Information processing using a single dynamical node as complex system

Appeltant, Lennert; Soriano, Miguel C.; Sande, Guy Van der; Danckaert, Jan; Massar, Serge; Dambre, Joni; Schrauwen, Benjamin; Mirasso, Claudio R.; Fischer, Ingo

doi:10.1038/ncomms1476

Cited by 1,335 publications

(1,251 citation statements)

References 23 publications

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“…This is particularly attractive when the information is already in the optical domain as in the case of many telecom and image processing applications. Optical reservoirs based on a fibre and one dynamical node [14][15][16][17][18] as well as reservoirs based on ring resonators 19 have been demonstrated. In our own previous work we have shown through reservoir simulations that integrated optical chips with a network of coupled semiconductor optical amplifiers can also be used, with the advantage of a much smaller footprint 20 .…”

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confidence: 99%

Experimental demonstration of reservoir computing on a silicon photonics chip

et al. 2014

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In today's age, companies employ machine learning to extract information from large quantities of data. One of those techniques, reservoir computing (RC), is a decade old and has achieved state-of-the-art performance for processing sequential data. Dedicated hardware realizations of RC could enable speed gains and power savings. Here we propose the first integrated passive silicon photonics reservoir. We demonstrate experimentally and through simulations that, thanks to the RC paradigm, this generic chip can be used to perform arbitrary Boolean logic operations with memory as well as 5-bit header recognition up to 12.5 Gbit s À 1 , without power consumption in the reservoir. It can also perform isolated spoken digit recognition. Our realization exploits optical phase for computing. It is scalable to larger networks and much higher bitrates, up to speeds 4100 Gbit s À 1 . These results pave the way for the application of integrated photonic RC for a wide range of applications.

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confidence: 99%

Experimental demonstration of reservoir computing on a silicon photonics chip

et al. 2014

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“…For instance, this might be one of the mechanisms behind the appearance of irregular spiking in neuronal models with delayed feedback [25] and timing jitter in semiconductor laser systems with delayed feedback [26]. For applications which exploit complex transient behavior such as liquid state machines [27] the high dimension of the unstable manifold at the bifurcation can be interesting. Furthermore, in view of the possibility of a huge number of coexisting attracting orbits beyond the bifurcation the system can serve as a memory device by associating inputs with the attractors to which they make the system converge.…”

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confidence: 99%

Multistable Jittering in Oscillators with Pulsatile Delayed Feedback

et al. 2015

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Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in recent years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. At the bifurcation point numerous regimes with non-equal interspike intervals emerge. We show that the number of the emerging, so-called "jittering" regimes grows exponentially with the delay value. Although this appears as highly degenerate from a dynamical systems viewpoint, the "multi-jitter" bifurcation occurs robustly in a large class of systems. We observe it not only in a paradigmatic phasereduced model, but also in a simulated Hodgkin-Huxley neuron model and in an experiment with an electronic circuit. PACS numbers: 87.19.ll, 05.45.Xt, 87.19.lr, 89.75 Interaction via pulse-like signals is important in neuron populations [1][2][3], biological [4,5], optical and optoelectronic systems [6]. Often, time delays are inevitable in such systems as a consequence of the finite speed of pulse propagation [7]. In this letter we demonstrate that the pulsatile and delayed nature of interactions may lead to novel and unusual phenomena in a large class of systems. In particular, we explore oscillatory systems with pulsatile delayed feedback which exhibit periodic regular spiking (RS). We show that this RS regime may destabilize via a scenario in which a variety of higher-periodical regimes with non-equal interspike intervals (ISIs) emerge simultaneously. The number of the emergent, so-called "jittering" regimes grows exponentially as the delay increases. Therefore we adopt the term "multi-jitter" bifurcation.Usually, the simultaneous emergence of many different regimes is a sign of degeneracy and it is expected to occur generically only when additional symmetries are present [2,8].However, for the class of systems treated here no such symmetry is apparent. Nevertheless, the phenomenon can be reliably observed when just a single parameter, for example the delay, is varied. This means that the observed bifurcation has codimension one [9]. In addition to the theoretical analysis of a simple paradigmatic model, we provide numerical evidence for the occurrence of the multi-jitter bifurcation in a realistic neuronal model, as well as an experimental confirmation in an electronic circuit.As a universal and simplest oscillatory spiking model in the absence of the feedback, we consider the phase oscillator dϕ/dt = ω, where ϕ ∈ R ( mod 1), and ω = 1 without loss of generality. When the oscillator reaches ϕ = 1 at some moment t, the phase is reset to zero and the oscillator produces a pulse signal. If this signal is sent into a delayed feedback loop [ Fig. 1(a)] the emitted pulses affect the oscillator after a delay τ at the time instant t * = t+τ . When the pulse is received, the phase of the oscillator undergoes an instantaneous shift by an amount ∆ϕ = Z(ϕ(t * − 0)), where Z(ϕ) is the phase resetting curve (PRC).Thus, the dynamics of the oscillator can be describ...

