Nanophotonic reservoir computing with photonic crystal cavities to generate periodic patterns

Reservoir computing (RC) is a technique in machine learning inspired by neural systems. RC has been used successfully to solve complex problems such as signal classification and signal generation. These systems are mainly implemented in software, and thereby they are limited in speed and power efficiency. Several optical and optoelectronic implementations have been demonstrated, in which the system has signals with an amplitude and phase. It is proven that these enrich the dynamics of the system, which is beneficial for the performance. In this paper, we introduce a novel optical architecture based on nanophotonic crystal cavities. This allows us to integrate many neurons on one chip, which, compared with other photonic solutions, closest resembles a classical neural network. Furthermore, the components are passive, which simplifies the design and reduces the power consumption. To assess the performance of this network, we train a photonic network to generate periodic patterns, using an alternative online learning rule called first-order reduced and corrected error. For this, we first train a classical hyperbolic tangent reservoir, but then we vary some of the properties to incorporate typical aspects of a photonics reservoir, such as the use of continuous-time versus discrete-time signals and the use of complex-valued versus real-valued signals. Then, the nanophotonic reservoir is simulated and we explore the role of relevant parameters such as the topology, the phases between the resonators, the number of nodes that are biased and the delay between the resonators. It is important that these parameters are chosen such that no strong self-oscillations occur. Finally, our results show that for a signal generation task a complex-valued, continuous-time nanophotonic reservoir outperforms a classical (i.e., discrete-time, real-valued) leaky hyperbolic tangent reservoir (normalized root-mean-square errors = 0.030 versus NRMSE = 0.127)

Principles of Neuromorphic Photonics

In an age overrun with information, the ability to process reams of data has become crucial. The demand for data will continue to grow as smart gadgets multiply and become increasingly integrated into our daily lives. Next-generation industries in artificial intelligence services and high-performance computing are so far supported by microelectronic platforms. These data-intensive enterprises rely on continual improvements in hardware. Their prospects are running up against a stark reality: conventional one-size-fits-all solutions offered by digital electronics can no longer satisfy this need, as Moore's law (exponential hardware scaling), interconnection density, and the von Neumann architecture reach their limits. With its superior speed and reconfigurability, analog photonics can provide some relief to these problems; however, complex applications of analog photonics have remained largely unexplored due to the absence of a robust photonic integration industry. Recently, the landscape for commercially-manufacturable photonic chips has been changing rapidly and now promises to achieve economies of scale previously enjoyed solely by microelectronics. The scientific community has set out to build bridges between the domains of photonic device physics and neural networks, giving rise to the field of \emph{neuromorphic photonics}. This article reviews the recent progress in integrated neuromorphic photonics. We provide an overview of neuromorphic computing, discuss the associated technology (microelectronic and photonic) platforms and compare their metric performance. We discuss photonic neural network approaches and challenges for integrated neuromorphic photonic processors while providing an in-depth description of photonic neurons and a candidate interconnection architecture. We conclude with a future outlook of neuro-inspired photonic processing.Comment: 28 pages, 19 figure

Learning as a Nonlinear Line of Attraction for Pattern Association, Classification and Recognition

Development of a mathematical model for learning a nonlinear line of attraction is presented in this dissertation, in contrast to the conventional recurrent neural network model in which the memory is stored in an attractive fixed point at discrete location in state space. A nonlinear line of attraction is the encapsulation of attractive fixed points scattered in state space as an attractive nonlinear line, describing patterns with similar characteristics as a family of patterns. It is usually of prime imperative to guarantee the convergence of the dynamics of the recurrent network for associative learning and recall. We propose to alter this picture. That is, if the brain remembers by converging to the state representing familiar patterns, it should also diverge from such states when presented by an unknown encoded representation of a visual image. The conception of the dynamics of the nonlinear line attractor network to operate between stable and unstable states is the second contribution in this dissertation research. These criteria can be used to circumvent the plasticity-stability dilemma by using the unstable state as an indicator to create a new line for an unfamiliar pattern. This novel learning strategy utilizes stability (convergence) and instability (divergence) criteria of the designed dynamics to induce self-organizing behavior. The self-organizing behavior of the nonlinear line attractor model can manifest complex dynamics in an unsupervised manner. The third contribution of this dissertation is the introduction of the concept of manifold of color perception. The fourth contribution of this dissertation is the development of a nonlinear dimensionality reduction technique by embedding a set of related observations into a low-dimensional space utilizing the result attained by the learned memory matrices of the nonlinear line attractor network. Development of a system for affective states computation is also presented in this dissertation. This system is capable of extracting the user\u27s mental state in real time using a low cost computer. It is successfully interfaced with an advanced learning environment for human-computer interaction