3 Figure 1.3 Next-generation atomic switching network ASN device structure…… 6 Figure 1.4 Result of RC benchmark task: waveform generation for ASN device with Ag/Ag2S nanowire junction……
INTRODUCTION
Research background
Advances in Moore's law have led to significant performance improvements in von Neumann architecture by miniaturizing transistors However, the limit of transistors has been reached, prompting the exploration of new chip platforms Neuromorphic computing emerged as a solution, mimicking the structure of neurons and synapses Human brains, with their superior power efficiency and computing speed, inspire this approach Neurons transmit signals through synapses that play a crucial role in learning and analog logic By replicating brain functions electronically, neuromorphic devices aim to imitate the brain's operation Unconventional computing, inspired by natural systems, investigates non-von Neumann solutions with low power consumption and enhanced problem-solving capabilities.
Artificial neural networks (ANNs) are computational models that simulate neurons and their networks An ANN is made up of three layers: input layer, hidden layer, and output layer They are represented a neuron-like network interconnected via binding weights between layers, known as synapse-like weighted links, which indicates the strength of the connections between neurons Feedforward networks (FNNs) and recurrent networks (RNNs) are the two most common ANN network architectures FNNs are recommended for static (non-temporal) data processing, whereas RNNs are preferable for dynamic (temporal) data processing Besides that, because of their distinct feedback connections, RNNs are capable of simulating dynamical systems driven by sequential inputs
Figure 1.1 Structure comparison between feedforward neural network (FNN, left) and recurrent neural network (RNN, right) The yellow circles, blue circles and green circles represented input layer, hidden layer, and output layer, respectively While FNN recommended to independent data, the output of RNN depend on the prior elements within the sequence, hence, the RNN has their distinct feedback connections in the hidden layer
The motivation for physical neural network implementation is to create fast information processing devices with low learning cost We rely primarily on advanced material science for this physical implementation ANNs models have recently been widely used in material science because of their unique features, which
Reservoir computing (RC), a promising approach within material-based neural networks, offers an alternative for electrical circuits involved in dynamic data processing Originating from recurrent neural networks (RNNs), RC excels in dynamic information processing due to its ability to learn quickly and efficiently In RC, an RNN in the reservoir transforms input data into high-dimensional spatiotemporal patterns, enabling pattern analysis for readout Crucially, the reservoir's internal state changes with input, allowing it to encode both past and present inputs, ensuring temporal information processing capabilities.
Figure 1.2 RC framework where a reservoir for nonlinear mapping input into a high- dimensional computational space (Left) The reservoir random network is unregulated and only the readout is trained by a simple supervised readout layer to learn the linear combinations of network states Here, Ag/Ag 2 S aggregated NPs plays the role as reservoir layer by create a randomly connected network and combining with electrodes pattern to replicate RC system (Right)
As illustrated in Figure 1.2, on the left side, a RC system consists of the input layer transmits time inputs, the reservoir, a nonlinear randomly connected network, for mapping input into a high-dimensional computational space, and the outputs layer is linked to a higher dimensional computational space The reservoir random network is unregulated and only the readout is trained by a simple supervised readout layer to
Reservoir computing (RC) employs nonlinear dynamical systems to perform computation tasks By optimizing output weights, RC enables target tasks to be constructed through weighted linear combinations of all outputs This approach offers quick learning, reducing training costs RC can also leverage the dynamic behavior of random networks by implementing hardware using various physical systems As a result, it finds applications in diverse physical systems, including photonic and memristive systems The realization of RC models in physical systems has garnered significant attention Key requirements for efficient reservoir computing include nonlinearity, phase shift, and high dimensionality Setting system parameters close to the edge of chaos, where the transformation by a reservoir is neither very expanding nor contracting, is crucial for optimal performance.
RC computing However, because it is difficult to check in a material reservoir, these three properties are chosen instead of the edge of chaos These electrical characteristics are needed for in-materio RC devices because they must demonstrate nonlinear sequential input into a high-dimensional computational space The nonlinearity property enables reservoir to function as a nonlinear mapping, it is also essential for efficiently extracting nonlinear dependencies of input High dimensionality is necessary to map input into high-dimensional space The dimensionality related to the number of independent signals obtained from reservoir This characteristic enables the extraction of input's spatiotemporal dependencies Another essential property is phase shift, which represent for the influence of past inputs on current reservoirs state This feature is especially crucial for describing sequential data with short-term memory
In this nanoscale era, the advances in nanoscale technology are boosting a great impulse towards the miniaturization of device manufacturing, integration, and system design Furthermore, nanoscale techniques have an enormous potential for developing novel materials and devices with distinct properties, balancing thermodynamic and kinetic effects A hardware technique created employing nano- architectural approaches, provides a framework for the development of biologically inspired nanoscale logic and memory devices, known as the atomic switch [13] The atomic switch is a memristive electro-ionic circuit element which provides multistate, nonlinear switching and synapse-like memory characteristics, operating through a bias-driven filamentary switching mechanism across a metal–insulator–metal junction [14] A complex network comprised of nanomaterials (such as overlapping nanowire junctions [15] or aggregated nanoparticles [16]) enables the formation of a group of atomic switches The distributed nonlinear dynamics of the atomic switching network (ASN) make it an ideal candidate for RC
Considering their properties, noble metals such as silver nanomaterials are among the most intriguing elements Recently, there has been a surge of interest in the study of the electrical characteristics of Ag/Ag2S, especially for its atomic switching network construction Some Ag/Ag2S topologies and structures such as thin films [17] or nanowires [14] was investigated which manifesting atomic switching behavior, results in a consistent in I-V nonlinearity behavior and higher harmonics generation, exhibiting neuromorphic features Such traits are projected to be improved by increasing relative surface area and built more interaction between the nanomaterials Here, we investigated Ag/Ag2S nanoparticles (NPs) which has large surface area In this study, the purpose is to investigate whether Ag/Ag2S aggregated NPs enable to play the role as reservoir layer by create a randomly connected network and combining with electrodes pattern to replicate RC system, as illustrated on the right side of Figure 1.2 Several investigations on nanomaterial-enabled RC computing in physical devices have been conducted, which are combined as references and
6 guidelines to inspire us to perform this work Some representations were discussed in the following section.
Literature survey: in-materio unconventional computing
1.2.1 Atomic switch networks for reservoir computing
A next-generation computing system by ASN device which utilize Ag/Ag2S nanowire junction has been reported [15] This ASN device contained 128 measurement electrodes, which is fabricated by using conventional lithographic methods by patterning platinum onto a thermally oxidized Si wafer followed by insulation with SU-8 and evaporated copper grid (Figure 1.3(a)) In the center, a complex network of overlapping silver nanowire junctions grown onto a multi- electrode array is functionalized to produce Ag∣Ag2S∣Ag atomic switches with controllable densities of up to 10 9 junctions/cm 2 , as shown in insect of Figure 1.3(b) The atomic switch operation is regulated by filament formation between silver nanowire junctions, result in this ASN device exhibit non-linear characteristics, validated for memristive activity, as depicted in Figure 1.3(b)
The next-generation atomic switching network (ASN) device (Fig 1.3a) consists of 128 lithographically patterned platinum measurement electrodes, insulating SU-8 dielectric layer point contacts, and an evaporated copper grid The ASN device exhibits memristive-like non-linear characteristics observed in single junctions (Fig 1.3b) Notably, the silver nanowire junctions in the device center region are shown in an enlarged inset view.
