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![(a,b) Schematic pictures of the vortex dynamics (red) in the presence of two ((k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th and kth) pulses (black), where the kth and (k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th pulses are the same in (a) and different in (b). The blue circles represent the nodes. (c,d), Schematic views of similar dynamics with three pulses, where the solid and dotted lines show the cases when the values of the (k-2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-2)$$\end{document}th and (k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th binary pulses are different and the same.](publication/346521578/figure/fig4/AS:963859414274054@1606813400662/a-b-Schematic-pictures-of-the-vortex-dynamics-red-in-the-presence-of-two.png)
(a,b) Schematic pictures of the vortex dynamics (red) in the presence of two ((k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th and kth) pulses (black), where the kth and (k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th pulses are the same in (a) and different in (b). The blue circles represent the nodes. (c,d), Schematic views of similar dynamics with three pulses, where the solid and dotted lines show the cases when the values of the (k-2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-2)$$\end{document}th and (k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k-1)$$\end{document}th binary pulses are different and the same.
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Physical reservoir computing is a type of recurrent neural network that applies the dynamical response from physical systems to information processing. However, the relation between computation performance and physical parameters/phenomena still remains unclear. This study reports our progress regarding the role of current-dependent magnetic dampin...
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Citations
... [15][16][17][18][19] One of the characteristics of PRC is the short-term memory (STM) task, which is an index that reproduces past time-series input data. In the STM task, the retention performance is called the memory capacity (MC), 20 and MC in PRC using Au nanogap devices, 21 spintronic devices, [22][23][24][25] and piezoelectric devices 26 has been reported. Analogous to the correlation between human synapses and the brain, the STP of artificial synapses should affect the computational performance of the PRC. ...
The correlation between the short-term plasticity (STP) of artificial synapses and the computational performance of physical-reservoir computing (PRC) using artificial synapses has not yet been clarified. We investigate the correlation between the paired-pulse facilitation (PPF) index, which is an evaluation indicator of STP, and the memory capacity (MC) of the short-term memory task, which is one of the computational performance indicators of PRC, using a simple artificial synapse based on a series circuit comprising a resistor and a capacitor. The results show that a higher PPF index of the artificial synapse does not necessarily indicate a higher MC of the PRC using that artificial synapse. The maximum MC is obtained when the time constant of the artificial synapse and the pulse width of the input pulse are comparable. Typically, the MC is found to be the maximum at a PPF index of 114%. This correlation provides valuable guidelines for the design of artificial synapses for PRC applications, as the performance of PRC can be predicted from the STP parameters of artificial synapses.
... That is why research on hardware-oriented reservoir computing (physical reservoir computing) is being conducted. 7) Various physical reservoirs are currently being devised, such as reservoirs using electronic circuits, 8) magnetic spins, [9][10][11] soft materials, 12) nanomaterials [13][14][15] and atomic switches. [16][17][18][19] As one of them, Ag S 2 island network reservoir has been proposed. ...
Recently, a physical reservoir operation utilizing atomic switch technologies was demonstrated. Atomic switch operates by controlling the formation and annihilation of a metal filament between two electrodes using solid-state electrochemical reactions. In this study, we simulated the operation of an atomic switch-based reservoir by arranging modeled atomic switches in a network. The aim of this study is to confirm that nonlinear transformation and short-term memory in a reservoir operation observed in the experiment can be realized by the integration of atomic switches showing nonvolatile bipolar operation. We incorporated these characteristics by making a simple operating model of a single atomic switch, which successfully reproduced major characteristics of the experimental results of a reservoir operation.
... Aside from purely dynamical reservoir models, many physical reservoirs have been proposed to date . Among them, magnetic reservoirs [20][21][22][23][24][25][26][27] , including the systems involving skyrmions [28][29][30][31][32][33][34] , have several advantages such as nonvolatility 35 (namely, the magnetic system should retain its initial texture after the removal of inputs to fulfill the reproducibility), durability 36,37 , low energy consumption as compared to CMOS architectures [38][39][40] , and quick responses 21 . ...
By performing numerical simulations for the handwritten digit recognition task, we demonstrate that a magnetic skyrmion lattice confined in a thin-plate magnet possesses high capability of reservoir computing. We obtain a high recognition rate of more than 88%, higher by about 10% than a baseline taken as the echo state network model. We find that this excellent performance arises from enhanced nonlinearity in the transformation which maps the input data onto an information space with higher dimensions, carried by interferences of spin waves in the skyrmion lattice. Because the skyrmions require only application of static magnetic field instead of nanofabrication for their creation in contrast to other spintronics reservoirs, our result consolidates the high potential of skyrmions for application to reservoir computing devices.
... Promising spintronic reservoirs based on spin-waves have been proposed 10 , though the difficulty in probing the spin-wave states impedes practical system demonstrations. Other spintronic proposals utilize spin torque nano-oscillators with constant bias currents [11][12][13][14][15][16][17] or require additional circuitry for post-processing before feeding into the output layer 13,14,16,[18][19][20][21] , while skyrmion reservoir proposals are insufficiently mature for reliable characterization [22][23][24][25] . Another spintronic reservoir proposal uses arrays of nanomagnets which are actively clocked [26][27][28][29] , making these reservoirs neither passive nor minimal. ...
