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Artificial neural networks have advanced due to scaling dimensions, but conventional computing faces inefficiency due to the von Neumann bottleneck. In-memory computation architectures, like memristors, offer promise but face challenges due to hardware non-idealities. This work proposes and experimentally demonstrates layer ensemble averaging, a technique to map pre-trained neural network solutions from software to defective hardware crossbars of emerging memory devices and reliably attain near-software performance on inference. The approach is investigated using a custom 20,000-device hardware prototyping platform on a continual learning problem where a network must learn new tasks without catastrophically forgetting previously learned information. Results demonstrate that by trading off the number of devices required for layer mapping, layer ensemble averaging can reliably boost defective memristive network performance up to the software baseline. For the investigated problem, the average multi-task classification accuracy improves from 61 % to 72 % (< 1 % of software baseline) using the proposed approach.

Superparamagnetic tunnel junctions are important devices for a range of emerging technologies, but most existing compact models capture only their mean switching rates. Capturing qualitatively accurate analog dynamics of these devices will be important as the technology scales up. Here we present results using a one-dimensional overdamped Langevin equation that captures statistical properties of measured time traces, including voltage histograms, drift and diffusion characteristics as measured with Kramers-Moyal coefficients, and dwell times distributions. While common macrospin models are more physically-motivated magnetic models than the Langevin model, we show that for the device measured here, they capture even fewer of the measured experimental behaviors., Comment: 22 pages (13 pages of main text), 21 figures

Superparamagnetic tunnel junctions (SMTJs) are promising sources of randomness for compact and energy efficient implementations of probabilistic computing techniques. Augmenting an SMTJ with electronic circuits, to convert the random telegraph fluctuations of its resistance state to stochastic digital signals, gives a basic building block known as a probabilistic bit or $p$-bit. Though scalable probabilistic computing methods connecting $p$-bits have been proposed, practical implementations are limited by either minimal tunability or energy inefficient microprocessors-in-the-loop. In this work, we experimentally demonstrate the functionality of a scalable analog unit cell, namely a pair of $p$-bits with programmable electrical coupling. This tunable coupling is implemented with operational amplifier circuits that have a time constant of approximately 1us, which is faster than the mean dwell times of the SMTJs over most of the operating range. Programmability enables flexibility, allowing both positive and negative couplings, as well as coupling devices with widely varying device properties. These tunable coupling circuits can achieve the whole range of correlations from $-1$ to $1$, for both devices with similar timescales, and devices whose time scales vary by an order of magnitude. This range of correlation allows such circuits to be used for scalable implementations of simulated annealing with probabilistic computing.

The increasing scale of neural networks needed to support more complex applications has led to an increasing requirement for area- and energy-efficient hardware. One route to meeting the budget for these applications is to circumvent the von Neumann bottleneck by performing computation in or near memory. An inevitability of transferring neural networks onto hardware is that non-idealities such as device-to-device variations or poor device yield impact performance. Methods such as hardware-aware training, where substrate non-idealities are incorporated during network training, are one way to recover performance at the cost of solution generality. In this work, we demonstrate inference on hardware neural networks consisting of 20,000 magnetic tunnel junction arrays integrated on a complementary metal-oxide-semiconductor chips that closely resembles market-ready spin transfer-torque magnetoresistive random access memory technology. Using 36 dies, each containing a crossbar array with its own non-idealities, we show that even a small number of defects in physically mapped networks significantly degrades the performance of networks trained without defects and show that, at the cost of generality, hardware-aware training accounting for specific defects on each die can recover to comparable performance with ideal networks. We then demonstrate a robust training method that extends hardware-aware training to statistics-aware training, producing network weights that perform well on most defective dies regardless of their specific defect locations. When evaluated on the 36 physical dies, statistics-aware trained solutions can achieve a mean misclassification error on the MNIST dataset that differs from the software-baseline by only 2 %. This statistics-aware training method could be generalized to networks with many layers that are mapped to hardware suited for industry-ready applications., Comment: 17 pages, 9 figures