Utilizing the dynamic, non-linear guided by interacting atomic switches from silver
7 nanowire junctions, the ASN device was applied to the RC benchmark task of waveform generation A 11 Hz bipolar sinusoidal voltage was injected to ASN for inducing switching activity, and the readout output was collected to optimized target wave forms: cosine, triangle, sawtooth square The experimental accuracies in the 70–90% range were obtained, using 62 measurement electrodes, as shown in Figure 1.4
Figure 1.4 Result of RC benchmark task: waveform generation for ASN device with Ag/Ag 2 S nanowire junction
1.2.2 Gold nanoparticles network for reconfigurable Boolean logic
In the realm of materials engineering, a novel approach seeks to integrate unconventional computing principles This approach leverages computational models to train new materials, enabling their evolution into artificial intelligent systems capable of mimicking logic gate functions A notable example of in-materio unconventional computing was observed in disordered gold nanoparticles, where the non-linear negative differential resistance response was optimized using evolutionary algorithms to achieve reconfigurable Boolean logic operations in real-time This groundbreaking research opens up exciting possibilities for the development of unconventional computing systems.
8 nanoparticle network assembly in a 200 nm diameter circular area between the eight Ti/Au electrodes At a low-temperature environment (≈ 0.3 𝐾), the device exhibits Coulomb blockade and employs single-electron tunneling (SET) features VIN1 and
VIN2 are used as two electrodes input which introduced time-varying voltage signals The other six electrodes are used to apply static control voltages V1–V5 and measure the resultant current IOUT A static voltage V6 is also applied to the back gate Based on the strongly nonlinear (switching) behavior of the SETs and their mutual interactions, these configuration voltages are repeatedly utilized to realize fully reconfigurable, robust Boolean logic in disordered Au NP networks
Figure 1.5 Schematic of disordered Au nanoparticles network reconfigurable Boolean logic The Au NPs, which are coupled by insulating molecules (1-octanethiols), are confined in a circular area (200 nm in diameter) constructed from 8 radial metal (Ti/Au) electrodes on top of a highly doped Si/SiO 2 substrate, which serves as a back gate At low temperature (≈
0.3 𝐾), as a result of the Coulomb oscillations of the individual NPs, this disordered NP assembly generates an interconnected network of robust nonlinear periodic switches These non-linear negative differential resistance output responses were reconstructed to reconfigurable Boolean logic operations via real-time voltage optimizations with Evolutionary algorithm.
However, the drawback for this demonstration lay in the operating temperature condition is near-zero K, along with time inefficient training as each V parameter had to be trained individually Therefore, in the field of material-based machine intelligence, what we desire for is a room temperature computation with straightforward and simultaneous parameter optimization model
1.2.3 Spoken digit classification with silver iodide (AgI) nanowire networks
Another investigation the ability of silver nanomaterials enables to realize physical
RC was conducted by Sam Lilak et al [18] An atomic switch networks comprising silver iodide (AgI) junctions has been physically characterized and utilized to classify spoken digit audio data In this work, silver iodide was produced at ambient temperature by reaction of iodine vapor with silver nanowires in vapor phase This material provides voltage-controlled resistance in both the bulk and when integrated into crossbar architectures, rendering it suitable as a memristive material for RC applications As show in Figure 1.6, a 16-electrode grid of Pt was fabricated by photolithography, metal deposition and lift-off process, served as substrate for AgI ASN device enabling spatiotemporal stimulation and monitoring AgI nanowire networks was tested for non-linear, temporal computation through the spoken digit classification
An AgI-based artificial synaptic network (ASN) device consists of nanowire junctions (Figure 1.6a) Scanning electron microscopy (SEM) reveals interconnected AgI nanowires, forming a network (Figure 1.6b) This network serves as the synaptic junctions, enabling the formation of filaments and mimicking neuronal behavior.
Figure 1.7 (a) Flow chart for spoken digit recognition RC task using ASN-based devices involved encoding and separation of raw audio data into mel-frequency Individual mel- frequency was arranged to minimize input thrashing and then introduced as input voltage to the ASN device Output data was collected from the rest electrodes (b) Performance of the spoken digit classification task, as compared to using the “Input Only” mode, task performance was improved by the “Reservoir” readout method, as depicted via mean accuracy and standard deviation Task performance still can be maintained under low- power operation of AgI ASNs
AgI nanowire networks exhibit nonlinear dynamics, enabling stable signal modification This property makes them suitable for spoken digit recognition tasks Raw audio data is encoded into mel-frequency cepstrum coefficients (MFCCs), optimized for input minimization, and then introduced into the AgI nanowire network as input voltage Output data is collected and optimized using linear regression Results show high accuracy in digit recognition using the "Reservoir" readout method compared to the "Input Only" mode Task performance remains consistent even under low-power operation across a wide range of input voltages.
The novel AgI-based ASN devices described here acted as a dynamic, memristive reservoir for nonlinear temporal data processing and proved the potential to effectively classify spoken digits with high accuracy
Combining all those preceding studies, these silver nanomaterial networks constitute both a promising material system ripe for further exploration and a possibility to advance the paradigm of in-materio RC computing forward practical applications Hence, silver nanomaterials, particularly silver nanoparticles are considered as ideally research subjects in our study
Outline of research
In the present study, we report the utilizing of Ag/Ag2S nanoparticles for developing material-based RC The purpose is to investigate the possibility of using Ag/Ag2S nanoparticles to develop a new computing paradigm called in-materio reservoirs
Firstly, chapter one introduces the motivation, research field and literature survey to draw the objective and research scope for this study Chapter two explains detail about synthesis material process, device fabrication and experiment set up for characterizing Ag/Ag2S NPs device
X-ray diffractometry (XRD) and transmission electron microscopy (TEM) verified the structural properties of Ag/Ag2S nanoparticles The electrical characteristics were analyzed through current-voltage (I-V) and voltage-time (V-t) measurements using a Source Meter and a data acquisition system Chapter three presents these procedures and results, which demonstrate the characteristics essential for implementing physical reservoir computing, including nonlinearity, high dimensionality, and phase shift.
Lastly, after demonstrating that the Ag/Ag2S nanoparticle aggregates had the nonlinearity electrical behavior and additional characteristics required for RC hardware namely phase-shift and higher harmonics which are vital for the implementation of RC computing, in chapter four, RC benchmark task waveform generation is realized by a linear combination of outputs Others more complicated
RC task such as: objects classification, Boolean logic operations and spoken digit classification are also performed with microscale platinum electrodes to implement the nonlinear dynamics of Ag/Ag2S nanoparticles Finally, chapter five presents the conclusion of this study along with some specific suggestions.
