Experimental control of mode-competition dynamics in a chaotic multimode semiconductor laser for decision making.

Photonic computing is widely used to accelerate the computational performance in machine learning. Photonic decision making is a promising approach utilizing photonic computing technologies to solve the multi-armed bandit problems based on reinforcement learning. Photonic decision making using chaotic mode-competition dynamics has been proposed. However, the experimental conditions for achieving a superior decision-making performance have not yet been established. Herein, we experimentally investigate mode-competition dynamics in a chaotic multimode semiconductor laser in the presence of optical feedback and injection. We control the chaotic mode-competition dynamics via optical injection and observe that positive wavelength detuning results in an efficient mode concentration to one of the longitudinal modes with a small optical injection power. We experimentally investigate two-dimensional bifurcation diagram of the total intensity of the laser dynamics. Complex mixed dynamics are observed in the presence of optical feedback and injection. We experimentally conduct decision making to solve the bandit problem using chaotic mode-competition dynamics. A fast mode-concentration property is observed at positive wavelength detunings, resulting in fast convergence of the correct decision rate. Our findings could be useful in accelerating the decision-making performance in adaptive optical networks using reinforcement learning.

Asymmetric leader-laggard cluster synchronization for collective decision-making with laser network.

Photonic accelerators have recently attracted soaring interest, harnessing the ultimate nature of light for information processing. Collective decision-making with a laser network, employing the chaotic and synchronous dynamics of optically interconnected lasers to address the competitive multi-armed bandit (CMAB) problem, is a highly compelling approach due to its scalability and experimental feasibility. We investigated essential network structures for collective decision-making through quantitative stability analysis. Moreover, we demonstrated the asymmetric preferences of players in the CMAB problem, extending its functionality to more practical applications. Our study highlights the capability and significance of machine learning built upon chaotic lasers and photonic devices.

Conflict-free joint decision by lag and zero-lag synchronization in laser network.

With the end of Moore's Law and the increasing demand for computing, photonic accelerators are garnering considerable attention. This is due to the physical characteristics of light, such as high bandwidth and multiplicity, and the various synchronization phenomena that emerge in the realm of laser physics. These factors come into play as computer performance approaches its limits. In this study, we explore the application of a laser network, acting as a photonic accelerator, to the competitive multi-armed bandit problem. In this context, conflict avoidance is key to maximizing environmental rewards. We experimentally demonstrate cooperative decision-making using zero-lag and lag synchronization within a network of four semiconductor lasers. Lag synchronization of chaos realizes effective decision-making and zero-lag synchronization is responsible for the realization of the collision avoidance function. We experimentally verified a low collision rate and high reward in a fundamental 2-player, 2-slot scenario, and showed the scalability of this system. This system architecture opens up new possibilities for intelligent functionalities in laser dynamics.

Acceleration of Approximate Matrix Multiplications on GPUs.

Matrix multiplication is important in various information-processing applications, including the computation of eigenvalues and eigenvectors, and in combinatorial optimization algorithms. Therefore, reducing the computation time of matrix products is essential to speed up scientific and practical calculations. Several approaches have been proposed to speed up this process, including GPUs, fast matrix multiplication libraries, custom hardware, and efficient approximate matrix multiplication (AMM) algorithms. However, research to date has yet to focus on accelerating AMMs for general matrices on GPUs, despite the potential of GPUs to perform fast and accurate matrix product calculations. In this paper, we propose a method for improving Monte Carlo AMMs. We also give an analytical solution for the optimal values of the hyperparameters in the proposed method. The proposed method improves the approximation of the matrix product without increasing the computation time compared to the conventional AMMs. It is also designed to work well with parallel operations on GPUs and can be incorporated into various algorithms. Finally, the proposed method is applied to a power method used for eigenvalue computation. We demonstrate that, on an NVIDIA A100 GPU, the computation time can be halved compared to the conventional power method using cuBLAS.

Bandit Algorithm Driven by a Classical Random Walk and a Quantum Walk.

Quantum walks (QWs) have a property that classical random walks (RWs) do not possess-the coexistence of linear spreading and localization-and this property is utilized to implement various kinds of applications. This paper proposes RW- and QW-based algorithms for multi-armed-bandit (MAB) problems. We show that, under some settings, the QW-based model realizes higher performance than the corresponding RW-based one by associating the two operations that make MAB problems difficult-exploration and exploitation-with these two behaviors of QWs.