The magnetic tunnel junction (MTJ) is a backbone device for spintronics. Realizing next generation energy efficient MTJs will require operating mechanisms beyond the standard means of applying magnetic fields or large electrical currents. Here, we demonstrate a new concept for programmable MTJ operation via strain control of the magnetic states of CrSBr, a layered antiferromagnetic semiconductor used as the tunnel barrier. Switching the CrSBr from antiferromagnetic to ferromagnetic order generates a giant tunneling magnetoresistance ratio without external magnetic field at temperatures up to ~ 140 K. When the static strain is set near the phase transition, applying small strain pulses leads to active flipping of layer magnetization with controlled layer number and thus magnetoresistance states. Further, finely adjusting the static strain to a critical value turns on stochastic switching between metastable states, with a strain-tunable sigmoidal response curve akin to the stochastic binary neuron. Our results highlight the potential of strain-programmable van der Waals MTJs towards spintronic applications, such as magnetic memory, random number generation, and probabilistic and neuromorphic computing.

Data-driven modeling approaches such as jump tables are promising techniques to model populations of resistive random-access memory (ReRAM) or other emerging memory devices for hardware neural network simulations. As these tables rely on data interpolation, this work explores the open questions about their fidelity in relation to the stochastic device behavior they model. We study how various jump table device models impact the attained network performance estimates, a concept we define as modeling bias. Two methods of jump table device modeling, binning and Optuna-optimized binning, are explored using synthetic data with known distributions for benchmarking purposes, as well as experimental data obtained from TiOx ReRAM devices. Results on a multi-layer perceptron trained on MNIST show that device models based on binning can behave unpredictably particularly at low number of points in the device dataset, sometimes over-promising, sometimes under-promising target network accuracy. This paper also proposes device level metrics that indicate similar trends with the modeling bias metric at the network level. The proposed approach opens the possibility for future investigations into statistical device models with better performance, as well as experimentally verified modeling bias in different in-memory computing and neural network architectures.

The increasing scale of neural networks and their growing application space have produced demand for more energy- and memory-efficient artificial-intelligence-specific hardware. Avenues to mitigate the main issue, the von Neumann bottleneck, include in-memory and near-memory architectures, as well as algorithmic approaches. Here we leverage the low-power and the inherently binary operation of magnetic tunnel junctions (MTJs) to demonstrate neural network hardware inference based on passive arrays of MTJs. In general, transferring a trained network model to hardware for inference is confronted by degradation in performance due to device-to-device variations, write errors, parasitic resistance, and nonidealities in the substrate. To quantify the effect of these hardware realities, we benchmark 300 unique weight matrix solutions of a 2-layer perceptron to classify the Wine dataset for both classification accuracy and write fidelity. Despite device imperfections, we achieve software-equivalent accuracy of up to 95.3 % with proper tuning of network parameters in 15 x 15 MTJ arrays having a range of device sizes. The success of this tuning process shows that new metrics are needed to characterize the performance and quality of networks reproduced in mixed signal hardware., Comment: 22 pages plus 8 pages supplemental material; 7 figures plus 7 supplemental figures

We show analytically using a macrospin approximation that easy-plane spin Hall nano-oscillators excited by a spin-current polarized perpendicularly to the easy-plane have phase dynamics analogous to that of Josephson junctions. Similarly to Josephson junctions, they can reproduce the spiking behavior of biological neurons that is appropriate for neuromorphic computing. We perform micromagnetic simulations of such oscillators realized in the nano-constriction geometry and show that the easy-plane spiking dynamics is preserved in an experimentally feasible architecture. Finally we simulate two elementary neural network blocks that implement operations essential for neuromorphic computing. First, we show that output spikes energies from two neurons can be summed and injected into a following layer neuron and second, we demonstrate that outputs can be multiplied by synaptic weights implemented by locally modifying the anisotropy., Comment: 9 pages, 11 figures

Superparamagnetic tunnel junctions (SMTJs) are promising sources for the randomness required by some compact and energy-efficient computing schemes. Coupling SMTJs gives rise to collective behavior that could be useful for cognitive computing. We use a simple linear electrical circuit to mutually couple two SMTJs through their stochastic electrical transitions. When one SMTJ makes a thermally induced transition, the voltage across both SMTJs changes, modifying the transition rates of both. This coupling leads to significant correlation between the states of the two devices. Using fits to a generalized N\'eel-Brown model for the individual thermally bistable magnetic devices, we can accurately reproduce the behavior of the coupled devices with a Markov model., Comment: 12 pages, 11 figures