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“…Additionally, this work expands possibilities of STNOs to high-dimensional dynamics including ultra-efficient synchronization, 29 the possible occurrence and use of chaotic regimes, 30 and brain-inspired reservoir computing. 31 7 Acknowledgements …”

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confidence: 99%

Critical current and linewidth reduction in spin-torque nano-oscillators by delayed self-injection

Khalsa

Stiles

Grollier

2015

Applied Physics Letters

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ABSTRACT:Based on theoretical models, the dynamics of spin-torque nano-oscillators can be substantially modified by re-injecting the emitted signal to the input of the oscillator after some delay. Numerical simulations for vortex magnetic tunnel junctions show that with reasonable parameters this approach can decrease critical currents as much as 25 % and linewidths by a factor of 4. Analytical calculations, which agree well with simulations, demonstrate that these results can be generalized to any kind of spin-torque oscillator.Spin-torque nano-oscillators (STNOs) based on magnetic tunnel junctions (MTJs) provide the framework for current driven and tunable frequency sources with enormous range 1 (from megahertz to gigahertz) that are compatible with existing semiconductor processes. With a direct electrical current applied to the devices, spin-transfer torques transfer angular momentum from a fixed polarizing magnetic layer to a free magnetic layer and induce oscillatory magnetization dynamics. 2,3 The oscillation of the magnetization causes an oscillatory electrical response through the magnetoresistance effect. Due to their small scale, frequency range, and technological compatibility, STNOs may have applications in the telecommunications industry. 4,5 Hurdles to their use come from the large critical current needed to sustain magnetization oscillations with sufficient spectral purity for industrial adoption, as well as low power output. Research has therefore focused on reducing the critical current, 6 decreasing the linewidth, 7 and increasing the power output of STNOs. 6,8 The nonlinearity inherent to STNOs is both the boon and bane of these devices: non-linearities couple the frequency and amplitude of the oscillator, allowing for the large frequency tunability, but also providing the main source of linewidth broadening. 9-11 Experimentally, linewidth reduction has been recently achieved through strategies aimed at controlling the oscillator's phase 12 such as injection locking to an external signal, 13 self-synchronization of several oscillators 14-16 and phase-locked loop techniques. 17 In this study, we calculate the effect of delayed self-injection on the critical current, frequency response, and linewidth of STNOs. This strategy, where the oscillating output current is re-injected at the 2 input of the oscillator has been shown efficient at improving phase noise in other types of oscillators. 18,19 Using numerical simulations for the dynamics, we find that both the critical current and linewidth of STNOs can be reduced with this technique, while still allowing for frequency tunability. Additionally, we develop simplified analytic expressions that are in good agreement with numerical simulations of the frequency response, critical current, and linewidth -simplifying future experimental and theoretical work. We focus our numerical results on vortex MTJs because they exhibit good output power spectral purity, but emphasize that the analytic results are general to any kind of STNO. The main result i...

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Information processing using a single dynamical node as complex system

Cited by 1,335 publications

References 23 publications

Experimental demonstration of reservoir computing on a silicon photonics chip

Experimental demonstration of reservoir computing on a silicon photonics chip

Multistable Jittering in Oscillators with Pulsatile Delayed Feedback

Critical current and linewidth reduction in spin-torque nano-oscillators by delayed self-injection

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