Mixed Delay/Nondelay Embeddings Based Neuromorphic Computing with Patterned Nanomagnet Arrays

TL;DR

This paper addresses the practicality gap in PNA-based neuromorphic reservoirs by introducing mixed delay/nondelay embeddings implemented on a single PNA node. By concatenating current nondelay embeddings with a history of delayed embeddings, the approach enriches the reservoir state without requiring many physical nodes, and a TMR-based readout maps the augmented state to time-series targets. The method achieves state-of-the-art imitation of NARMA sequences and highly accurate Mackey-Glass predictions while maintaining a compact reservoir, though long-horizon tasks still demand larger history or readout capabilities. Overall, the work demonstrates a scalable path to accurate, hardware-efficient time-series processing with PNAs, highlighting the tradeoffs between topology, memory, and readout complexity.

Abstract

Patterned nanomagnet arrays (PNAs) have been shown to exhibit a strong geometrically frustrated dipole interaction. Some PNAs have also shown emergent domain wall dynamics. Previous works have demonstrated methods to physically probe these magnetization dynamics of PNAs to realize neuromorphic reservoir systems that exhibit chaotic dynamical behavior and high-dimensional nonlinearity. These PNA reservoir systems from prior works leverage echo state properties and linear/nonlinear short-term memory of component reservoir nodes to map and preserve the dynamical information of the input time-series data into nondelay spatial embeddings. Such mappings enable these PNA reservoir systems to imitate and predict/forecast the input time series data. However, these prior PNA reservoir systems are based solely on the nondelay spatial embeddings obtained at component reservoir nodes. As a result, they require a massive number of component reservoir nodes, or a very large spatial embedding (i.e., high-dimensional spatial embedding) per reservoir node, or both, to achieve acceptable imitation and prediction accuracy. These requirements reduce the practical feasibility of such PNA reservoir systems. To address this shortcoming, we present a mixed delay/nondelay embeddings-based PNA reservoir system. Our system uses a single PNA reservoir node with the ability to obtain a mixture of delay/nondelay embeddings of the dynamical information of the time-series data applied at the input of a single PNA reservoir node. Our analysis shows that when these mixed delay/nondelay embeddings are used to train a perceptron at the output layer, our reservoir system outperforms existing PNA-based reservoir systems for the imitation of NARMA 2, NARMA 5, NARMA 7, and NARMA 10 time series data, and for the short-term and long-term prediction of the Mackey Glass time series data.

Figures (7)

• Figure 1: (a) A schematic representation of the core idea of physical reservoir computing. (b) A schematic illustration of the computational flow of reservoir computing. (a) and (b) are reproduced from yan_emerging_2024.
• Figure 2: X-ray magnetic circular dichroism (XMCD) photoemission electron microscopy (PEEM) image of a square topology PNA under the influence of external magnetic field. Dark and light-colored nanomagnets in the PNA represent two spin directions of the nanomagnet dipoles. When the external magnetic field amplitude changes from -20 Oe to -50 Oe to -80 Oe, the spin directions of different numbers of nanomagnets flip due to the collective dynamical behavior of the nanomagnets.
• Figure 3: Schematic of our proposed delay/nondelay embeddings based PNA reservoir system. (a) Mixed delay/nondelay embeddings generated by our proposed PNA reservoir system. The embeddings are a combination of nondelay and delay reservoir responses. (b) The layout of the perceptron at the output of the system that enables time series imitation and prediction tasks. A multiplayer perceptron with SELU activation function is shown but our design also works well with a single linear layer perceptron.
• Figure 4: NARMA predictions with the square ASI topology, showing improved tracking of the target signal as the order increases from 2 to 10.
• Figure 5: Comparison of short-term Mackey-Glass prediction error against implementations in prior works. Our system outperforms designs with much higher reservoir state dimensionality, by an order of magnitude or more.