Race logic is a relative timing code that represents information in a wavefront of digital edges on a set of wires in order to accelerate dynamic programming and machine learning algorithms. Skyrmions, bubbles, and domain walls are mobile magnetic configurations (solitons) with applications for Boolean data storage. We propose to use current-induced displacement of these solitons on magnetic racetracks as a native temporal memory for race logic computing. Locally synchronized racetracks can spatially store relative timings of digital edges and provide non-destructive read-out. The linear kinematics of skyrmion motion, the tunability and low-voltage asynchronous operation of the proposed device, and the elimination of any need for constant skyrmion nucleation make these magnetic racetracks a natural memory for low-power, high-throughput race logic applications., Comment: 9 pages, 3 figures, submitted for review

The movement of large quantities of data during the training of a Deep Neural Network presents immense challenges for machine learning workloads. To minimize this overhead, especially on the movement and calculation of gradient information, we introduce streaming batch principal component analysis as an update algorithm. Streaming batch principal component analysis uses stochastic power iterations to generate a stochastic k-rank approximation of the network gradient. We demonstrate that the low rank updates produced by streaming batch principal component analysis can effectively train convolutional neural networks on a variety of common datasets, with performance comparable to standard mini batch gradient descent. These results can lead to both improvements in the design of application specific integrated circuits for deep learning and in the speed of synchronization of machine learning models trained with data parallelism.

Superparamagnetic tunnel junctions (SMTJs) have emerged as a competitive, realistic nanotechnology to support novel forms of stochastic computation in CMOS-compatible platforms. One of their applications is to generate random bitstreams suitable for use in stochastic computing implementations. We describe a method for digitally programmable bitstream generation based on pre-charge sense amplifiers. This generator is significantly more energy efficient than SMTJ-based bitstream generators that tune probabilities with spin currents and a factor of two more efficient than related CMOS-based implementations. The true randomness of this bitstream generator allows us to use them as the fundamental units of a novel neural network architecture. To take advantage of the potential savings, we codesign the algorithm with the circuit, rather than directly transcribing a classical neural network into hardware. The flexibility of the neural network mathematics allows us to adapt the network to the explicitly energy efficient choices we make at the device level. The result is a convolutional neural network design operating at $\approx$ 150 nJ per inference with 97 % performance on MNIST -- a factor of 1.4 to 7.7 improvement in energy efficiency over comparable proposals in the recent literature., Comment: 20 pages (12 pages main text), 12 figures

Neuromorphic networks based on nanodevices, such as metal oxide memristors, phase change memories, and flash memory cells, have generated considerable interest for their increased energy efficiency and density in comparison to graphics processing units (GPUs) and central processing units (CPUs). Though immense acceleration of the training process can be achieved by leveraging the fact that the time complexity of training does not scale with the network size, it is limited by the space complexity of stochastic gradient descent, which grows quadratically. The main objective of this work is to reduce this space complexity by using low-rank approximations of stochastic gradient descent. This low spatial complexity combined with streaming methods allows for significant reductions in memory and compute overhead, opening the doors for improvements in area, time and energy efficiency of training. We refer to this algorithm and architecture to implement it as the streaming batch eigenupdate (SBE) approach., Comment: 13 pages, 5 figures

Recent advances in the physics of current-driven antiferromagnetic skyrmions have observed the absence of a Magnus force. We outline the symmetry reasons for this phenomenon, and show that this cancellation will fail in the case of spin polarized currents. Pairing micromagnetic simulations with semiclassical spin wave transport theory, we demonstrate that skyrmions produce a spin-polarized transverse magnon current, and that spin-polarized magnon currents can in turn produce transverse motion of antiferromagnetic skyrmions. We examine qualitative differences in the frequency dependence of the skyrmion Hall angle between ferromagnetic and antiferromagnetic cases, and close by proposing a simple skyrmion-based magnonic device for demultiplexing of spin channels., Comment: 11 pages, 7 figures

