Vowel recognition with four coupled spin-torque nano-oscillators.

In recent years, artificial neural networks have become the flagship algorithm of artificial intelligence1. In these systems, neuron activation functions are static, and computing is achieved through standard arithmetic operations. By contrast, a prominent branch of neuroinspired computing embraces the dynamical nature of the brain and proposes to endow each component of a neural network with dynamical functionality, such as oscillations, and to rely on emergent physical phenomena, such as synchronization2-6, for solving complex problems with small networks7-11. This approach is especially interesting for hardware implementations, because emerging nanoelectronic devices can provide compact and energy-efficient nonlinear auto-oscillators that mimic the periodic spiking activity of biological neurons12-16. The dynamical couplings between oscillators can then be used to mediate the synaptic communication between the artificial neurons. One challenge for using nanodevices in this way is to achieve learning, which requires fine control and tuning of their coupled oscillations17; the dynamical features of nanodevices can be difficult to control and prone to noise and variability18. Here we show that the outstanding tunability of spintronic nano-oscillators-that is, the possibility of accurately controlling their frequency across a wide range, through electrical current and magnetic field-can be used to address this challenge. We successfully train a hardware network of four spin-torque nano-oscillators to recognize spoken vowels by tuning their frequencies according to an automatic real-time learning rule. We show that the high experimental recognition rates stem from the ability of these oscillators to synchronize. Our results demonstrate that non-trivial pattern classification tasks can be achieved with small hardware neural networks by endowing them with nonlinear dynamical features such as oscillations and synchronization.

Neuromorphic computing with nanoscale spintronic oscillators.

Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 108 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

Spintronic reservoir computing without driving current or magnetic field.

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.

Input-driven chaotic dynamics in vortex spin-torque oscillator.

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.

Binding events through the mutual synchronization of spintronic nano-neurons.

The brain naturally binds events from different sources in unique concepts. It is hypothesized that this process occurs through the transient mutual synchronization of neurons located in different regions of the brain when the stimulus is presented. This mechanism of 'binding through synchronization' can be directly implemented in neural networks composed of coupled oscillators. To do so, the oscillators must be able to mutually synchronize for the range of inputs corresponding to a single class, and otherwise remain desynchronized. Here we show that the outstanding ability of spintronic nano-oscillators to mutually synchronize and the possibility to precisely control the occurrence of mutual synchronization by tuning the oscillator frequencies over wide ranges allows pattern recognition. We demonstrate experimentally on a simple task that three spintronic nano-oscillators can bind consecutive events and thus recognize and distinguish temporal sequences. This work is a step forward in the construction of neural networks that exploit the non-linear dynamic properties of their components to perform brain-inspired computations.

Control of the stochastic response of magnetization dynamics in spin-torque oscillator through radio-frequency magnetic fields.

Neuromorphic computing using spintronic devices, such as spin-torque oscillators (STOs), has been intensively studied for energy-efficient data processing. One of the critical issues in this application is stochasticity in magnetization dynamics, which limits the accuracy of computation. Such stochastic behavior, however, plays a key role in stochastic computing and machine learning. It is therefore important to develop methods for both suppressing and enhancing stochastic response in spintronic devices. We report on experimental investigations on control of stochastic quantity, such as the width of a distribution of transient time in magnetization dynamics in vortex-type STO. The spin-transfer effect can suppress stochasticity in transient dynamics from a non-oscillating to oscillating state, whereas an application of a radio-frequency magnetic field is effective in reducing stochasticity on the time evolution of the oscillating state.

Step-like dependence of memory function on pulse width in spintronics reservoir computing.

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 damping in the computational performance of reservoir computing. The current-dependent relaxation dynamics of a magnetic vortex core results in an asymmetric memory function with respect to binary inputs. A fast relaxation caused by a large input leads to a fast fading of the input memory, whereas a slow relaxation by a small input enables the reservoir to keep the input memory for a relatively long time. As a result, a step-like dependence is found for the short-term memory and parity-check capacities on the pulse width of input data, where the capacities remain at 1.5 for a certain range of the pulse width, and drop to 1.0 for a long pulse-width limit. Both analytical and numerical analyses clarify that the step-like behavior can be attributed to the current-dependent relaxation time of the vortex core to a limit-cycle state.

