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Towards smart sensing with a spintronic reservoir computer

G. Venkat¹, I. Vidamour¹, T. J. Hayward¹, L. Manneschi², M. O. A. Ellis², C. Swindells¹, E. Vasilaki², P. W. Fry³,D. A. Allwood¹

¹Department of Materials Science and Engineering, University of Sheffield, Sheffield, S1 3JD, UK

²Department of Computer Science, University of Sheffield, Sheffield, S1 4DP, UK

³Nanoscience and Technology Centre, University of Sheffield, Sheffield, S3 7HQ, UK

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Take home: Magnetic ring arrays can do computation with multiple physical stimuli!

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Need for smart sensing

Modern applications have a large number of sensors
Significant overhead due to central hub communication and processing
Smart sensors offer an exciting alternative where sensing, processing and actuating is done in a single device

https://learnmech.com/car-sensors-types-function-of-vehicle-sensor/

Majumder, Sumit, and M. Jamal Deen. "Smartphone sensors for health monitoring and diagnosis." Sensors 19.9 (2019): 2164.

Lorincz, Josip, Antonio Capone, and Jinsong Wu. "Greener, energy-efficient and sustainable networks: State-of-the-art and new trends." Sensors 19.22 (2019): 4864.

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In-materia computing

Microprocessor based processing required A/D-D/A conversion
In-materia computing can use the dynamics of material response to stimuli
Magnetic systems respond to various stimuli like fields, currents, temperature, strain, light

https://realpars.com/smart-sensor/

Tanaka, Gouhei, et al. "Recent advances in physical reservoir computing: A review." Neural Networks 115 (2019): 100-123.

A typical smart sensor used a base sensor and a microprocessor for processing incoming data and generated required output signals. Because of the digital architectures of microprocessors, A/D and D/A converters are required and this might not be suitable for all data streams and have their own energy overheads.

In recent years, in-materia computing has been proposed which uses the dynamics materials excited by stimuli for computation. The idea is that the states and variations in response of these materials can provide properties suitable for processing information. Evidently, one feature that is looked for in physical systems to be suitable for this computation is the ability to be stimulated by various methods and magnetic systems are particularly attractive as they respond to magnetic fields, currents, temperature, strain and light.

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Reservoir Computing

Reservoir computing is a development of recurrent neural networks.
Recurrent network with fixed synaptic weights (the reservoir) connected to a trainable readout layer.

Good at analysing time-dependent data (e.g. human speech, other time series)

Interesting for hardware realisations as the reservoir can be replaced any physical system that has the following properties:

Non-linear response to input.
Fading memory of past inputs.

Input

Reservoir

Readout

Input

Readout

Feed inputs into device

Reservoir

Physical System

-Non linear response

-Fading memory

Read out state of device

Role of the reservoir is to transform input data into a form that is more easily classifiable.

So, let’s go into a bit more details in this type of computation. The specific type of computation that we are considering is Reservoir computing (which has been mentioned a few times before). Basically, RC, in its original form is a recurrent neural network with fixed internal weights which is called a reservoir. It is connected to a trainable readout layer and only this part of the network is trained. RC is suitable for processing of signals in the time domain such as human speech or ambient condition variations.

Now, since the reservoir has fixed weights, it can be replaced with a physical system and this is what makes RC very attractive. This physical system should have certain properties for it to behave as a reservoir:

A non-linear response to stimuli (which is our data input)
Fading memory to past inputs – basically asymptotic washing out of inputs

One can think of the role of the reservoir as transforming input data into a space where is becomes more easily classifiable into categories. This is vary useful for a lot of real-life tasks

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Domain Walls in Ring-shaped Nanowires

Ring-shaped nanowires form two magnetic states.

Onion state – DWs rotate with rotating applied field.
Vortex state – circulating magnetisation.

When multiple rings are connected the junctions act as pinning sites.

Produce domain wall interactions that may cause population or depopulation of DWs in the rings.

At intermediate applied fields these processes will be stochastic!