METHODOLOGY
Ag/Ag 2 S nanoparticles synthesis
The Ag/Ag2S nanoparticles were synthesized at room temperature by modified Brust- Schiffrin procedure [19] referring from earlier study of C Battocchio et al [20] As illustrated in Figure 2.1, experiment process is as follow: 200 mg silver nitrate (Signa- Aldrich, MW: 79.55 gr/mol) in deionized (DI) water was mixed with toluene solution of 360 mg tetraoctylammonium bromide (Signa-Aldrich, MW: 546.79 gr/mol), then 0.37 ml allyl mercaptan (Tokyo Chemical Industry, MW: 17.03 gr/mol) in toluene was added to the solution and left to react for 30 minutes while being stirred magnetically Subsequently, a reducing agent of 260 mg sodium borohydride (Tokyo Chemical Industry, MW: 37.83 gr/mol) solution in DI water was added to the mixture and allowed to react for 2 hours under magnetically stirred The water phase was then removed, and 250 ml ethanol was added to wash the excess of allyl mercaptan and toluene solution The obtained solution then centrifugated at 4000 rpm for 20 minutes to separate the nanoparticles from the liquid phase The Ag/Ag2S NPs was attained and ready to be used for further experiments
Figure 2.1 Ag/Ag 2 S NPs was synthesized following Brust-Schiffrin method
Device fabrication
For device realization, the optical lithography along with metal deposition was used to create the metal 16 electrodes Firstly, electrodes pattern was designed by LayoutEditor software and used as the model for optical lithography Next, SiO2/Si substrate was washed with acetone, immersed in isopropyl alcohol (IPA), washed again by DI water, each step takes 5 minutes, then dried with N2 gas Thereafter, 1 àm thickness of LOR-10 was put onto substrate using spin coater under 3000 rpm for
50 s, followed by heated it on hot place in 5 mins under 180 ℃ Then, 1.8 àm thin, homogenous layer of photosensitive resist is covered the substrate by sprinkling resist solution (S1818G filtered by 0.45 àm PTFE filter paper) onto the sample, which is then spun at 4000 rpm for 20 s After baking the resist on hot plate (90 ℃, 5 mins), the sample is placed in a mask aligner, which is equipped with a high-powered light source performed by SUSS MicroTec photolithography machine, that exposes the resist film through the mask By immersing the sample in developer MF-319 for 1 min, the corresponding parts of the resist film are removed, then rinse by DI water and dried with N2 gas The metallization step was done by depositing Pt/Ti (electrode material) with 24/6 nm of thickness on a SiO2/Si substrate, following metallization, the resist is typically removed by dimethyl-sulfoxide at 80 ℃ for 40 mins under sonicating in a lift-off process There is a circular gap with 30 àm diameter in the central of electrodes array and the distance between two nearest electrodes is 4.5 àm The 16 platinum electrodes pattern was archived and the RC in-materio reservoir device was formed by drop-casted 5 àL of the synthesized Ag/Ag2S NPs on the center of electrodes while putting on a hot plate set at 50 ℃ for ethanol solvent evaporation
A chip package was fabricated for the device, facilitating simultaneous recording of multiple output electrodes This setup allows for the investigation of dynamic computing processes within a reservoir The device fabrication process is summarized in Figure 2.2.
Figure 2.2 (a) The Ag/Ag 2 S NPs in-materio RC device realization by drop-casting those particles onto 16-electrodes produced by optical lithography, as a result the device was fabricated The optical microscope image shows the center area enlarged view of electrodes pattern There is a circular gap with 30 àm diameter in the central of electrodes array and the distance between two nearest electrodes is 4.5 àm (b) A chip package was fabricated for the device with each electrode was connected to a pin for simultaneously measurement
Characteristic measurement
To explore the characteristics of produced nanoparticles, a variety of characterization approaches were studied X-ray diffraction spectrometry (XRD) and transmission electron microscopy (TEM) were used to investigate the structural properties of Ag/Ag2S NPs such as element identification, morphology, and particle size
X-ray diffraction (XRD) is a method for analyzing crystalline materials Ag/Ag2S NPs sample preparing for XRD characterization is required in powder form Following a successful synthesis as mentioned above, the Ag/Ag2S nanoparticle in ethanol solvent was collected and centrifuged, followed by a drying of the precipitates to get nanoparticle powder as show in Figure 2.3 (a) In this study, the sample was analysis using an X-ray diffractometer (Rigaku RINT-2100) with Cu Kα radiation at
40 kV (λ = 0.154 nm) The scan rate was 0.02 degrees per second This method's operating process relies on an emitted X-ray beam with a λ wavelength that assails lattice structure in a crystal plane at an θ angle The result for XRD characterization will be shown in section 3.1.1
Figure 2.3 (a) The sample holder covered by Ag/Ag 2 S powder prepared for X-ray diffraction (XRD) analysis process (b) X-ray diffractometer (Rigaku RINT-2100) picture.
Transmission electron microscopy (TEM) is a method for examining the characteristics of extremely tiny objects particularly in nanoscale In this study, transmission electron microscopy (TEM, JEOL-2100) with acceleration voltage at
200 kV was utilized for morphology analysis of Ag/Ag2S nanoparticles Because the wavelength of an electron is substantially short, TEM was used to examine particles at much higher magnification and resolution Compared to scanning electron microscope, which can only scan and observed the sample's surface, TEM also produces better resolution pictures From TEM image the morphology of nanoparticles is able to observe, and the particles diameter can be calculated Sample preparation for TEM is also simple, there is a sample holder have grid shape and the Ag/Ag2S NPs in ethanol solvent was drop into the grid then get it dry by using hot plate at 50 ℃, the sample holder image and sample preparation are briefly illustrated in Figure 2.4 This is how TEM operate: a beam of electrons is fired by an electron gun Using extreme high-level voltages of up to several million volts, electrons were accelerated to exceedingly high speeds The vacuum system is required to ensure the acceleration process Then, a condenser lens focuses the electron beam into a narrow beam Electrons pass through the ultra-thin specimen and depending on the transparent degree of the sample to electrons, some components of the beam are transmitted The objective lens converts the sample's output beam into a picture The TEM analysis result will be shown in section 3.1.2
Figure 2.4 Transmission electron microscopy (TEM) sample preparation and TEM sample grid holder structure
The purpose of fabricating the device is to investigate the possibility of Ag/Ag2S nanoparticles to be used as an in-materio reservoir computing hard-ware Therefore, the required electrical property of RC devices must appear on this Ag/Ag2S NPs device Several characterization techniques, including current-voltage (I-V) characteristics and RC characterize measurement, were used to explore the electrical properties of the Ag/Ag2S nanoparticles-based device
Current-voltage measurement was carried out by using a Source Meter (Keithley 2400) The experiment set up was shown in Figure 2.5, the Ag/Ag2S NPs device was connected to probe via a Source Meter, to extract the electrical responses a bias 0 V to 4 V with 0.02 V step voltage in 1000 milliseconds time step was repeatedly applied sweeping of forward and reversed to the device, a 1 mA compliance current was set at to prevent the device damage A PC wired to Source Meter with LabView software functionalized to control the measurement procedure The I-V data were recorded at ambient temperature
Figure 2.5 Current-voltage measurement set up by using a Source Meter (Keithley 2400) The experiment was carried out under room temperature.