Influence of flicker noise and nonlinearity on the frequency spectrum of spin torque nano-oscillators.

The correlation of phase fluctuations in any type of oscillator fundamentally defines its spectral shape. However, in nonlinear oscillators, such as spin torque nano-oscillators, the frequency spectrum can become particularly complex. This is specifically true when not only considering thermal but also colored 1/f flicker noise processes, which are crucial in the context of the oscillator's long term stability. In this study, we address the frequency spectrum of spin torque oscillators in the regime of large-amplitude steady oscillations experimentally and as well theoretically. We particularly take both thermal and flicker noise into account. We perform a series of measurements of the phase noise and the spectrum on spin torque vortex oscillators, notably varying the measurement time duration. Furthermore, we develop the modelling of thermal and flicker noise in Thiele equation based simulations. We also derive the complete phase variance in the framework of the nonlinear auto-oscillator theory and deduce the actual frequency spectrum. We investigate its dependence on the measurement time duration and compare with the experimental results. Long term stability is important in several of the recent applicative developments of spin torque oscillators. This study brings some insights on how to better address this issue.

Role of non-linear data processing on speech recognition task in the framework of reservoir computing.

The reservoir computing neural network architecture is widely used to test hardware systems for neuromorphic computing. One of the preferred tasks for bench-marking such devices is automatic speech recognition. This task requires acoustic transformations from sound waveforms with varying amplitudes to frequency domain maps that can be seen as feature extraction techniques. Depending on the conversion method, these transformations sometimes obscure the contribution of the neuromorphic hardware to the overall speech recognition performance. Here, we quantify and separate the contributions of the acoustic transformations and the neuromorphic hardware to the speech recognition success rate. We show that the non-linearity in the acoustic transformation plays a critical role in feature extraction. We compute the gain in word success rate provided by a reservoir computing device compared to the acoustic transformation only, and show that it is an appropriate bench-mark for comparing different hardware. Finally, we experimentally and numerically quantify the impact of the different acoustic transformations for neuromorphic hardware based on magnetic nano-oscillators.

Scaling up electrically synchronized spin torque oscillator networks.

Synchronized nonlinear oscillators networks are at the core of numerous families of applications including phased array wave generators and neuromorphic pattern matching systems. In these devices, stable synchronization between large numbers of nanoscale oscillators is a key issue that remains to be demonstrated. Here, we show experimentally that synchronized spin-torque oscillator networks can be scaled up. By increasing the number of synchronized oscillators up to eight, we obtain that the emitted power and the quality factor increase linearly with the number of oscillators. Even more importantly, we demonstrate that the stability of synchronization in time exceeds 1.6 milliseconds corresponding to 105 periods of oscillation. Our study demonstrates that spin-torque oscillators are suitable for applications based on synchronized networks of oscillators.

Self-Injection Locking of a Vortex Spin Torque Oscillator by Delayed Feedback.

The self-synchronization of spin torque oscillators is investigated experimentally by re-injecting its radiofrequency (rf) current after a certain delay time. We demonstrate that the integrated power and spectral linewidth are improved for optimal delays. Moreover by varying the phase difference between the emitted power and the re-injected one, we find a clear oscillatory dependence on the phase difference with a 2π periodicity of the frequency of the oscillator as well as its power and linewidth. Such periodical behavior within the self-injection regime is well described by the general model of nonlinear auto-oscillators including not only a delayed rf current but also all spin torque forces responsible for the self-synchronization. Our results reveal new approaches for controlling the non-autonomous dynamics of spin torque oscillators, a key issue for rf spintronics applications as well as for the development of neuro-inspired spin-torque oscillators based devices.