Chapter 8 Photonic Neuromorphic Signal Processing and Computing Alexander N. Tait, Mitchell A. Nahmias, Yue Tian, Bhavin J. Shastri and Paul R. Prucnal Abstract There has been a recent explosion of interest in spiking neural networks (SNNs), which code information as spikes or events in time. Spike encoding is widely accepted as the information medium underlying the brain, but it has also inspired a new generation of neuromorphic hardware. Although electronics can match biologi- cal time scales and exceed them, they eventually reach a bandwidth fan-in trade-off. An alternative platform is photonics, which could process highly interactive infor- mation at speeds that electronics could never reach. Correspondingly, processing techniques inspired by biology could compensate for many of the shortcomings that bar digital photonic computing from feasibility, including high defect rates and signal control problems. We summarize properties of photonic spike processing and ini- tial experiments with discrete components. A technique for mapping this paradigm to scalable, integrated laser devices is explored and simulated in small networks. This approach promises to wed the advantageous aspects of both photonic physics and unconventional computing systems. Further development could allow for fully scalable photonic networks that would open up a new domain of ultrafast, robust, and adaptive processing. Applications of this technology ranging from nanosecond response control systems to fast cognitive radio could potentially revitalize special- ized photonic computing. 8.1 Introduction The brain, unlike the von Neumann processors found in conventional computers, is very power efficient, extremely effective at certain computing tasks, and highly adaptable to novel situations and environments. While these favorable properties are often largely credited to the unique connectionism of biological nervous systems, it is A. N. Tait · M. A. Nahmias · Y. Tian · B. J. Shastri · P. R. Prucnal (B) Lightwave Communications Laboratory, Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA e-mail: [email protected] M. Naruse (ed.), Nanophotonic Information Physics, 183 Nano-Optics and Nanophotonics, DOI: 10.1007/978-3-642-40224-1_8, © Springer-Verlag Berlin Heidelberg 2014 184 A. N. Tait et al. clear that the cellular dynamics of individual neurons also play an indispensable role in attaining these performance advantages. On the cellular level, neurons operate on information encoded as events or spikes, a type of signal with both analog and digital properties. Spike processing exploits the efficiency of analog signals while overcom- ing the problem of noise accumulation inherent in analog computation, which can be seen as a first step to attaining the astounding capabilities of bio-inspired process- ing [1]. Other physical and signal processing features at the single neuron level, including hybrid analog-digital signals, representational interleaving, co-location of memory and processing, unsupervised statistical learning, and distributed represen- tations of information, have been implicated in various positive and conventionally impossible signal processing capabilities. Engineers have tried for nearly half a cen- tury to take inspiration from neuroscience by separating key properties that yield performance from simple idiosyncrasies of biology. If some biological properties are distilled while others deemed irrelevant, then a bio-inspired engineered system could also incorporate nonbiological properties that may lead to computational domains that are potentially unexplored and/or practically useful. Many microelectronic platforms have attempted to emulate some advantages of neuron-like architectures while incorporating techniques in technology; however, the majority target rather than exceed biological time scales. What kind of signal processing would be possible with a bio-inspired visual front-end that operates ten million times faster than its biological counterpart? Unfortunately, microelectronic neural networks that are both fast and highly interconnected are subject to a funda- mental bandwidth connection-density tradeoff, keeping their speed limited. Photonic platforms offer an alternative approach to microelectronics. The high speeds, high bandwidth, and low cross-talk achievable in photonics are very well suited for an ultrafast spike-based information scheme with high interconnection densities. In addition, the high wall-plug efficiencies of photonic devices may allow such implementations to match or eclipse equivalent electronic systems in low energy usage. Because of these advantages, photonic spike processors could access a picosecond, low-power computational domain that is inaccessible by other technolo- gies. Our work aims to synergistically integrate the underlying physics of photonics with bio-inspired spike-based processing. This novel processing domain of ultra- fast cognitive computing could have numerous applications where quick, temporally precise and robust systems are necessary, including: adaptive control, learning, per- ception, motion control, sensory processing, autonomous robotics, and cognitive processing of the radio frequency spectrum. In this chapter, we consider the system implications of wedding a neuron-inspired computational primitive with the unique device physics of photonic hardware. The result is a system that could emulate neuromorphic algorithms at rates millions of times faster than biology, while also overcoming both the scaling problems of digital optical computation and the noise accumulation problems of analog optical computation by taking inspiration from neuroscience. Our approach combines the picosecond processing and switching capabilities of both linear and nonlinear optical device technologies to integrate both analog and digital optical processing into a single hardware architecture capable of ultrafast computation without the need for 8 Photonic Neuromorphic Signal Processing and Computing 185 conversion from optical signals to electrical currents. With this hybrid analog-digital processing primitive, it will be possible to implement processing algorithms of far greater complexity than is possible with existing optical technologies, and far higher bandwidth than is possible with existing electronic technologies. The design and implementation of our devices is based upon a well-studied and paradigmatic example of a hybrid computational primitive: the spiking neuron. These simple computational elements integrate a small set of basic operations (delay, weighting, spatial summation, temporal integration, and thresholding) into a single device which is capable of performing a variety of computations depending on how its parameters are configured (e.g., delays, weights, integration time constant, thresh- old). The leaky-integrate-and-fire (LIF) neuron model is a mathematical model of the spiking dynamics which pervade animal nervous systems, well-established as the most widely used model of biological neurons in theoretical neuroscience for studying complex computation in nervous systems [2]. LIF neurons have recently attracted the attention of engineers and computer scientists for the following reasons: • Algorithmic Expressiveness: They provide a powerful and efficient computational primitive from the standpoint of computational complexity and computability theory; • Hardware Efficiency/Robustness: They are both robust and efficient processing elements. Complex algorithms can be implemented with less hardware; • Utility in signal processing: There are known pulse processing algorithms for complex signal processing tasks (drawn from neuro-ethology). Pulse processing is already being used for implementing robust sensory processing algorithms in analog VLSI. After comparing the fundamental physical traits of electronic and photonic plat- forms for implementation of neuromorphic architectures, this chapter will present a detailed cellular processing model (i.e. LIF) and describe the first emulation of this model in ultrafast fiber-optic hardware. Early experiments in photonic learning devices, critical for controlling the adaptation of neural networks, and prototypical demonstrations of simple bio-inspired circuits will be discussed. Recent research has sought to develop a scalable neuromorphic primitive based on the dynamics of semiconductor lasers which could eventually be integrated in very large lightwave neuromorphic systems on a photonic chip. This chapter will focus on the compu- tational primitive, how it can be implemented in photonics, and how these devices interact with input and output signals; a detailed account of the structure and imple- mentation of a network that can link many of these devices together is beyond the scope of this chapter. 8.2 Neuromorphic Processing in Electronics and Photonics The harmonious marriage of a processing paradigm to the physical behaviors that bear it represents an important step in efficiency and performance over approaches that aim to abstract physics away entirely. Both thalamocortical structures observed 186 A. N. Tait et al. in biology and emerging mathematical models of network information integration exhibit a natural separation of computation and communication. Computation rarely takes place in the axons of a neuron, but these communication pathways and their rich configurability are crucial for the informatic complexity of the network as a whole. Because of their favorable communication properties (i.e. low dispersion,