# Fileset [Nishioka_2025_Jpn._J._Appl._Phys._64_11SP25.pdf](https://mdr.nims.go.jp/filesets/09c38cc0-d39f-4824-bcfb-f7b348117850/download) ## Creator [Daiki Nishioka](https://orcid.org/0000-0002-3369-7700), Kaoru Shibata, [Wataru Namiki](https://orcid.org/0000-0003-4053-7366), [Kazuya Terabe](https://orcid.org/0000-0003-3988-3456), [Takashi Tsuchiya](https://orcid.org/0000-0002-6950-6160) ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Physical masking-induced enhancement of information processing capacity in a redox-type ion-gating reservoir](https://mdr.nims.go.jp/datasets/06ce0dfc-0c9c-4ec5-b4df-f582664d7ffb) ## Fulltext Physical masking-induced enhancement of information processing capacity in a redox-type ion-gating reservoirJapanese Journal ofApplied Physics      REGULAR PAPER • OPEN ACCESSPhysical masking-induced enhancement ofinformation processing capacity in a redox-typeion-gating reservoirTo cite this article: Daiki Nishioka et al 2025 Jpn. J. Appl. Phys. 64 11SP25 View the article online for updates and enhancements.You may also likeEvaluation of fundamental properties andhole transport characteristics of 3,3-Bi [1,4]benzoxazino [2,3,4-kl] phenoxazine (HN-D2) thin films for BaSi2 solar cellapplicationsMizuki Hirai, Yuka Fukaya, Yoichiro Kodaet al.-Structure and electronic properties ofRuSi, OsSi, RhSi, ReSi and IrSiDmitri B. Migas, Andrew B. Filonov,Nikolay G. Galkin et al.-Transition metal monosilicide films onsilicon for thermoelectronics andspintronicsNikolay G. Galkin, Konstantin N. Galkin,Dmitrii L. Goroshko et al.-This content was downloaded from IP address 144.213.253.16 on 06/12/2025 at 14:40https://doi.org/10.35848/1347-4065/ae1d84/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1b13/article/10.35848/1347-4065/ae1842/article/10.35848/1347-4065/ae1842/article/10.35848/1347-4065/ae12fd/article/10.35848/1347-4065/ae12fd/article/10.35848/1347-4065/ae12fdhttps://pagead2.googlesyndication.com/pcs/click?xai=AKAOjsvkvytKtH6L1iEwWBXHwMjlXbxMKOjElaQoHcy9roUh1toH1P0zoIEh2tHNhf5SnNMV_4Xq6K_0NPuNgRjbkFnQa6xeKFM1CSExmRmD6YC5WbZQbVPUbYxaHPT7V3zz75Bnc_uxAqmqAd7FalXx2ejIUwSfYv8LHIYS-bgM3QwanCUPIEt-jsKenRNEoq2Nz6RwsWBJD4Ec9JB4G6FjPEJLbPO0j4i6QDP09vjR8e8z2bc14OmX5M8lvDMzHoX18iQvUSSToZMC9fly-eIkPCT8Xg2eVInVskcsS45BVGatxB13zNHJMCpKMcN5ILbVvQdFcbz_b5qaFtuVfr7kvatnfHUK9sNnwSsKQYf1NiPO0ufVgBLnoJQK&sig=Cg0ArKJSzNni0ImtSmE7&fbs_aeid=%5Bgw_fbsaeid%5D&adurl=https://www.electrochem.org/250%3Futm_source%3DIOP%26utm_medium%3Dbanner%26utm_campaign%3D250_IOP%26utm_id%3DIOP%2B250%2BsubmissionaaaPhysical masking-induced enhancement of information processing capacity in aredox-type ion-gating reservoirDaiki Nishioka1* , Kaoru Shibata2,3, Wataru Namiki2 , Kazuya Terabe2 , and Takashi Tsuchiya2,3*1International Center for Young Scientists (ICYS), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2Research Center for Materials Nanoarchitectonics (MANA), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044,Japan3Department of Applied Physics, Tokyo University of Science, Katsushika, Tokyo 125-8585, Japan*E-mail: NISHIOKA.Daiki@nims.go.jp; TSUCHIYA.Takashi@nims.go.jpReceived October 22, 2025; revised October 31, 2025; accepted November 9, 2025; published online November 24, 2025We analyzed the computational mechanism of redox-type ion-gating reservoirs (Redox-IGRs)—a class of physical reservoir computing (PRC)devices that utilize redox dynamics induced by ion gating for information processing—operated with physical masking (PM), in which a simpletriangular drain voltage dynamically modulates the conductance of the device. The periodic drain perturbation enriches the temporal diversity ofthe conductance response, leading to enhanced nonlinear dynamics. Information-processing-capacity (IPC) analysis revealed that PM markedlyincreases nonlinear capacity while maintaining linear memory capacity, resulting in a total IPC increase from 11 to 20. This doubling of IPCindicates an expansion of the reservoir’s effective dimensionality and explains the improved performance observed in nonlinear dynamical systemprediction tasks. These findings demonstrate that PM effectively enhances the expressive power of Redox-IGRs and provides a simple, generalstrategy for boosting the high-dimensional dynamics of PRC systems. © 2025 The Author(s). Published on behalf of The Japan Society of AppliedPhysics by IOP Publishing LtdSupplementary material for this article is available online1. IntroductionThe remarkable progress of artificial intelligence (AI) in recentyears has brought significant benefits to human society,1) yet ithas also raised the critical challenge of exponentially increasingpower consumption. This issue largely arises from the intrinsicmismatch