Time series data is commonly used for reservoir computing (RC) tasks To effectively train RC, it's crucial to exploit the material network's dynamics Measuring multiple output signals from various points of the network over time provides reservoir states An Ag/Ag2S NPs device was connected to a custom-built measuring system for RC characterization An input signal drives network dynamics, which is captured by a signal generating device The multifunction DAQ system acquires output signals from multiple electrode pads simultaneously Electrode connections are made via DAQ wires, while a PC with a LabVIEW interface manages I/O signals between the signal generator and DAQ.
Electrical measurements involve utilizing a setup that includes a Ag/Ag2S reservoir device connected to a signal-generating device via input probes The device's multiple electrodes generate individual outputs, which are captured by a data acquisition (DAQ) system through output probes The DAQ system then sends the data to a PC running LabVIEW software for processing and optimization This setup enables the characterization and execution of resistive-capacitive (RC) tasks.
DEVICE CHARACTERIZATION
Structural properties
3.1.1 X-ray diffraction spectrometer (XRD) result
For element identification for obtained nanoparticles, X-ray diffractometry (XRD, Rigaku RNIT-2100) with Cu Kα radiation 40kV (λ = 0.154 nm) and scanning rate was 0.02 °/s was performed Figure 3.1 show the XRD profiles of the synthesized nanoparticles with the inset is enlarged view for the Ag2S peaks area indicated by blue squares which is overwhelmed by Ag peaks intensity indicated by orange circles The Ag and Ag2S phase in XRD result was matched with the references of PDF No: 01-071-3762 Quality: I [21] and PDF No: 01-075-1061 Quality: B [22], respectively
As shown in the XRD profile, these two substances were assigned to the acquired peaks, and it was proven that the Ag2S phase and the Ag phase coexistence in the produced nanoparticles
Figure 3.1 Synthesized Ag/Ag 2 S NPs structure characteristics X-ray diffractometry (XRD) pattern for archived nanoparticles sample, the obtained peaks were attributed to Ag and
Ag 2 S peaks, and it was confirmed that these two substances coexistence in the produced nanoparticles
3.1.2 Transmission electron microscopy (TEM) result
The morphology of Ag/Ag2S nanoparticles were confirmed by transmission electron microscopy (TEM, JEOL-2100) with acceleration voltage at 200 kV As shown in Figure 3.2(a), nanoparticles have spherical forms, the average particle sizes were estimated by calculating the diameter from measuring the area of nanoparticles from TEM images using Image J software To determine the average diameter of nanoparticles, a Gaussian curve was fitted to the histogram of particle size distribution obtained from TEM image analysis, the average diameter was specified around 31.37 nm, which is depicted in Figure 3.2(b)
Figure 3.2 (a) Transmission electron microscopy (TEM) image of Ag/Ag 2 S NPs with 100 nm scale bar (b) The distribution of the diameters of particles calculated from TEM image, the average diameter of synthesized sample was extracted by fitting with Gaussian curve for histogram of particles size distribution The average of particles diameter approximate 31.37 nm with standard deviation is around 15.53.
Electrical properties
3.2.1 Current-voltage characteristic result (Non-linearity behavior)
To investigate the electrical properties, current-voltage measurement was carried out by using a Source Meter (Keithley 2400) The repeated sweeping of forward and reversed bias 0 V to 4 V with step voltage 0.02 V each one second was applied to the
22 device, the compliance current was set at 1 mA to prevent the device damage As depicted in Figure 3.3(a) an intensely nonlinear response and a gradually increase in the output current were observed In the first sweep, the current began to raise at 3 V and reached 0.5 mA, allowing the development of certain silver filaments among the nanoparticles During the first sweep's reverse bias, the output current displayed nonlinear response with the curve of forward sweep and the current slowly decreased, representing filament disintegration Following that, in the second sweep, the output current began to rise at an applied bias voltage of around 0.8 V, which was lower than the first sweep Furthermore, considerable current variations occurred in the 2V to 4V range, indicating the production and destruction process of conduction paths proceeded randomly at various gap sites among NPs A sufficient potential applied across the nanoparticles is the source for the production and destruction of silver filament between the particles When the bias voltage was connected to the system, an amount of charging electrons was introduced into the device, initiating the redox reaction process at the surface of Ag/Ag2S nanoparticles [23] The gap between each nanoparticle was created by Ag2S and the organic layer, after the voltage was applied,
Ag nanoparticles oxidized the electrode, Ag + ions were reduced by the electron injected, silver metallic bridges were generated by the breakage of the insulating layer, and the conduction paths was formed among the nanoparticles Additional bias sweep results in the gradually increase of the output current up to reach the compliance current 1 mA, indicating a strong connection was generated in the Ag/Ag2S nanoparticles network, as shown in the third sweeping voltage
Figure 3.3 Electrical characteristics of Ag/Ag 2 S RC device (a) Current-voltage curves of the device after multiple reverse and forward bias sweeps 0 to 4 V that showing nonlinear responds and gradually increase in currents, indicating the randomly forming process of conduction paths inside Ag/Ag 2 S networks (b) Input a cycle bias in the range of -4 V to 4 V result in switching with pinched hysteresis can be observed in both negative and positive voltage regions
For further understanding the nonlinear transformation characteristic provided by the Ag/Ag2S reservoir systems, a cycle bias in the range of -4 V to 4 V also with 0.02 V step voltage in 1000 milliseconds time step was injected to the device As shown in Figure 3.3(b), there were switching with pinched hysteresis can be observed in both negative and positive voltage regions It worth to notice that the current start to
24 behave switching at approximately same voltage value around 3 V to 4 V in both areas, indicating the nonlinear switching characteristic of Ag/Ag2S NPs device enable to manifest in bipolar or unipolar potential applied
Beside the non-linearity feature, a reservoir must also create diverse dynamics inside the network to assist in reservoir task The current state of the reservoir is dependent on current input and previous reservoir state as described in Equation 3.1 [11]:
The reservoir computing (RC) device requires a phase shift property that delays output signals to achieve complex dynamics To investigate this property, an Ag/Ag2S NPs network was stimulated with a sinusoidal wave, and multiple responses were recorded using a data acquisition system The resulting voltage-time curves exhibited varying forms and phases in the output waves, as seen in Figure 3.4(a) To determine phase differences, Lissajous curve plots were generated for all output readouts from the device, depicted in Figure 3.4(b).