Effect of temporal resolution on the reproduction of chaotic dynamics via reservoir computing.

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous generation of chaotic time series, as well as time series prediction and classification. Furthermore, novel possibilities have been demonstrated, such as inferring the existence of previously unseen attractors. Sampling, in contrast, has a strong influence on such functions. Sampling is indispensable in a physical reservoir computer that uses an existing physical system as a reservoir because the use of an external digital system for the data input is usually inevitable. This study analyzes the effect of sampling on the ability of reservoir computing to autonomously regenerate chaotic time series. We found, as expected, that excessively coarse sampling degrades the system performance, but also that excessively dense sampling is unsuitable. Based on quantitative indicators that capture the local and global characteristics of attractors, we identify a suitable window of the sampling frequency and discuss its underlying mechanisms.

Information-theoretical analysis of statistical measures for multiscale dynamics.

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as clocks and lasers, ranging from short to long time scales. Although these two statistical measures were developed independently for different purposes in different fields, their interest lies in examining the multiscale temporal structures of physical phenomena under study. We demonstrate that from an information-theoretical perspective, they share some foundations and exhibit similar tendencies. We experimentally confirmed that similar properties of the MSE and Allan variance can be observed in low-frequency fluctuations (LFF) in chaotic lasers and physiological heartbeat data. Furthermore, we calculated the condition under which this consistency between the MSE and Allan variance exists, which is related to certain conditional probabilities. Heuristically, natural physical systems including the aforementioned LFF and heartbeat data mostly satisfy this condition, and hence, the MSE and Allan variance demonstrate similar properties. As a counterexample, we demonstrate an artificially constructed random sequence, for which the MSE and Allan variance exhibit different trends.

Pairing Optimization via Statistics: Algebraic Structure in Pairing Problems and Its Application to Performance Enhancement.

Fully pairing all elements of a set while attempting to maximize the total benefit is a combinatorically difficult problem. Such pairing problems naturally appear in various situations in science, technology, economics, and other fields. In our previous study, we proposed an efficient method to infer the underlying compatibilities among the entities, under the constraint that only the total compatibility is observable. Furthermore, by transforming the pairing problem into a traveling salesman problem with a multi-layer architecture, a pairing optimization algorithm was successfully demonstrated to derive a high-total-compatibility pairing. However, there is substantial room for further performance enhancement by further exploiting the underlying mathematical properties. In this study, we prove the existence of algebraic structures in the pairing problem. We transform the initially estimated compatibility information into an equivalent form where the variance of the individual compatibilities is minimized. We then demonstrate that the total compatibility obtained when using the heuristic pairing algorithm on the transformed problem is significantly higher compared to the previous method. With this improved perspective on the pairing problem using fundamental mathematical properties, we can contribute to practical applications such as wireless communications beyond 5G, where efficient pairing is of critical importance. As the pairing problem is a special case of the maximum weighted matching problem, our findings may also have implications for other algorithms on fully connected graphs.

Controlling chaotic itinerancy in laser dynamics for reinforcement learning.

Photonic artificial intelligence has attracted considerable interest in accelerating machine learning; however, the unique optical properties have not been fully used for achieving higher-order functionalities. Chaotic itinerancy, with its spontaneous transient dynamics among multiple quasi-attractors, can be used to realize brain-like functionalities. In this study, we numerically and experimentally investigate a method for controlling the chaotic itinerancy in a multimode semiconductor laser to solve a machine learning task, namely, the multiarmed bandit problem, which is fundamental to reinforcement learning. The proposed method uses chaotic itinerant motion in mode competition dynamics controlled via optical injection. We found that the exploration mechanism is completely different from a conventional searching algorithm and is highly scalable, outperforming the conventional approaches for large-scale bandit problems. This study paves the way to use chaotic itinerancy for effectively solving complex machine learning tasks as photonic hardware accelerators.

Decision making for large-scale multi-armed bandit problems using bias control of chaotic temporal waveforms in semiconductor lasers.

