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

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.

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.

Chaotic mode-competition dynamics in a multimode semiconductor laser with optical feedback and injection

Photonic computing has attracted increasing interest for the acceleration of information processing in machine learning applications. The mode-competition dynamics of multimode semiconductor lasers are useful for solving the multi-armed bandit problem in reinforcement learning for computing applications. In this study, we numerically evaluate the chaotic mode-competition dynamics in a multimode semiconductor laser with optical feedback and injection. We observe the chaotic mode-competition dynamics among the longitudinal modes and control them by injecting an external optical signal into one of the longitudinal modes. We define the dominant mode as the mode with the maximum intensity; the dominant mode ratio for the injected mode increases as the optical injection strength increases. We deduce that the characteristics of the dominant mode ratio in terms of the optical injection strength are different among the modes owing to the different optical feedback phases. We propose a control technique for the characteristics of the dominant mode ratio by precisely tuning the initial optical frequency detuning between the optical injection signal and injected mode. We also evaluate the relationship between the region of the large dominant mode ratios and the injection locking range. The region with the large dominant mode ratios does not correspond to the injection-locking range. The control technique of chaotic mode-competition dynamics in multimode lasers is promising for applications in reinforcement learning and reservoir computing in photonic artificial intelligence.

Analysis of temporal structure of laser chaos by Allan variance

Allan variance has been widely utilized for evaluating the stability of the time series generated by atomic clocks and lasers, in time regimes ranging from short to extremely long. This multiscale examination capability of the Allan variance may also be beneficial in evaluating the chaotic oscillating dynamics of semiconductor lasers- not just for conventional phase stability analysis. In the present study, we demonstrated Allan variance analysis of the complex time series generated by a semiconductor laser with delayed feedback, including low-frequency fluctuations (LFFs), which exhibit both fast and slow dynamics. While the detection of LFFs is difficult with the conventional power spectrum analysis method in the low-frequency regime, the Allan variance approach clearly captured the appearance of multiple time-scale dynamics, such as LFFs. This study demonstrates that Allan variance can help in understanding and characterizing diverse laser dynamics, including LFFs, spanning a wide range of timescales.

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.

Photonic decision-making for arbitrary-number-armed bandit problem utilizing parallel chaos generation

In this paper, we propose and experimentally demonstrate a novel scheme that helps to solve an any-number-armed bandit problem by utilizing two parallel simultaneously-generated chaotic signals and the epsilon (ɛ)-greedy strategy. In the proposed scheme, two chaotic signals are experimentally generated, and then processed by an 8-bit analog-to-digital conversion (ADC) with 4 least significant bits (LSBs), to generate two amplitude-distribution-uniform sequences for decision-making. The correspondence between these two random sequences and different arms is established by a mapping rule designed in virtue of the ɛ-greedy-strategy. Based on this, decision-making for an exemplary 5-armed bandit problem is successfully performed, and moreover, the influences of the mapping rule and unknown reward probabilities on the correction decision rate (CDR) performance for the 4-armed to 7-armed bandit problems are investigated. This work provides a novel way for solving the arbitrary-number-armed bandit problem.

Fast dynamics of low-frequency fluctuations in a quantum-dot laser with optical feedback

We experimentally investigate the complex dynamics of a multi-mode quantum-dot semiconductor laser with time-delayed optical feedback. We examine a two-dimensional bifurcation diagram of the quantum-dot laser as a comprehensive dynamical map by changing the injection current and feedback strength. We found that the bifurcation diagram contains two different parameter regions of low-frequency fluctuations. The power-dropout dynamics of the low-frequency fluctuations are observed in the sub-GHz region, which is considerably faster than the conventional low-frequency fluctuations in the MHz region. Comparing the dynamics of quantum-dot laser with those of single- and multi-mode quantum-well semiconductor lasers reveals that the fast low-frequency fluctuation dynamics are unique characteristics of quantum-dot lasers with time-delayed optical feedback.