Figure 3.4 (a) Voltage-time curves of a sinusoidal input signal with frequency 11 Hz, 1 V peak amplitude and their corresponding nonlinear outputs (b) Lissajous plot of output from
15 electrode pads versus input voltage shown the ellipse shape indicated phase shift properties of Ag/Ag 2 S NPs RC device
The voltage–time plots show various phase differences between the input and the outputs, indicating delayed output All of 15 delayed outputs were then plot as Lissajous curves exhibited nonlinear relationship between the input and output voltages via amplitude and phase changes The elliptical shape of the Lissajous plot obtained for the NPs-based device is desirable since it reveals as a complex network Ag/Ag2S NPs enable to induce phase delays Thus, from the above result the device possessed phase shift property and has the potential for developing RC device
RC devices must have nonlinearly transformed sequential input into high- dimensional computational spaces as an electrical attribute [11] To further investigate RC characteristics of the device, a bipolar sinusoidal wave with frequency
11 Hz and peak amplitude 1 V, 3 V and 4 V respectively was applied to the device for perturbation After recording the output signal and converted it by fast Fourier transform (FFT) to obtain an output amplitude characteristic in frequency domain and plotted in log-scale The current response contains harmonics of the excitation frequency A harmonic frequency is one that is equal to an integer multiplied by the fundamental frequency As depicted in Figure 3.5(a)-(c), the even and odd harmonic were generated in all the cases The intensity and quantity of higher harmonic were increase with the higher amplitude of input sinusoidal wave Especially, in case of 4Vpp the device was achieved the richest higher harmonic with over 15 odd and even overtones Moreover, as compared in Figure 3.5(d) the averaged intensities of 15 readout channels for odd and even harmonics frequency for each input peak amplitude showing the outstanding rate of harmonic generation when 4Vpp was applied This phenomenon results from the aggregated of Ag/Ag2S NPs which creates non-linear redox reactivity in various levels at multiple gap-points in the network, thus conduction paths with different electrical properties of resistive or capacitive were created [15][16] As a result, high dimensional information of the outputs with regard to amplitude and frequencies was generated When these random networks are perturbed by sinusoidal wave, charge-discharge processes from simultaneously
27 varied input intensities occur due to their diverse redox states and varying degree between Ag/Ag2S nanoparticles This result is consistent with the current-voltage characteristic as previous analysis in Figure 3.3(a), there was an intense fluctuation in current occurred around bias voltage 4 V, indicate the charge-discharge process strongly arise between various gap-points of nanoparticles Therefore, input amplitude 4 V was used to perform these following supervised learning tasks to Ag/Ag2S NPs in-materio reservoir device The device exhibits high-dimensional mapping, which is required for attaining classification tasks with high accuracy
Figure 3.5 Fast Fourier transform spectrum of output current after applied a bipolar sinusoidal wave with 11 Hz frequency and peak amplitude 1 V (a), 3 V (b), 4 V (c), respectively Higher harmonic generation property was observed in frequency domain indicates that the device exhibits high-dimensional mapping (d) Average intensities of 15 outputs for odd and even harmonics frequency compared between peak amplitude 1 V, 3 V and 4 V showing the outstanding rate of harmonics generation in case of 4 V peak applied
One concept that also essential for RC time-series data task performance is time constant, which affected to the way reservoir process the data injected and generate reservoir states [24] Electrochemical impedance spectroscopy (EIS) was conducted to investigate the Ag/Ag2S NPs device time constant A Nyquist plot with real part of impedance is plotted on the X axis, and the imaginary part is plotted on the Y axis, was shown in Figure 3.6(a) The Nyquist plot result depicted an almost full semicircle, which indicate the presence of parallel resistor–capacitor circuit components In order to perform curve fitting, an equivalent circuit model was established based on these results (Figure 3.6(b)) In this circuit, CPE is the “Constant Phase Element” which is the capacitive component with inhomogeneous structure in RC circuit The experimental plots and fitting curves match well for the majority of the electrodes in the device From equivalent circuit, the capacitance and resistance value were evaluated with averagely values of 𝑅 ≈ 309151 𝛺 and 𝐶 ≈ 1.29 × 10 &' 𝐹 Following that the time constant of this RC circuit was calculated by the formula:
Figure 3.6 (a) Impedance spectroscopy of one electrode from Ag/Ag 2 S NPs device depicted an almost full semicircle, which indicate the presence of parallel resistor–capacitor circuit components (b) An analogous circuit model was demonstrated based on fitting impedance curve results.
RESERVOIR COMPUTING DEMONSTRATION
Waveform generation
To demonstrate the necessity of nonlinearity and high dimensionality for improving
RC performance, waveform generation was carried out as a representative RC benchmark task The same input that was used for investigating higher harmonics generation was reused, a bipolar sinusoidal wave with frequency 11 Hz and peak amplitude 1 V and 4 V was applied to the device for perturbation A multifunction data acquisition DAQ (National Instruments PXIe-6363) system was used for input signal generation and output data recording The 15 output responses were collected over 60 s with a sampling rate of 1000, each output had a different internal state of reservoir Xi(t), with i represent the number of outputs, as illustrated in Figure 4.1
In the waveform generation task depicted in Figure 4.1, a bipolar sinusoidal wave with a frequency of 11 Hz and varying peak amplitudes of 1 V and 4 V was used as the input Fifteen output responses were collected and underwent supervised training to generate specific target waveforms, including cosine, triangular, square, and sawtooth.
From the time series data obtained, a total of 1 s epoch was used for the data analysis with 70 % for training and 30 % for testing In training, ridge regression was carried out to optimize the output weights of the reservoir state to the supervised target 𝑌 The weights are calculated as Equation 4.1 follow:
𝑊 &'( = (𝑋 ) 𝑋 + 𝜆𝐼)𝑋 ) 𝑌 (4.1) where 𝑋, 𝜆, 𝐼, 𝑌 are reservoir state matrix, ridge regularization co-efficient, identity
30 matrix, and target matrix, respectively In this waveform generation task, 𝜆 was set to 0.1, the target waves were cosine, triangular, square, sawtooth, sin2ω and sin3ω The Fourier series uses an infinite series of periodic sine trigonometric functions of different coefficients to produce other forms of complex function like: cosine (Equation 4.2), triangular (Equation 4.3), square (Equation 4.4), sawtooth (Equation 4.5) [25] On the other hand, sin2ω and sin3ω are just double and triple frequency of input data for demonstrating the role of higher harmonics
Multiple linear regression optimized the weights of our Ag/Ag2S NPs reservoir device weight training The optimized weights were used to construct the predicted reservoir output 𝑍(𝑡) via weighted linear combination (Equation 4.6) The fitting value between predicted and target data was assessed using normalized mean square error (NMSE) calculation (Equation 4.7).