Decision making using photonic technologies has been intensively researched for solving the multi-armed bandit problem, which is fundamental to reinforcement learning. However, these technologies are yet to be extended to large-scale multi-armed bandit problems. In this study, we conduct a numerical investigation of decision making to solve large-scale multi-armed bandit problems by controlling the biases of chaotic temporal waveforms generated in semiconductor lasers with optical feedback. We generate chaotic temporal waveforms using the semiconductor lasers, and each waveform is assigned to a slot machine (or choice) in the multi-armed bandit problem. The biases in the amplitudes of the chaotic waveforms are adjusted based on rewards using the tug-of-war method. Subsequently, the slot machine that yields the maximum-amplitude chaotic temporal waveform with bias is selected. The scaling properties of the correct decision-making process are examined by increasing the number of slot machines to 1024, and the scaling exponent of the power-law distribution is 0.97. We demonstrate that the proposed method outperforms existing software algorithms in terms of the scaling exponent. This result paves the way for photonic decision making in large-scale multi-armed bandit problems using photonic accelerators.

Laser network decision making by lag synchronization of chaos in a ring configuration.

Photonic technologies are promising for solving complex tasks in artificial intelligence. In this paper, we numerically investigate decision making for solving the multi-armed bandit problem using lag synchronization of chaos in a ring laser-network configuration. We construct a laser network consisting of unidirectionally coupled semiconductor lasers, whereby spontaneous exchange of the leader-laggard relationship in the lag synchronization of chaos is observed. We succeed in solving the multi-armed bandit problems with three slot machines using lag synchronization of chaos by controlling the coupling strengths among the three lasers. Furthermore, we investigate the scalability of the proposed decision-making principle by increasing the number of slot machines and lasers. This study suggests a new direction in laser network-based decision making for future photonic intelligent functions.

Decision making for the multi-armed bandit problem using lag synchronization of chaos in mutually coupled semiconductor lasers.

We numerically and experimentally demonstrate the utilization of the synchronization of chaotic lasers for decision making. We perform decision making to solve the multi-armed bandit problem using lag synchronization of chaos in mutually coupled semiconductor lasers. We observe the spontaneous exchanges of the leader-laggard relationship under lag synchronization of chaos, and we find that the leader laser can be controlled by changing the coupling strengths between the two lasers. To solve the multi-armed bandit problem, we select one of the slot machines with unknown hit probabilities based only on the identity of the leader laser while reconfiguring the coupling strength to determine the correct decision. We successfully perform an on-line experimental demonstration of the decision making based on the two-laser coupled architecture. This is the first time that synchronization in chaotic lasers is utilized for decision making, and this study paves the way for novel resources for future photonic intelligence.

On-chip photonic decision maker using spontaneous mode switching in a ring laser.

Efficient and accurate decision making is gaining increased importance with the rapid expansion of information communication technologies including artificial intelligence. Here, we propose and experimentally demonstrate an on-chip, integrated photonic decision maker based on a ring laser. The ring laser exhibits spontaneous switching between clockwise and counter-clockwise oscillatory dynamics; we utilize such nature to solve a multi-armed bandit problem. The spontaneous switching dynamics provides efficient exploration to find the accurate decision. On-line decision making is experimentally demonstrated including autonomous adaptation to an uncertain environment. This study paves the way for directly utilizing the fluctuating physics inherent in ring lasers, or integrated photonics technologies in general, for achieving or accelerating intelligent functionality.

Scalable photonic reinforcement learning by time-division multiplexing of laser chaos.

Reinforcement learning involves decision-making in dynamic and uncertain environments and constitutes a crucial element of artificial intelligence. In our previous work, we experimentally demonstrated that the ultrafast chaotic oscillatory dynamics of lasers can be used to efficiently solve the two-armed bandit problem, which requires decision-making concerning a class of difficult trade-offs called the exploration-exploitation dilemma. However, only two selections were employed in that research; hence, the scalability of the laser-chaos-based reinforcement learning should be clarified. In this study, we demonstrated a scalable, pipelined principle of resolving the multi-armed bandit problem by introducing time-division multiplexing of chaotically oscillated ultrafast time series. The experimental demonstrations in which bandit problems with up to 64 arms were successfully solved are presented where laser chaos time series significantly outperforms quasiperiodic signals, computer-generated pseudorandom numbers, and coloured noise. Detailed analyses are also provided that include performance comparisons among laser chaos signals generated in different physical conditions, which coincide with the diffusivity inherent in the time series. This study paves the way for ultrafast reinforcement learning by taking advantage of the ultrahigh bandwidths of light wave and practical enabling technologies.