In recent years, artificial neural networks have become the flagship algorithm of artificial intelligence 1 . 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 synchronization 2-7 , for computing complex problems with small size networks [7][8][9][10][11] . This approach is especially interesting for hardware implementations, as emerging nanoelectronic devices can provide highly compact and energy-efficient non-linear auto-oscillators that mimic the periodic spiking activity of biological neurons [12][13][14][15][16] . The dynamical couplings between oscillators can then be used to mediate the synaptic communication between neurons. However, one major challenge towards implementing these models with nano-devices is to achieve learning, which requires finely controlling and tuning their coupled oscillations 17 . The dynamical features of nanodevices can indeed be difficult to control, and prone to noise and variability 18 . In this work, we show that the outstanding tunability of spintronic nano-oscillators, i.e. the possibility to widely and accurately control their frequency through electrical current and magnetic field, can solve 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 outstanding 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 non-linear dynamical features: here, oscillations and synchronization. This demonstration of real-time learning with an array of four spin-torque nano-oscillators is a milestone for spintronics-based neuromorphic computing.Spin-torque nano-oscillators are natural candidates for building hardware neural networks made of coupled nanoscale oscillators [8][9][10]13,15,18,19 . These nanoscale magnetic tunnel junctions emit microwave

Superparamagnetic tunnel junctions 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 which is more energy efficient than previously explored alternatives. The energy savings offered by this digital generator survive when we use them as the fundamental units of a 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 compensates for explicitly energy efficient choices we make at the device level. The result is a convolutional neural network design operating at ≈ 150 nJ per inference with 97 % performance on MNIST-nearly an order of magnitude more energy efficiency than comparable proposals in the recent literature. * matthew.daniels@nist.gov † mark.stiles@nist.govThe low energy, truly random behavior, ease of control, and established compatibility with complementarymetal-oxide-semiconductor (CMOS) circuitry has led to the use of SMTJs as the basis for a number of novel computing schemes [11][12][13]. SMTJs were proposed to implement the concept of probabilistic bits, or "p-bits," which were leveraged for applications as Bayesian neural networks [14][15][16], invertible Boolean logic [17,18], reservoir computing [19], and Ising network models applied to optimization problems [20,21]. SMTJs were also proposed as stochastic neural units [22] that can interact with synaptic units, emulated by crossbar arrays of mag-

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.