The performance of each wave target was plotted with train and predict part (blue and red dot, respectively) corresponding to desired target wave (black line) as depicted in Figure 4.2
Figure 4.2 Waveform generation of sinusoidal wave input (11 Hz frequency, V PP = 1.0 V
AC bias voltage) for (a) cosine, (b) triangular, (c) square, (d) sawtooth, (e) sin2ω and (f) sin3ω The train data (blue dot) and the predict data (red dot) are plotted against the target wave (black line) 1 s epoch was used for the data analysis with 70 % for training and 30 % for testing Fitting value between predict and target data was presented by normalized mean square error (NMSE) calculate from Equation 4.7
The multiple outputs voltage from 15 electrode channels were recorded simultaneously and used to construct various target waveforms of cosine, triangular, square, sawtooth sin2ω and sin3ω The output weights were trained via supervised linear regression For quantifying the performance, NMSE was calculated The cosine wave in Figure 4.2(a) showed the lowest NMSE value of 0.003 (red dot) after training (blue dot), followed by triangular (0.023), square (0.208) and sawtooth (0.323) in the increasing order Compared to cosine and triangular, the square of odd and sawtooth of both odd and even harmonics are more complex and require rather large series of such harmonic combinations to be replicated, thereby the NMSE value got higher for these two targets waveforms Whereas the NMSE of sin2ω and sin3ω are significantly higher than others target waveform with 0.697 and 0.743, respectively Indicating that under this input condition, the second and third harmonics exhibited from the device are inadequate to reconstruct the double and triple frequency waveform of input data To check the importance of the rich harmonic generation towards waveform reconstruction, 4Vpp amplitude of bipolar sinusoidal input was also applied to the Ag/Ag2S reservoir device performance As previously compared in Figure 3.5(d), the averaged intensities of odd and even harmonics frequency for input peak amplitude showing the outstanding rate of harmonic generation when 4 V was applied Moreover, the second and third harmonics are completely overwhelming the others Hence, there are an expectation for better performance which can reconstruct all desired waveform with better NMSE, especially for the case of sin2ω and sin3ω The waveform generation results for 4 V input were shown in Figure 4.3
Figure 4.3 Waveform generation of sinusoidal wave input (11 Hz frequency, V PP = 4.0 V
AC bias voltage) for (a) cosine, (b) triangular, (c) square, (d) sawtooth, (e) sin2ω and (f) sin3ω The train data (blue dot) and the predict data (red dot) are plotted against the target wave (black line) 1 s epoch was used for the data analysis with 70 % for training and 30 % for testing Fitting value between predict and target data was presented by normalized mean square error (NMSE) calculate from Equation (6)
Figure 4.3 demonstrates a significant improvement in the NMSE of triangular, square, and sawtooth waveforms with 4 V peak input amplitude, with cosine being the least affected The complexity of a waveform influences the reservoir's learning efficiency, as complex waveforms require numerous harmonics to be linearly summed The NMSE for sin2ω and sin3ω waveforms shows a notable enhancement, particularly for sin3ω, corroborating the higher harmonic intensities in Figure 3.5(d) Increasing the input voltage improves the NMSE due to the acquisition of richer information An adequate input voltage amplitude is crucial for optimizing the performance of RC benchmark tasks.
Nonlinearity – memory
To investigate more about nonlinearity characteristic and establish the sort of RC task that the device can accomplish, an analyzing the degree of non-linearity and memory inherent was performed A simple function approximation task as show in Equation 4.8 [26] was studied, which allows to control the degree of the nonlinearity and the memory required in the tasks separately
𝑦(𝑡) = 𝑓-𝑠(𝑡 − 𝜏)3 = 𝑠𝑖𝑛-𝜈𝑠(𝑡 − 𝜏)3 (4.8) Where 𝑓 is a nonlinear function, in this case 𝑓(𝑥) =𝑠𝑖𝑛 𝑠𝑖𝑛 𝑥 and 𝜈𝑠(𝑡 − 𝜏) is the
35 input signal with (𝜈, 𝜏) are task parameter that control the “extent” of the required nonlinearity and “degree” of the required memory, respectively
To perform the simple approximation task, a uniform distribution 𝜇(−4, 4) was introduced to the device as the input signal The 15 output responses were collected over 60 s using a multifunction DAQ system Each output had a different internal state of reservoir Among them, 80 % of the datasets were used for training and 20 % were used for testing In training, ridge regression was carried out to optimize the output weights of the reservoir state to the supervised target 𝑦(𝑡) The weights are calculated as Equation 4.9 follow:
Where 𝑋, 𝜆, 𝐼, 𝑦(𝑡) are reservoir state matrix, ridge regularization co-efficient, identity matrix, and target matrix, respectively In this task, 𝜆 was set to 0.1 After optimizing the weight, the predicted reservoir output 𝑍(𝑡) was constructed using a weighted linear combination of the optimized weights and the test accuracy was calculated from fitting value between predicted and target data according to Equation 4.10:
Figure 4.4 presents a heatmap summarizing the impact of varying nonlinearity and memory task parameters on comparison test accuracy The heatmap depicts accuracy as a color gradient, with green indicating optimal performance and red indicating poor performance Despite varying nonlinearity parameter 𝜈, device performance remained consistent However, accuracy declined significantly when memory task parameter 𝜏 exceeded 3, corresponding to the I-V characteristic's observation of reduced device performance at higher delay steps.
36 nonlinearity response in output currents with pinched hysteresis Through this investigation we can confirm the strength of nonlinearity and the depth of memory of the device There is a general tendency of decreasing accuracy for every 𝜈, with rising
𝜏, demonstrating that, regardless of the growing degree of non-linearity, tasks with the least past memory construction usually outperform higher ones These results indicate that, the nonlinear dynamic of Ag/Ag2S NPs device is suitable for the tasks requiring strong nonlinear transformation with short memory
Figure 4.4 Nonlinear-memory heat-map table summarizing the results of comparison test accuracy by changing of the pair nonlinearity and memory task parameter ( 𝜈 , 𝜏 ).
Objects classification
For demonstrating the classification ability by utilizing the nonlinearity and higher harmonic generation properties, Ag/Ag2S NPs device was used to perform the object classification task for tactile sensory information of grasped objects getting from Toyota Human Support Robot (HSR) [27] As depicted in Figure 4.5, a force-torque sensor mounted to a robot arm produces tactile sensory information of grabbed items
Four different toys, including a block, bus, dog, and hedgehog, provided varying hardness levels to generate tactile sensory input datasets Grasping data involves measuring the torque magnitude of a robot hand grasping an object with consistent force The force-torque sensor records measurements every 0.1N, and the corresponding torque values for each toy are organized into grasping datasets.
A time-series dataset of individual objects was obtained by sampling 5 bits/s information at 1000 points/s and applying a 4 V amplifier over the data range The input dataset was fed to the device, and the corresponding outputs were collected from 15 electrode pads via a DAQ system The outputs were used for binary classification using one-hot vector encoding, with weights optimized to represent target vector values of '1' (correctly classified) and '0' (incorrectly classified) 80% of the datasets were used for training, and the classification performance was evaluated using the remaining 20% The reservoir outputs of two objects were used as test datasets for supervised binary classification, and the results were plotted as shown in Figure 4.6.
