Convolutional neural networks (CNN) are state of the art algorithms for image processing. Despite a small number of synaptic weights, the CNNs remain computationally costly to train in software due to the necessity to exchange huge data flows between memory and processing units. Unconventional hardware is suited to address this limitation. In neuromorphic spintronics, it has been previously demonstrated that the spin diode effect can be used to apply a synaptic weight on a radiofrequency signal [1][2]. Here we go a step beyond, to show an experimental implementation of a convolutional layer employing chains of spin-diodes. We design a compact architecture of 3 chains with 3 spin-diodes connected in series, that performs a padded convolution with a filter of 3 pixels on 5 input pixels multiplexed in frequency in one RF signal (See Figure 1). The synaptic weights corresponding to the filter are encoded by a small frequency detuning between the inputs and the spin-diodes resonance and are controlled in parallel using currents in 3 strip lines. This architecture exploits the intrinsic weight redundancy of convolutions (all filters share the same weights) to enhance the compacity of the hardware and greatly simplify the process of updating a weight, only requiring updating a the current in one strip line. We will also present processed experimental results highlighting the scalability of the proposed architecture. An error on the performed convolution as low as 0.28% was achieved (See Figure 2). The proposed architecture enables us to both reduce the size of this hardware implementation while, at the same time, performing the convolution in one timestep contrary to previous time-multiplexed implementations. According to a previous study [3] we can achieve to decrease by one order of magnitude the energy consumption compared to current GPUs and two orders of magnitude in operating latency. This proof of concept of spintronic CNN, opens the path to spintronic neural networks that can exploit the power of convolutional layers in a fully parallel, compact, and energy efficient way.

Fully Parallel Convolution with Chains of Spin

The combination of the two key effects of spintronics, magnetization dynamics and magneto-resistive effects, allows the realization of nano-neurons and nano-synapses with high computational capabilities. However, multilayer spintronic neural networks have never been realized with these nanodevices because there is no way to connect them that can work on a large scale. I will show that it is possible to exploit the two key effects of spintronics to connect together magnetic tunnel junctions that implement both neurons and synapses of a multilayer network. The magnetic tunnel junctions perform neural operations on DC signals and output the result as RF, operate synaptic operations on RF signals and output the result as DC thus giving rise to multilayer networks based on successive, clean, and fast conversions from RF to DC and from DC to RF. I will give a proof of concept with a two-layer neural network composed of nine interconnected magnetic tunnel junctions functioning as both synapses and neurons and experimentally demonstrate its ability to solve non-linear tasks with high performance. I will show that with junctions downscaled to 20 nm, such a network would consume 10fJ per synaptic operation and 100fJ per neuronal operation, several orders of magnitude less than current software neural network implementations. Finally, I will show through physical simulations that these networks, which can process DC data, can also natively classify RF inputs, achieving state-of-the-art drone identification from their RF transmissions. This study lays the foundation for deep spintronic neural networks at the nanoscale.

Series of synaptic and neuronal operations in a multilayer magnetic tunnel junction network through RF to

A key challenge of neuromorphic computing is to build hardware neural networks with dense connectivity between nanoscale synapses and neurons, approaching the brain’s thousands of synapses per neuron (1). In this talk, I will show that spin diodes are microwave nano-synapses that naturally and densely interface with neurons made of spin-torque nano-oscillators (2). I will describe the principle of these novel synapses and explain how their microwave features can be harnessed to achieve the multiply-and-accumulate operations at the core of neural networks, with over 500 synapses/neuron. I will show that they implement all-to-all connections as well as convolutional operations in a fully parallel way with high density and speed. I will describe our experiments highlighting these functionalities (3), and show that they open the path to radio-frequency deep learning.

Radio-Frequency Spintronic Neural Networks

Spin Torque Nano-Oscillators are magnetic devices that use tunnel magnetoresistance to emit microwaves. They hold great promise for neuromorphic computing [1], as we can use their non-linear dynamic to emulate neurons and they can be integrated by millions in CMOS chips. In previous works, it has been shown that their transient or coupled dynamics can be used to perform pattern recognition [2], [3]. In order to build deep neural networks [4] it is now crucial to find a way to interconnect different layers of neurons with artificial tunable synapses. Here we present an architecture using spintronic resonators to weight the microwave encoded signals of artificial RF spintronic nano-neurons. These synaptic resonators leverage the spin-diode effect [5,6]. The resistance of the devices oscillates at the same frequency as the signal they receive. The rectified voltages are proportional to the power of the microwaves and depend strongly on the frequency mismatch between the signal and the resonance frequency of the device. Hence to tune these resonance frequencies is analog to tune the synaptic weights. And because of the frequency selectivity of our resonators, each of them rectifies only the signal of its corresponding neuron. We use an analytical model and dynamical simulations to show that a chain of spintronic resonators wired in series, rectifying different microwave signals, is equivalent to the key operation of neural networks, called Multiply-And-Accumulate (MAC), despite the nonlinearity of these components. We also demonstrate experimentally with Magnetic Tunnel Junctions as resonators and several RF generators, the validity of this MAC operation. Finally, we simulate a full network with spintronic oscillators and resonators to test our architecture. We manage to achieve state-of-the-art recognition on a handwritten digit dataset. These are encouraging results for high density hardware neural network, as it is the first demonstration of a fully-spintronic radio-frequency neural network.References: [1] J. Grollier, D. Querlioz and M. D. Stiles, Proceedings of the IEEE, Vol. 104, p. 2024-2039 (2016) [2] J. Torrejon, M. Riou et al, Nature, Vol. 547, p. 428 (2017) [3] M. Romera, P. Talatchian, S. Tsunegi et al, Nature, Vol. 563 (7730), p. 230-234 (2018) [4] Yann LeCun et al, Nature, Vol. 521, p. 436-44 (2015) [5] C. Wang, Y.-T. Cui et al, Phys. Rev. B Vol. 79, p. 224416 (2009) [6] D. Marković, N. Leroux, A. Mizrahi, et al, Phys. Rev. Appl, Vol. 13 (4), p. 044050 (2020)

Radio-frequency synapses for neural networks made of spin-torque nano-oscillators

DOC: Neuromorphic Computing

technical paper

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SF: Computing with Spintronic Oscillators

**Session chairs:** Riccardo Tomasello, Politecnico di Bari and Mario Carpentieri, Politecnico of Bari



Symposium SB: Spintronic Diodes: Challenges and New Directions

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Q3: Neuromorphic Computing with Spin-Torque Oscillators

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Nathan Leroux

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Presentations

Fully Parallel Convolution with Chains of Spin

Series of synaptic and neuronal operations in a multilayer magnetic tunnel junction network through RF to

Radio-Frequency Spintronic Neural Networks

Radio-frequency synapses for neural networks made of spin-torque nano-oscillators

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