Reservoir Computing with Nanowire Exchange-Coupled Spin Torque Oscillator Arrays

Abstract

Spin torque oscillators (STOs) feature transient non-linear behaviour that can be exploited for computation. When combined in arrays, they can be networked to produce more complex collective behaviours than single devices alone. We simulate a physical reservoir computer comprising an array of STOs, using a macro spin approximation. We demonstrate that STOs can be networked together in arrays using nanowires, and that by altering the properties of these nanowires we can optimise the magnetic exchange coupling between the oscillators for computational purposes. We train a simulated array of coupled oscillators to compute various time-independent and time-dependent benchmark tasks. We explore the effects of array size, heterogeneous coupling, and connection topologies. We demonstrate the computational potential of programming the exchange coupling in arrays of oscillators through nanowires.

A Benchmark Tasks

1.1 A.1 Spiral Classification

This task involves the nonlinear classification of two spirals in Cartesian space. The dataset consists of 400 data points describing samples taken from two spirals with random noise added. The task is to classify which spiral each sample belongs to using only the (x, y) Cartesian coordinates. The spiral classes are encoded as two outputs and the predicted class is chosen as the output with highest value via a softmax function.

1.2 A.2 PIMA Indians Diabetes Classification

This dataset¹ contains real-world data related to medical diagnosis. The objective of the dataset is to diagnostically predict whether or not a patient has diabetes, based on certain diagnostic measurements. The dataset consists of several independent medical predictors including the BMI, blood pressure, and age of females at least 21 years old of Pima Indian heritage.

The database consists of 768 records. There are 268 positive and 500 negative classes. Each class is one-hot encoded into separate reservoir outputs. All input features (e.g., age) are normalised within [0, 1] before use. The training set consists of 75% of samples, and test set 25%. Each sample is randomly chosen from the database and each set maintains the same percentage of each class, respectively.

1.3 A.3 NARMA-10

The NARMA (nonlinear autoregressive moving average) task [2] evaluates a reservoir’s ability to model a 10-th order non-linear dynamical system. The task contains both non-linearity and a long-term dependency created by the 10-th order time-lag. The task is to predict the output $y(n+1)$ given by eq.(2) when supplied with $u(n)$ from a uniform distribution of interval [0, 0.5]. For the 10-th order systems $\alpha = 0.3$, $\beta = 0.05$, $\delta = 10$ and $\gamma = 0.1$.

$$\begin{aligned} y(n+1) = \alpha y(n)+\beta y(n)\Bigg (\sum _{i=0}^{\delta }y(n-i)\Bigg ) + 1.5u(n-\delta )u(n)+\gamma \end{aligned}$$

(2)

A total of 5,000 values are generated and split into: 3,000 training, 1,000 validation, and 1,000 test. The first 50 values of each sub-set are discarded as an initial washout period.

1.4 A.4 Japanese Vowels

The Japanese vowels dataset [9] consists of time-series data for multi-speaker classification. The data contains utterances of two Japanese vowels ‘ae’ by nine different male speakers. The dataset consists of 270 training utterances (30 utterances by 9 speakers) and 370 different utterances for testing (24–88 utterances by the same 9 speakers). Each utterance is pre-processed using linear prediction analysis into a discrete-time series of between 7–29 frames in length with twelve LPC cepstral coefficients.

Both the training and test data are randomly shuffled, because the original dataset groups each speaker into consecutive blocks. After every utterance is ran through the reservoir, the states of all nodes are concatenated for training. To decide on the final predicted speaker, a softmax function is used. This assigns a probability to each speaker, with the highest probability used to assign the predicted speaker.