H

Onion State

H

Vortex State

Propagation

Depopulation

m

Repopulation

High Fields

Low Pinning

Low Fields

High Pinning

Stochastic Region

4 µm

Micromagnetics (mumax³)

t = 20 nm

So, from the take home message, it is obvious that we are working with magnetic rings. Let us look at basic magnetic states in a ring. The two meta-stable ground states of a ring is the:

Onion state with two 180 deg separated domain walls and this is usually obtained at remanence after saturating the ring
Vortex state is a flux closure magnetic state with no domain walls

Things get more interesting when we consider two rings – Depending on the strength of fields applied, we can get different behaviours of domain walls. At high fields, propagation of domain walls in the system will occur. At other field regimes, we can get repopulation and depopulation of DWs. Importantly, this can happen stochastically and so this provides a richness of states in the system and the dynamic variation of the system response which is very useful.

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Creating Electrical Devices

Rich signals produced when rotating magnetic fields applied.

Frequency components at 1x and 2x field frequency.
Transient dynamics between states.
Non-linear response, fading memory…
We have a reservoir!

I+

V+

I-

V-

H

20 µm

t = 10 nm

Vidamour et al. arXiv preprint arXiv:2206.04446 (2022). (under review)

Voltage (V)

H = 20 Oe

H = 34 Oe

H = 30 Oe

Voltage (V)

Dawidek et al, Adv. Funct. Mater. 2021 2008389.

The dynamics in an array of rings become even more richer and useful. We have studied the behaviour of ring arrays in details and these can be found in this publication. Here, I am going to concentrate on electrical devices made using these ring arrays. We have electrical contacts for reading anisotropic magnetoresistance (AMR) signals from these arrays and apply a rotating magnetic field as stimuli or data inputs. The electrical responses of these arrays are quite rich and we obtain two distinct frequency components:

One at the frequency of the rotating field
Other at the twice the frequency of the rotating field (which is more conventional for AMR)

We also observe transient dynamics at different input regimes and shown here is

a strongly non-linear AMR response with rotating field amplitude
And different settling times of the AMR response at different fields

So, we get a strongly non-linear response and fading memory of the system which makes it a reservoir!

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How does one physically reservoir compute?

Modulate applied field strength according to input

Measure evolving AMR response

Split AMR response into 1f and 2f components

Extract features from envelope of signals

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Speech Recognition

Demonstrate computational ability with benchmark speech recognition task.
TI-46 spoken digit database.
Use Computation Quality (CQ) to identify input encodings that perform well in classification tasks.

CQ = KR – GR.

<2 % error when trained using SpaRCe online training algorithm.

50 Virtual Nodes.
Output = raw signal, 1f and 2f signals sampled 2x per input

5x female speakers from TI-46 database
Data pre-processed via a Mel-Frequency Cepstral filter

Vidamour et. al. arXiv preprint arXiv:2206.04446 (2022). (under review)

L. Manneschi et. al. IEEE Transactions on Neural Networks and Learning Systems 34, 2, 824-838 (2023)

ΔH (Oe)

Appeltant, Lennert, et al., Nature communications 2.1 (2011): 468.

So, how good is the computation?

We consider the example of speech recognition. There is a standard dataset called the TI-46 with digits spoken by 5 female speakers. Data here is pre-processed using a mel-frequency cepstral filter and input to the system. Note that this task involved multi-dimensional input and so the single dynamical node approach introduced by Appeltant et al. was used here. This approach basically leads to a time multiplexed form of inputting information and has been used for other magnetic systems.

So, one method of judging how good physical systems can reservoir compute is to look at task agnostic metrics. Two of them being the:

Kernel rank – which tells us how to well the reservoir can separate distinct inputs
Generalisation rank – which tells us how well the reservoir can generalise similar inputs

Computational quality is their difference and we want a high CQ for computation. So, by finding this metric as a function of input encoding, we can find the reservoirs computational suitability and also regions of operation. In fact by improving on methods of learning (using online learning systems such as SpaRCe), we can report some of the highest accuracies of >98% in this task

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How can magnetic ring arrays be used as smart sensors?