Non-coplanar spin textures with scalar spin chirality can generate effective magnetic field that deflects the motion of charge carriers, resulting in topological Hall effect (THE), a powerful probe of the ground state and low-energy excitations of correlated systems. However, spin chirality fluctuation in two-dimensional ferromagnets with perpendicular anisotropy has not been considered in prior studies. Herein, we report direct evidence of universal spin chirality fluctuation by probing the THE above the transition temperatures in two different ferromagnetic ultra-thin films, SrRuO$_3$ and V doped Sb$_2$Te$_3$. The temperature, magnetic field, thickness, and carrier type dependences of the THE signal, along with our Monte-Carlo simulations, unambiguously demonstrate that the spin chirality fluctuation is a universal phenomenon in two-dimensional Ising ferromagnets. Our discovery opens a new paradigm of exploring the spin chirality with topological Hall transport in two-dimensional magnets and beyond, Comment: accepted by nature materials

We present a semiclassical formalism for antiferromagnetic (AFM) magnonics which promotes the central ingredient of spin wave chirality, encoded in a quantity called magnonic isospin, to a first-class citizen of the theory. We use this formalism to unify results of interest from the field under a single chirality-centric formulation. Our main result is that the isospin is governed by unitary time evolution, through a Hamiltonian projected down from the full spin wave dynamics. Because isospin is SU(2)-valued, its dynamics on the Bloch sphere are precisely rotations - which, in general, do not commute. Consequently, the induced group of operations on AFM spin waves is nonabelian. This is a paradigmatic departure from ferromagnetic magnonics, which operates purely within the abelian group generated by spin wave phase and amplitude. Our investigation of this nonabelian magnonics in AFM insulators focuses on studying several simple gate operations, and offering in broad strokes a program of study for interesting new logic families in antiferromagnetic spin wave systems, Comment: 21 pages including appendix, 6 figures

In a collinear antiferromagnet with easy-axis anisotropy, symmetry dictates that the spin wave modes must be doubly degenerate. Theses two modes, distinguished by their opposite polarization and available only in antiferromagnets, give rise to a novel degree of freedom to encode and process information. We show that the spin wave polarization can be manipulated by an electric field induced Dzyaloshinskii-Moriya interaction and magnetic anisotropy. We propose a prototype spin wave field-effect transistor which realizes a gate-tunable magnonic analog of the Faraday effect, and demonstrate its application in THz signal modulation. Our findings open up the exciting possibility of digital data processing utilizing antiferromagnetic spin waves and enable the direct projection of optical computing concepts onto the mesoscopic scale., Comment: 3 figures

Layered transition metal trichalcogenides with the chemical formula $ABX_3$ have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate the magnetic ground states of monolayers of Mn- and Cr-based semiconducting trichalcogenides. We show that the second and third nearest-neighbor exchange interactions ($J_2$ and $J_3$) between magnetic ions, which have been largely overlooked in previous theoretical studies, are crucial in determining the magnetic ground state. Specifically, we find that monolayer $\text{CrSiTe}_3$ is an antiferromagnet with a zigzag spin texture due to significant contribution from $J_3$, whereas $\text{CrGeTe}_3$ is a ferromagnet with a Curie temperature of 106 K. Monolayers of Mn-compounds ($\text{MnPS}_3$ and $\text{MnPSe}_3$) always show antiferromagnetic Neel order. We identify the physical origin of various exchange interactions, and demonstrate that strain can be an effective knob for tuning the magnetic properties. Possible magnetic ordering in the bulk is also discussed. Our study suggests that $\text{ABX}_3$ can be a promising platform to explore 2D magnetic phenomena., Comment: 7 pages, 5 figures, 1 table

Picosecond switching of the staggered antiferromagnetic order is shown to be realizable through spin-transfer torques from a short current pulse. The coupled dynamics of sublattice magnetization is mapped onto a classical pendulum subject to gravity and a driving pulse, where switching occurs if the pendulum acquires sufficient kinetic energy during the pulse to overcome the maximum of the effective gravity potential. The optimal switching scheme is explored through the dependence of switch angle and magnetic loss on the duration and strength of the current pulse. The physics discussed here provides a general route towards multi-functional THz applications via the spin-transfer torque in antiferromagnetic materials., Comment: 5 pages, 4 figures

We explore the possibility of exciting spin waves in insulating antiferromagnetic films by injecting spin current at the surface. We analyze both magnetically compensated and uncompensated interfaces. We find that the spin current induced spin-transfer torque can excite spin waves in insulating antiferromagnetic materials and that the chirality of the excited spin wave is determined by the polarization of the injected spin current. Furthermore, the presence of magnetic surface anisotropy can greatly increase the accessibility of these excitations., Comment: 8 pages, 5 figures