonstration of a category theoretic interpretation of decision making, and provides a solid understanding and a design fundamental for intelligence.
Decision making is a vital function in the era of artificial intelligence; however, its physical realizations and their theoretical fundamentals are not yet known. In our former study [Sci. Rep. 5, 513253 (2015)], we demonstrated that single photons can be used to make decisions in uncertain, dynamically changing environments. The multi-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. Herein, we present the category theoretic foundation of the single-photon-based decision making, including quantitative analysis that agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure in triangulated categories provides a clear understanding of the underlying mechanisms of the single-photon decision maker. This is the first demonstration of a category theoretic interpretation of decision making, and provides a solid understanding and a design fundamental for intelligence.
Decision making is a vital function in the age of machine learning and artificial intelligence; however, its physical realization and theoretical fundamentals are not yet well 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 agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure and the braid structure in triangulated categories provide better understandings and quantitative metrics of the underlying mechanisms for the single-photon decision maker. This study provides insight and a foundation for analyzing more complex and uncertain problems for machine learning and artificial intelligence.
Decision making is critical in our daily lives and for society in general and is finding evermore practical applications in information and communication technologies. Herein, we demonstrate experimentally that single photons can be used to make decisions in uncertain, dynamically changing environments. Using a nitrogen-vacancy in a nanodiamond as a single-photon source, we demonstrate the decision-making capability by solving the multi-armed bandit problem. This capability is directly and immediately associated with single-photon detection in the proposed architecture, leading to adequate and adaptive autonomous decision making. This study makes it possible to create systems that benefit from the quantum nature of light to perform practical and vital intelligent functions.
Decision making in dynamically changing uncertain environments is one of the most important elements in information and communications technology, in applications ranging from resource assignment in data centers to wireless communications and search functions. Here, we review our research on the efficient physical realization or acceleration of decision making using photonics. The problem of interest is the multi-armed bandit (MAB) problem, where the purpose is to maximize the total rewards in unknown environments that involve difficult tradeoffs in the so-called exploration-exploitation dilemma. We describe the principle of solving MAB problems by utilizing the wave-particle duality of single photons in which the probabilistic attributes of single light quanta are employed for exploration. The principle is transformed into ultrafast laser chaos, where the chaotically oscillating irregular time series provides fast and scalable decision making abilities. The problem becomes even more difficult when multiple players are involved, in the so-called competitive MAB (CMAB) problem, where the expected value is related to maximizing the social benefit and ensuring fairness among individuals. We demonstrate that entangled photons can resolve the CMAB problem. Theoretical studies on photonic decision making are also reviewed, showing that six entities in total interact with each other according to an octahedral structure.
Understanding and using photonic processes for intelligent functionalities, referred to as photonic intelligence, has recently attracted interest from a variety of fields, including postsilicon computing for artificial intelligence and decision making in the behavioral sciences. In a past study, we successfully used the wave–particle duality of single photons to solve the two-armed bandit problem, which constitutes one of the important foundations of decision making and reinforcement learning. In this paper, we propose and confirm a hierarchical architecture for single-photon-based decision making that verifies the scalability of the principle. Specifically, the four-armed bandit problem is solved given zero prior knowledge in a two-layer hierarchical architecture, where the polarization of single photons is autonomously adapted in order to effect adequate decision making. In the hierarchical structure, the notion of layer-dependent decisions emerges. The optimal solutions in the coarse layer and the fine layer, however, conflict with each other in some contradictory problems. We show that while what we call a tournament strategy resolves such contradictions, the probabilistic nature of single photons allows for the direct location of the optimal solution, even for contradictory problems, hence manifesting the exploration capability of single photons. This study provides insights into photon intelligence in hierarchical architectures for artificial intelligence as well as a novel aspect of photonic processes for intelligent functionalities.
Understanding and using natural processes for intelligent functionalities, referred to as natural intelligence, has recently attracted interest from a variety of fields, including post-silicon computing for artificial intelligence and decision making in the behavioural sciences. In a past study, we successfully used the wave-particle duality of single photons to solve the two-armed bandit problem, which constitutes the foundation of reinforcement learning and decision making. In this study, we propose and confirm a hierarchical architecture for single-photon-based reinforcement learning and decision making that verifies the scalability of the principle. Specifically, the four-armed bandit problem is solved given zero prior knowledge in a two-layer hierarchical architecture, where polarization is autonomously adapted in order to effect adequate decision making using single-photon measurements. In the hierarchical structure, the notion of layer-dependent decisions emerges. The optimal solutions in the coarse layer and in the fine layer, however, conflict with each other in some contradictive problems. We show that while what we call a tournament strategy resolves such contradictions, the probabilistic nature of single photons allows for the direct location of the optimal solution even for contradictive problems, hence manifesting the exploration ability of single photons. This study provides insights into photon intelligence in hierarchical architectures for future artificial intelligence as well as the potential of natural processes for intelligent functionalities.
The competitive multi-armed bandit (CMAB) problem is related to social issues such as maximizing total social benefits while preserving equality among individuals by overcoming conflicts between individual decisions, which could seriously decrease social benefits. The study described herein provides experimental evidence that entangled photons physically resolve the CMAB in the 2-arms 2-players case, maximizing the social rewards while ensuring equality. Moreover, we demonstrated that deception, or outperforming the other player by receiving a greater reward, cannot be accomplished in a polarization-entangled-photon-based system, while deception is achievable in systems based on classical polarization-correlated photons with fixed polarizations. Besides, random polarization-correlated photons have been studied numerically and shown to ensure equality between players and deception prevention as well, although the CMAB maximum performance is reduced as compared with entangled photon experiments. Autonomous alignment schemes for polarization bases were also experimentally demonstrated based only on decision conflict information observed by an individual without communications between players. This study paves a way for collective decision making in uncertain dynamically changing environments based on entangled quantum states, a crucial step toward utilizing quantum systems for intelligent functionalities.