... Boolean function evaluation. Two of the most widely used metrics for RC are short-term-memory (STM) and parity-check (PC) 11,[14][15][16][17]29 , which require the reservoir to, respectively, remember the previous k inputs of an input bitstream or to perform k-bit XOR on those bits. This provides gauges for the memory content (STM) and non-linear expressivity (PC). ...
... The nanomagnet reservoir illustrated in Fig. 4a-d and Supplementary Movie 3 performed the Boolean function evaluation task with 100% accuracy for both k = 2 and 3 bits, and 93.4% accuracy for k = 4. In contrast, the RC with no reservoir layer performed the Boolean function evaluation task with 99.6% accuracy for k = 2, 81.4% for k = 3, and 84.7% for k = 4. Furthermore, the nanomagnet reservoir achieved an STM content of 4.68 bits, which is standard for spintronic reservoirs, and a PC capability of 3.73 bits, which is close to the maximum PC reported in the literature for emerging hardware reservoirs 11,[14][15][16][17]29 (see the "Short-term memory and parity check capacity" section of the Methods). These results further demonstrate the ability of the NMRC to perform highdimensional information processing with large expressivity and memory content. ...
Reservoir computing (RC) has received recent interest because reservoir weights do not need to be trained, enabling extremely low-resource consumption implementations, which could have a transformative impact on edge computing and in-situ learning where resources are severely constrained. Ideally, a natural hardware reservoir should be passive, minimal, expressive, and feasible; to date, proposed hardware reservoirs have had difficulty meeting all of these criteria. We, therefore, propose a reservoir that meets all of these criteria by leveraging the passive interactions of dipole-coupled, frustrated nanomagnets. The frustration significantly increases the number of stable reservoir states, enriching reservoir dynamics, and as such these frustrated nanomagnets fulfill all of the criteria for a natural hardware reservoir. We likewise propose a complete frustrated nanomagnet reservoir computing (NMRC) system with low-power complementary metal-oxide semiconductor (CMOS) circuitry to interface with the reservoir, and initial experimental results demonstrate the reservoir’s feasibility. The reservoir is verified with micromagnetic simulations on three separate tasks demonstrating expressivity. The proposed system is compared with a CMOS echo state network (ESN), demonstrating an overall resource decrease by a factor of over 10,000,000, demonstrating that because NMRC is naturally passive and minimal it has the potential to be extremely resource efficient.
... Therefore, the STO recognizes the injection of the input data leading to a large short-term memory capacity. We also note that the magnitude relationship between the relaxation time and the pulse width affects the computational capability, which was studied in Ref. 63 . Comparing the results shown in Fig. 4 with those in Fig. 3 leads us to the following conclusions. ...
A new research topic in spintronics relating to the operation principles of brain-inspired computing is input-driven magnetization dynamics in nanomagnet. In this paper, the magnetization dynamics in a vortex spin-torque oscillator (STO) driven by a series of random magnetic field are studied through a numerical simulation of the Thiele equation. It is found that input-driven synchronization occurs in the weak perturbation limit, as found recently. As well, chaotic behavior is newly found to occur in the vortex core dynamics for a wide range of parameters, where synchronized behavior is disrupted by an intermittency. Ordered and chaotic dynamical phases are examined by evaluating the Lyapunov exponent. The relation between the dynamical phase and the computational capability of physical reservoir computing is also studied.
... Note that the memory capacity at the maximum was found to be about 3, which is comparable to the computational ability of echo-state network with approximately 10 nodes 20, 28 . The value is also comparable or larger than that obtained by the other single spintronics reservoirs without additional circuits 20,21,29 , driven by electric current and/or magnetic field. This might be due to a matching between the relaxation time of the output signal and the pulse width. ...
Recent studies have shown that nonlinear magnetization dynamics excited in nanostructured ferromagnets are applicable to brain-inspired computing such as physical reservoir computing. The previous works have utilized the magnetization dynamics driven by electric current and/or magnetic field. This work proposes a method to apply the magnetization dynamics driven by voltage control of magnetic anisotropy to physical reservoir computing, which will be preferable from the viewpoint of low-power consumption. The computational capabilities of benchmark tasks in single MTJ are evaluated by numerical simulation of the magnetization dynamics and found to be comparable to those of echo-state networks with more than 10 nodes.
... High performance is obtained when the magnitude of the current is relatively small and the magnetization points in a direction orthogonal to the x axis; see also Fig. 2. The maximum value of the short-term memory capacity is 4.02 at j 0 = −168 MA/cm 2 . The step-like behavior in the large current region is similar to that observed in a different STO [38]. When the current density j 0 is zero, the short-term memory capacity is zero because, according to Eq. (5), the total current is zero even if b k is finite, and thus, the input signal does not cause any change in the magnetization state. ...