Figure 4.5 Objects classification task schematic Toyota HSR’s arm with force-torque sensor that generates tactile sensory information of grasped objects by applying force from the gripper Four toys with different hardness were used as grasped objects to create tactile data: Bus, Block, Dog, Hedgehog (HH) Time-series dataset of grasped objects were generated from sensor data driven by LabVIEW program then fed to the device, and their outputs were collected, which were used for training and testing the binary classification Supervised target of one-hot vector binary classification where the true positive object predicted is Bus (blue) with supervised target vector ‘1’ and true negative predicted Block (black) with value ‘0’, as an example Other pairs of objects were tested by utilizing the same process
Based on the hardness characteristic, grasped objects were categorized into two groups for classifying label First group for objects with significant differences in hardness, which is named soft-hard (Hedgehog versus Block, Bus), and second one for objects having quite same hardness, which is named soft/soft (Hedgehog versus Dog) and hard/hard (Block versus Bus) The finest results we obtained showed in Figure 4.6, Ag/Ag2S NPs device succeeded to classify both type of object groups In
39 both cases, even though the line is not completely following the trend of ideal target but it’s still showing the clear separation between two lines of indicated objects The ability to achieve such separation lies in the Ag/Ag2S reservoir’s inherent non-linear high dimensional operation As described above and depicted in Figure 4.5, the series input signal was fed into device with different bias step levels over times, this was allowed the reservoir recurrent network to produce higher dimensional information over every time frame and fetch different spatial information particular to a given input, hence producing high dimensional outputs The nonlinear effect can process and sequentially map the incoming data to high dimensional output This can lead to feature extractions imparting the reservoir separability property useful for classifying different spatio-temporal inputs into various categories As a result, the device successful to perform classification task of the tactile objects data
Figure 4.6 One-hot vector binary classification of tactile grasped objects results For classification label, objects were categorized into 2 groups based on their hardness: (a) soft- hard pairs and (b) soft/soft hard/hard pairs The graph shows the classification result of the predicted objects of the test data for both type of groups, with corresponding colors codes for each toy The binary classification task for each pair of objects displayed a successful classification where the supervised object separated line following same tendency of ideal target vector with value ‘1’ for true positive object and others being ‘0’ for true negative object
Boolean logic configuration
The Ag/Ag2S NPs device was then integrated with a measurement system driven by LabVIEW software to carry out the RC task of Boolean logic optimization at ambient conditions As demonstrated in Figure 4.7(a), in a Boolean logic task, firstly, two inputs Vin1 and Vin2 series of ‘0’ and ‘1’ sampled as 1 bit/sec were generated and simultaneously passed onto the Ag/Ag2S reservoir layer through 2 electrode pads, with input voltage amplitude 0 V and 4 V represented for logic state ‘0’ and logic state ‘1’, respectively Subsequently, multiple outputs from the rest 14 electrode pads were collected via a multifunction DAQ system The time series data set was split into 70 % for training data (28 s) and 30 % (12 s) for testing data After supervised training by the output weights (Wout) with a multi linear regression model (using the Moore-Penrose pseudo inverse algorithm), the reservoir output signals R(t) was construct by weighted linearly combined all the outputs and added the regression intercept factor b0 as Equation 4.11 [28] The predicted output was evaluated over test dataset with the same trained optimized output weights that used to reconstruct the target y(t) of Boolean functions like OR, AND, XOR, NOR, NAND and XNOR gates The device performance was examined by calculating the accuracy from normalized mean square error (NMSE) as Equation 4.12 and Equation 4.13
Figure 4.7a illustrates the RC task for Boolean logic function optimization, where inputs '0' and '1' are fed to the Ag/Ag2S reservoir Multiple outputs are collected and weighted to reconstruct the OR gate target The training process is supervised to minimize error and fit the desired Boolean target Figure 4.7b explains how Boolean targets are optimized from two binary inputs, presenting truth tables for OR, AND, and XOR gates as reconstructed targets.
Using the supervised learning procedure described above, we succeeded to realize fully reconfigurable, robust Boolean logic from in-materio RC Ag/Ag2S NPs networks at room temperature Every desired target logic gate AND, OR, XOR, NAND, NOR, and XNOR as show in Figure 4.8(a), Figure 4.8(b), Figure 4.8(c), Figure 4.8(d), Figure 4.8(e) and Figure 4.8(f), respectively, were reconstructed as corresponded to the training and predicted data, indicating the successful implementation The repeatability of the task was proven by assessing the device performance on three different test datasets of the same time length The test accuracy was calculated from Equation 4.13 Figure 4.8 shows that the accuracy of about 94 % for OR, AND, NOR, NAND and 84 % for XOR and XNOR were achievable and referring standard deviation of approximately 1.2 (AND, NAND), 0.7 (OR, NOR) and 2.0 (XOR, XNOR) among all three datasets clearly suggests that the fitting is reproducible Basically, a reservoir with nonlinear dynamics is necessary to implement those logic operations with increasing classifiers complexity, especially XOR or XNOR gate [29] Although the training and predicted (blue and red dot line) followed their respective targets, however there were noise fluctuations appeared for all the gates at the step edges transitioning from ‘0’ to ‘1’ state and a mismatch in following the horizontal lines A reasonable reason can explain for that is because the sudden change in the device capacitance requiring time to adjust to the given voltage state when such linear drop in the voltage occurs, result in the weight adjustments on those parts give out noisy fitting [13] Notably, the behavior is more prominent for XOR and XNOR as these gates are exclusively complex and difficult to optimize relative to their counterparts right at the edges When compared to the other gates, XOR and XNOR are linearly inseparable and necessitating a high dimensional space to handle them The voltage readout dynamics of varying amplitudes from Ag/Ag2S network can be exploited as high dimensional spatial features when collected from different electrode pads, as analyzed in Figure 3.5 However, the chaotic and contingent of charge-discharge processes occurred due to their diverse redox states and varying degree of Ag/Ag2S capacitive junctions between nanoparticles results in the distortion responses Thereby reducing the performance of XOR /XNOR slightly
44 than AND, OR, NAND and NOR gates [30] These results are corresponding to previous report which utilized in-materio reservoir computing with single-walled carbon nanotube/porphyrin-polyoxometalate (SWNT/Por-POM) composite for optimizing Boolean function, Deep Banerjee et al [28] The accuracy for each logic gate in their case all above 90 %, especially for two complicated gate XOR/XNOR archived 93 %, based on the presence of negative differential resistance dynamics intrinsic of SWNT/Por-POM network, analogous to a mathematical additive and subtractive operation, making it desirable for the varied Boolean operations
Figure 4.8 Boolean logic operations task results Prediction of target logic gates: AND (a),
Utilizing supervised learning, various Boolean logic functions including OR, XOR, NAND, NOR, and XNOR were reconstructed with test accuracy exceeding 80% The training and predicted outputs are visualized in these plots, with black solid lines representing the target function, blue dotted lines indicating the training set, and red dotted lines showcasing the predicted values.
