Emergence of global synchronization in directed excitatory networks of type I neurons

The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (PRC) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs

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

Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topology

Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the network connectivities for generating cyclic patterns is fundamental for understanding the generation of rhythmic movements. In this paper, the storage of binary cycles in neural networks is investigated. We call a cycle $\Sigma$ admissible if a connectivity matrix satisfying the cycle's transition conditions exists, and construct it using the pseudoinverse learning rule. Our main focus is on the structural features of admissible cycles and corresponding network topology. We show that $\Sigma$ is admissible if and only if its discrete Fourier transform contains exactly $r={rank}(\Sigma)$ nonzero columns. Based on the decomposition of the rows of $\Sigma$ into loops, where a loop is the set of all cyclic permutations of a row, cycles are classified as simple cycles, separable or inseparable composite cycles. Simple cycles contain rows from one loop only, and the network topology is a feedforward chain with feedback to one neuron if the loop-vectors in $\Sigma$ are cyclic permutations of each other. Composite cycles contain rows from at least two disjoint loops, and the neurons corresponding to the rows in $\Sigma$ from the same loop are identified with a cluster. Networks constructed from separable composite cycles decompose into completely isolated clusters. For inseparable composite cycles at least two clusters are connected, and the cluster-connectivity is related to the intersections of the spaces spanned by the loop-vectors of the clusters. Simulations showing successfully retrieved cycles in continuous-time Hopfield-type networks and in networks of spiking neurons are presented.Comment: 48 pages, 3 figure