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Applying a temperature gradient

Ring array chip mounted on a Peltier cell – temperature can be controlled
Temperature monitored using a pyrometer above the sample
Field driven response shows a consistent shift with temperature – Linear shift

B_rot

Pyrometer

Heat sink

Peltier

Sample

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Temperature driven computation

Neural ODE model– approximates device output

Temperature driven shift in field response included in model

Used to identify regions of operation and predict device operation for tasks
Output layer of network is trained on measured temperature variation
Thermal variation in resistance is subtracted from the measured electrical signals

So, how do we use this temperature variation for computation?

We first modelled the response of the system using a neural ODE based model (developed by our colleagues in the Comp. Sci. department at UoS) which provides very good reproduction of the system AMR response. The temperature driven shift of the field driven response was also incorporated into the system. This model is very useful as it allows us to identify regions of operation of the device and predict utility for different tasks

For different tasks, different inputs in temperature was applied (as shall be described in next slides) and the output layer of the RC was trained on the measured temperature. I also want to point out that the thermal variation of the resistance (which is substantially higher than the thermal variation of the AMR) was subtracted from the measured AMR signal. So, we can be sure that the computation was being done by the magnetic (and thermally driven magnetic) response of the device.

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Demonstration : Signal transformation

Neural ODE predicts excellent reconstruction of signals from AMR output
Experimental reconstruction is good and some deviations observed in reconstruction of highly non-linear signals

Preliminary

ReLU

Sine²

Sawtooth

Prediction

Measured

Input to system caused sinusoid temperature variation

So, the first demonstration that I shall discuss is that of signal transformation. The input here was sinusoid to the Peltier and this is reflected in the measured temperature variation of the sample.

I want to point out that the data I am showing here and in the next slide is preliminary and ‘hot of the press’. The N-ODE model predicts that we have dynamics rich enough for a variety of transformation and I am showing here the cases of the transformation from sinusoid to ReLu (a standard machine learning response), sine-squared and sawtooth wave. The N-ODE predicts excellent transformation and experimentally we obtain good transformation which you can see visually. The error in transformation increases for more non-linear signals (like the sawtooth wave) and we are currently working in tuning the hyperparameters of the system for even better agreement. However, these results clearly show that the temperature and field driven dynamics of the system are rich enough for non-linear transformations which is useful for computation.

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Demonstration : Mackey-Glass oscillator

Mackey-Glass oscillator expresses delayed feedback dynamics – used for prediction tasks
Typical oscillating behaviour of error with prediction delay is seen
Experimental reconstruction is good and some deviations observed in larger amplitude regions of test signal

Preliminary

We also wanted to test the prediction capabilities of the system. To test this, we tried predicting the Mackey-Glass oscillator dynamics which is again used widely in machine learning as Jack showed in his talk. Again, the measured temperature variation of the system mimics the input applied to the system.

The reconstruction of the dynamics from the AMR response of the device shows some reasonably good predicting behaviour of the system and if we look at how the mean squared error of prediction varies with the number of future steps, we see a typical oscillating behaviour which is also seen in other systems.

Again, we think that more tuning hyperparameters of the system will give us better performance and we are working on that. However, these results do show that the system has capabilities of predicting temperature behaviours which will be very useful for smart sensing applications.

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Take home: Magnetic ring arrays can do computation with multiple physical stimuli!!

Poster 46:

Agent-Based Modelling of Magnetic Metamaterials

I. Vidamour

Poster 27:

Efficient Interfacing with Magnetic Metamaterials for Reservoir Computing

C. Swindells

Talk:

Magnetic binary stochastic synapses for machine learning applications

M. Ellis

Poster 26:

Nailed it: Reservoir computing with a rusty iron nail

C. Swindells

So, here is the take home message once again.