A numerical analysis on the computational capability of physical reservoir computing utilizing a spin-torque oscillator with two free layers is reported. Conventional spintronics devices usually consist of two ferromagnets, where the direction of magnetization in one layer, called the free layer, can move while that of the other, the reference layer, is fixed. Recently, however, devices with two free layers, where the reference layer is replaced by another free layer, have been developed for various practical applications. Adding another free layer drastically changes the dynamical response of the device through the couplings via the spin-transfer effect and the dipole magnetic field. A numerical simulation of the Landau-Lifshitz-Gilbert equation and a statistical analyses of the Lyapunov exponent and the synchronization index reveal the appearance of an amplitude-modulated oscillation and chaos in the oscillators with two free layers. Such complex dynamics qualitatively change the computational capability of physical reservoir computing because the computational resource is dynamics of the physical system. An evaluation of the short-term memory capacity clarifies that oscillators with two free layers have a larger capacity than those of conventional oscillators. An enhancement in capacity near the edge of echo state property, i.e., the boundary between zero and finite synchronization index, is also found.
... [1][2][3][4][5] Recently, physical reservoirs that use various physical phenomena for the nonlinear information processing attract much attention, especially due to the rapidly growing demand for edge artificial intelligence (AI) working with low computational cost and power consumption. 6) There have been various studies such as based on optoelectronics, 7,8) spintronics, 9,10) quantum mechanics, 11,12) nanomaterials, [13][14][15][16] analog circuits, 17,18) mechanical systems, 19,20) fluids, 21,22) Ferroelectric FETs, 23) biomaterials 24) and plants 25) When using as edge AI that processes information from the environment, it is preferable to use a signal from a sensing device as an input without any frequency conversion. In this sense, frequency range of input signals that a reservoir accepts is an important specification. ...
The rapid growth in demand for edge artificial intelligence increases importance of physical reservoirs that work at low computational cost with low power consumption. A Ag 2 S island network also works as a physical reservoir, in which various physicochemical phenomena contribute to a reservoir operation. In this study, we investigated its frequency dependence and found that diffusion of Ag ⁺ cations in a Ag 2 S island, which has a relaxation time of about 100 µs, plays a major role when performance is improved. MNIST classification task using an input pulse width of 100 µs resulted in the accuracy of 91 %. Iterative operations up to 10 million cycles revealed a small enough standard deviation of output, suggesting a potential for practical use of a Ag 2 S island network as a reservoir.
... Therefore, the STO recognizes the injection of the input data leading to a large short-term memory capacity. We also note that the magnitude relationship between the relaxation time and the pulse width affects the computational capability, which was studied in Ref. 63 . ...
A new research topic in spintronics relating to the operation principles of brain-inspired computing is input-driven magnetization dynamics in nanomagnet. In this paper, the magnetization dynamics in a vortex spin-torque oscillator driven by a series of random magnetic field are studied through a numerical simulation of the Thiele equation. It is found that input-driven synchronization occurs in the weak perturbation limit, as found recently. As well, chaotic behavior is newly found to occur in the vortex core dynamics for a wide range of parameters, where synchronized behavior is disrupted by an intermittency. Ordered and chaotic dynamical phases are examined by evaluating the Lyapunov exponent. The relation between the dynamical phase and the computational capability of physical reservoir computing is also studied.
... Moreover, from a hardware perspective, the randomness of the reservoir layer does not translate to performance deterioration, but on the contrary provides robustness against fabrication imperfections. These unique features of RCs render them a hardware-friendly solution for various implementations, exploiting diverse platforms ranging from spintronics 6 , polaritons, CMOS electronics 7 to free-space optics 8,9 and integrated photonic-based approaches 10 . Especially photonics technology constitutes a proliferating platform for such schemes, due to inherent advantages such as computational parallelism through signal multiplexing, low power consumption, high-bandwidth support and processing at the speed of light 10 . ...
Neuromorphic computing using photonic hardware is a promising route towards ultrafast processing while maintaining low power consumption. Here we present and numerically evaluate a hardware concept for realizing photonic recurrent neural networks and reservoir computing architectures. Our method, called Recurrent Optical Spectrum Slicing Neural Networks (ROSS-NNs), uses simple optical filters placed in a loop, where each filter processes a specific spectral slice of the incoming optical signal. The synaptic weights in our scheme are equivalent to the filters’ central frequencies and bandwidths. Numerical application to high baud rate optical signal equalization (>100 Gbaud) reveals that ROSS-NN extends optical signal transmission reach to > 60 km, more than four times that of two state-of-the-art digital equalizers. Furthermore, ROSS-NN relaxes complexity, requiring less than 100 multiplications/bit in the digital domain, offering tenfold reduction in power consumption with respect to these digital counterparts. ROSS-NNs hold promise for efficient photonic hardware accelerators tailored for processing high-bandwidth (>100 GHz) optical signals in optical communication and high-speed imaging applications.
