Antiferromagnetic Artificial Neural Networks with Symmetric Coupling

Abstract

Artificial neural networks (NN) running on traditional computing hardware tend to be relatively slow and power-hungry. One possible solution to this issue is to create hardware with neurons that spike in a manner similar to biological neurons. For example, Intel [1] and IBM [2] have recently fabricated neuromorphic chips based on spiking NN. Still, neurons in these chips are fabricated with multiple silicon transistors, which limits power efficiency of such an approach. The development of neuromorphic chips would benefit from a nanoscale, single element synthetic neuron that behaves in a manner that closely resembles a biological neuron. Such a synthetic neuron can be fabricated with nanometer dimensions from an antiferromagnetic (AFM) material mounted on platinum [3]. These “AFM neurons” are spin Hall oscillators driven by a sub-threshold spin current that can produce ultra-short (~ 5 ps) spikes in response to a weak external stimulus.In traditional spiking NN, synapses that connect artificial neurons are formed by complex active circuits. A much simpler approach would be to use passive memristors as artificial synapses [4]. However, memristors create symmetric coupling between neurons, which allows a spike produced by one neuron to travel to all neighboring neurons, both forwards and backwards. Unfortunately, this bi-directional signal propagation makes use of standard machine learning algorithms impossible. Therefore, it would be interesting to design NN in which unidirectional spike propagation is possible even with symmetrically coupled neurons.Here, we demonstrate that the unidirectional signal propagation is realizable in symmetrically-coupled NNs based on AFM neurons. This regime is possible due to an effective inertia that originates from exchange coupling between the two magnetic sublattices [3] and creates a relatively long refractory period - an interval of time after a neuron fires when it is unable to fire again. We show, that it is possible to adjust synapse weights such that each neuron is still in its refractory period when it receives a backward propagating signal from its neighbors. Then, a simple chain of neurons receiving an input at one end carry the signal to the opposite end without any reflections.However, for such a simple chain of AFM neurons, an input can occur at either end, and thus spikes would be able to travel in both directions. It would be beneficial to create an ‘isolator’ neuromorphic circuit, which would allow the propagation of spikes in only one direction. Figure 1 depicts the schematic of a possible ‘isolator’ circuit composed of AFM neurons. This figure uses circles to represent AFM neurons. The isolator is composed of neurons 4, 5, and 6. In the figure, double arrows represent symmetrical synapses with arrow width proportional to the coupling strength.This isolator allows spikes to be carried “forwards” from neuron 1 to 9, but stops signals carried “backwards” from neuron 9 to 1, as illustrated by the results of numerical simulations shown in Fig. 2. The isolator functions as follows. When the spike is initiated in neuron 1 (Fig. 2(a)), it travels along the chain to neuron 4. Then, the spike generated by neuron 4 travels to both neuron 5 and neuron 6. Neuron 5 also generates a spike, which is carried to neuron 6. The synaptic weights connecting to neuron 6 are small enough that a single input is not sufficient to induce a spike in the AFM neuron. However, when both spikes combine at neuron 6, they provide enough stimulus for neuron 6 to fire. The spike can then continue to propagate from neuron 6 to 9. When traveling backwards (Fig. 2(b)), a spike begins at neuron 9 and travels unidirectionally to neuron 6. Neuron 6 will generate a spike, but the synaptic weights from neuron 6 to 4/5 are insufficient to induce an additional spike. This, in effect, prevents the backward travel of spikes through the isolator.Using the proposed isolator NN, it is possible to design a number of other neuromorphic circuits supporting unidirectional information propagation, for example, neuromorphic combiners and unidirectional memory rings. The creation of such circuits with symmetric synapses shows hope for AFM neurons to be used to create more realistic spiking NN. The delay caused by the exchange inertia in the AFM neurons plays a key role in any neuromorphic circuit constructed with these neurons. These physically realistic neurons will increase the possibility for more functional spiking neural network hardware. **