I would like to also highlight a few posters and talks from our group which might interest you:

Ian has a poster on modelling the physical behaviour of these ring arrays with large number of rings and how our understanding has developed of the processes in them
I have been talking about readouts using AMR and driving magnetic behaviour using magnetic fields. Charles has a poster on more exotic and useful methods of inputs and outputs using SOTs and FMR readouts which will make the ring arrays more attractive as devices and make them useful for more advanced computation.
Charles also has another poster on using the inductive response of a rusty iron nail for RC which does not need any device fabrication at all!
Finally, later on in this session, Matt Ellis has a talk on using the stochastic DW interactions in magnetic nanowires for machine learning.

Thank you and any questions?

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Backup slides

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Demonstration : Mackey-Glass oscillator

Preliminary

We also wanted to test the prediction capabilities of the system. To test this, we tried predicting the Mackey-Glass oscillator dynamics which is again used widely in machine learning as Jack showed in his talk. Again, the measured temperature variation of the system mimics the input applied to the system.

The reconstruction of the dynamics from the AMR response of the device shows some reasonably good predicting behaviour of the system and if we look at how the mean squared error of prediction varies with the number of future steps, we see a typical oscillating behaviour which is also seen in other systems.

Again, we think that more tuning hyperparameters of the system will give us better performance and we are working on that. However, these results do show that the system has capabilities of predicting temperature behaviours which will be very useful for smart sensing applications.

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Interconnected ring arrays

Ring arrays fabricated using nanofabrication techniques
System perturbed using rotating magnetic fields

Highly non-linear response to rotating field amplitude
Intermediate regime where a combination of magnetic states stochastically exist

B

Nonlinear response!

Fading Memory!

Magnetic states show markedly different evolutions at successive field amplitudes
Washing out of evolution indicates fading memory

Dawidek et al, Adv. Funct. Mater. 2021 2008389.

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NARMA 5/NARMA 10

Previous reservoirs designs have low linear memory capacity.

MC < 3.
Due to temporal multiplexing.

Using the Rotating Neuron Reservoir (RNR) approach allows input mask to “freeze” nodes and use the non-volatility of the system to store data.

Enhances MC to ~12.

Use NARMA5/10 task to measure non-linear memory.

Vidamour et. al. arXiv preprint arXiv:2206.04446 (2022). (under review)

Liang et. al. Nature Comms 13 1549 (2022)

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Rapid Simulation of Ring Array Output

Recently proposed approach using Neural Ordinary Differential Equations
Neural network used to parametrise inputs to ODE solver
Learns to predict future outputs of system given delayed state and future inputs
Trained on experimentally gathered data from devices
Allows simulation of many NRA nodes simultaneously

ODE Solver

Outputs

Output

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Demonstration : Signal transformation

Ring array chip mounted on a Peltier cell – temperature can be controlled
Temperature monitored using a pyrometer above the sample
Field driven response shows a consistent shift with temperature – Shift is linear

ReLU

Sawtooth

Sine³

Square

Signal²

Signal[t+10]

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Reservoir Architecture

Device in current form only has one input and one output.
Need to use time-multiplexed approach to create reservoir state
Device dynamics connect “virtual nodes” together.

Appeltant et. al. Nat Commun 2, 468 (2011).

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Measuring Array Response

Magnetic response measured via AMR
2 mechanisms leading to resistance change

DWs propagating around rings → 2 x clock frequency
Stretching of pinned DWs → 1 x clock frequency

Sub-signals have different nonlinear relationships to field

I+

V+

I-

V-

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Talk Outline

Smart sensing
Magnetic states in rings and arrays of rings

Measurements of magnetic nanostructures

Lattice geometry variation in ring arrays

Dynamic responses of different lattices
Timescales of dynamics
What happens in the arrays microscopically?

Measuring reservoir metrics in arrays

Task independent metrics
Different reservoir architectures
How do we measure these metrics?
Computational quality and memory capacity of different lattices

Conclusions

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How do magnetic ring arrays work?