Spoken digits classification
Voice information is one of the most known and utilized time series data for RC tasks
In the majority of cases, researchers are interested in voice classification and recognition Can be mentioned as, the utilizing software modeling of several nonlinear responses executed spoken-digit classification [31] Moreover, Yuki Usami at el [32] demonstrated sulfonated polyaniline (SPAN) organic electrochemical network device (OEND) acts as an in-materio reservoir was succeeded to performed spoken-digit classification with accuracy up to 70 % Following those researchs, we carried out spoken-digit classification using the Ag/Ag2S NPs device The spoken- digit classification method is depicted schematically in Figure 4.9, with the free spoken-digit dataset (FSDD) v1.0.10 as input dataset [33] The digit data consists of ten numbers (from 0 to 9) pronounced 50 times each by six male speakers (George, Jackson, Lucas, Nicolas, Theo, and Yweweler) Lyon’s auditory model filtering [34] was used to generate cochleagrams from spoken-digit time-series signals to resampled (130Hz) intensities in four signal frequency regions, each cochleagram was made up of 100 timesteps [32] Four cochleagrams were normalized in the range of 0 to 4 V and simultaneously applied to Ag/Ag2S NPs device as time-series bias voltages using LabVIEW software Output response from the rest 12 electrodes were recorded, then, all generated signals were labeled as supervision signals for classification In this case, a one-hot vector was utilized as a target to optimize the classification for predicting the number The weights of the correctly classified numbers were optimized as a target vector value of “1,” while the others were optimized to the value of “0” The trained weights for individual number were optimized by ridge regression and used for testing Target length and the timesteps of the output signal are same The ratio of training to test data was 90 % and 10 % The ratio for splitting a dataset depends on the type of dataset, data characters, data size etc Hence, the partitioning ratio might be different between each task demonstration
It must be ensured that the training dataset should include all possible patterns used for defining the problem and should extend to edge of the modeling domain
Figure 4.9 A diagram of spoken-digit classification Using Lyon’s auditory model filtering, the spoken-digit time series signals in the dataset were transformed to cochleagrams by separating the intensities in four frequency bands.The cochleagrams were normalized and used as time series bias voltages on the Ag/Ag 2 S NPs network.Following the recording and labeling of the device’s output, the labeled outputs were categorized using a ridge regression to a one-hot target vector with training (90 %) and prediction (10 %)
Figure 4.10 (a) (a)Normalized confusion matrix of spoken-digit classification of Lucas one speaker from the FSDD dataset when using output readouts from Ag/Ag 2 S NPs RC device, the accuracy 72 % was attained (b) Dependence of spoken-digit classification on sampling rate
Figure 4.10(a) shows a normalized confusion matrix of the actual and predicted labels acquired from Lucas's vocal by using output readouts from Ag/Ag2S NPs RC device, with 1000 points/s sampling rate To confirm the role of sampling rate, we investigate
48 the dependence of spoken-digit classification on duration time of input data regulated by sampling rate The cochleagram was made up of 100 timesteps, by adjusting input sampling rate the duration time of injecting data can be modified The input and output sampling rate were unified to modulate duration time Figure 4.10(b) shows the accuracy versus sampling rate for spoken-digit classification with Lucas, one of male speaker in FSDD dataset From above result, the effective sample rate for input was between 1000 and 3000 point/s, which means the input duration time is in range 0.1s−0.03s, it’s corresponding to the time constant calculated in the equivalent RC circuit mentioned above As a result, time constant is one again confirmed the crucial role in this voice classification task Based on this investigation, we conducted spoken digits classification task with 1000 and 3000 point/s to validate the appropriate sampling rate for optimizing the classification ability
(a) Software simulations and Ag/Ag2S output signals demonstrated comparable accuracies in spoken-digit classification among individual speakers using the FSDD dataset (b) A normalized confusion matrix for the classification of six speakers using Ag/Ag2S nanorod (NP) resistor-capacitor (RC) device outputs revealed a respectable 61.7% accuracy rate.
For reservoir computing software simulation, the same four normalized cochleagrams fed into Ag/Ag2S NPs device were introduced in an echo state network, consisting of
12 fully connected nodes, ten outputs were linearly combined to optimize the target of a one-hot-vector, and the greatest unit was considered to be predicted number The spoken-digit classification ability of Ag/Ag2S NPs device was comparable with
49 software simulation of an echo state network, with an accuracy of up to 70% for all six speakers, as shown in Figure 4.11(a) Moreover, as mentioned, we compared two efficient sampling to verify which one is more effective for optimizing the classification of spoken digit The result depicted that 3000 points/s sampling rate is got better accuracy in most of the cases It was coincident with the time constant as calculated, hence, under this condition the duration time of input data is within the time constant, once again emphasized its critical impact The confusion matrix for all six speakers is shown in Figure 4.11(b), the accuracy for this classification task was archived 61.7 %, whereas software simulation for this task got 63 % accuracy, which indicated that Ag/Ag2S network could extract feature value of voice signals well, and improved accuracy of classification by utilizing the time-dynamics obtain various output readouts The outcome of this spoken digit classification is similar with previous report of Yuki Usami at el implemented by a sulfonated polyaniline network
The Ag/Ag2S nanoparticles (NPs), employed as in-material reservoirs, demonstrated high classification accuracy for time series dynamics This accuracy remained consistent across speakers and six different classification groups This finding highlights the potential of Ag/Ag2S NPs for in-material reservoir applications in various classification tasks, including speaker recognition and time series analysis.
SUMMARY AND CONCLUSION
In conclusion, the Ag/Ag2S NPs were successfully synthesized by following modified Brust-Schiffrin procedure The structural properties of Ag/Ag2S NPs were confirmed by X-ray diffractometry and transmission electron microscopy (TEM), the average diameter of particles also calculated Characteristics requirements for building the physical reservoir computing (RC), such as nonlinearity, phase shift, high dimensionality, have been investigated The current-voltage curve, after repeated sweeping of forward and reversed bias 0-4 V to the device, shows nonlinear response and fluctuations of current occurred, indicating the forming process randomly occurred at various gap points among NPs Another essential required property for
RC also studied by applying sine wave input then record output signal and converted by a fast Fourier transformation process to obtain output amplitude characteristics in the frequency domain, the output current amplitude was observed at integer multiples of the input frequency, which indicates high dimensionality Furthermore, the Lissajous plots shown elliptical shape represent the phase-shifting property Based on the above results the Ag/Ag2S NPs device possess important properties for realizing reservoir computing device: non-linearity, phase shift, high dimensionality By utilizing the non-linear, phase shift and high dimensional properties, the device was used to perform some RC tasks in the role of reservoir layer Ag/Ag2S NPs device succeeded in learning and generating waveform by applying a sine wave and performing linear combination to a desired waveform (cosine, triangle, square, sawtooth, sin2ω, sin3ω wave) exhibited over 80% accuracy for all waveform targets The analysis of degree of non-linearity and memory inherent were carried out to establish the sort of RC task that the device can accomplish For object classification task, after supervised training, a binary testing dataset of pairs of objects was successfully classified for both type of classification objects groups by using one-hot vector encoding In the case of Boolean logic task, a reservoir with nonlinear dynamics is necessary to implement those logic operations with increasing classifier complexity The results show the testing accuracy for all gate targets (AND, OR,
XOR, NAND, NOR, XNOR) are more than 80%, indicating the successful reconstruct of all logic gates by using Ag/Ag2S NPs RC device Moreover, a complicated classification task for time series data also carried out The spoken digit classification was realized with up to 70 % accuracy, proving that Ag/Ag2S NPs device can execute time series dynamic data operation in RC by combining nonlinear and dynamic electronic properties Based on these results, the Ag/Ag2S nanoparticles device proved to be used as an in-materio reservoir device, which has an extraordinary potential for further complex supervised learning
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