between conventional von Neumann computingarchitectures and the nature of information processing inbrain-inspired AI models. To overcome this limitation, neuro-morphic devices that directly emulate brain-like computationare attracting increasing attention.2) The excessive powerdemand of conventional computing is problematic not only interms of sustainability but also because it hinders the deploy-ment of high-performance AI functions in resource-constrainededge environments.3) Accordingly, the realization of energy-efficient neuromorphic computing systems is urgently required,particularly for edge applications. Among various approachesto neuromorphic computing, physical reservoir computing(PRC) has emerged as a promising candidate.4,5) In contrastto device-level implementations of hierarchical neural networksin in-memory computing, PRC ambitiously replaces neuronsand synapses in a randomly connected recurrent network layer—the reservoir6,7)—with one or a few physical systems. Byexploiting the inherent nonlinearity, short-term memory, andhigh dimensionality of the physical reservoir, input signals canbe mapped into a high-dimensional space, where classificationand regression tasks are performed using a small linear readoutlayer. Because the majority of computation is offloaded to thephysical processes of the reservoir and the learnable readout islinear, PRC offers substantial reductions in computational cost.Various physical systems have been explored as reservoirs,including spin-torque oscillators, spin waves, memristors,nanowire networks, soft bodies, photonic circuits, and soon.4,5,8–35) These systems have demonstrated the feasibility ofPRC for a wide range of information processing tasks such astime-series prediction, image recognition, and anomaly detec-tion. However, achieving both high computational performanceand small device footprints—essential for integration and edgeapplications—remains a formidable challenge.To address this limitation, we have recently developedion-gating reservoirs (IGRs) as a framework to fully exploitthe intrinsic information processing capability of ion-con-ducting materials.36–47) An IGR consists of electrodes forvoltage input, ion conductors that drives ionic carriers, andfunctional channel materials that exhibit nonlinear responsesunder ion gating. Depending on the choice of channelmaterial, diverse physical processes—such as electrostaticmodulation of electronic properties in ion-gated transistors,ionic control of spin-wave propagation in ferromagneticmaterials, or ionically induced modulation of molecularvibration dynamics—can serve as computational resourcesfor PRC. Notably, the electric double layer IGR (EDL-IGR),composed of a hydrogen-terminated diamond channel and aLi–Sr–Zr–O solid electrolyte, has successfully demonstratedthe coexistence of high computational performance andcompact device size in the standard nonlinear autoregressivemoving-average (NARMA2) benchmark task.36) For edge AIapplications, however, high performance and small size arenot sufficient: the temporal scale of the reservoir dynamicsmust also match the timescale of the target signals. Forexample, in sensor-processor integrated edge devices, slowdynamics such as biosignals or long-period seismic wavesrequire reservoirs that can operate efficiently below 1 Hz.Although EDL-IGRs exhibit relatively fast dynamics domi-nated by EDL effects, their operational frequency range istypically limited to above 10 Hz, making them unsuitable forsuch slow signals.36,42,47) Redox-based IGRs, in which thechannels are ion–electron mixed conductors, can operate atContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution ofthis work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.11SP25-1© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJapanese Journal of Applied Physics 64, 11SP25 (2025) REGULAR PAPERhttps://doi.org/10.35848/1347-4065/ae1d84https://crossmark.crossref.org/dialog/?doi=10.35848/1347-4065/ae1d84&domain=pdf&date_stamp=2025-11-24https://orcid.org/0000-0002-3369-7700https://orcid.org/0000-0003-4053-7366https://orcid.org/0000-0003-3988-3456https://orcid.org/0000-0002-6950-6160mailto:NISHIOKA.Daiki@nims.go.jpmailto:TSUCHIYA.Takashi@nims.go.jphttps://doi.org/10.35848/1347-4065/ae1d84https://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1347-4065/ae1d84lower frequencies, but their computational performance issignificantly inferior to that of EDL-IGRs.37,46) This limita-tion stems from the fact that redox dynamics generally yieldsimple relaxation-type responses, whereas EDL systemsexhibit complex pseudo-synaptic dynamics arising fromcoupled ion–electron interactions.In this study, we overcome this challenge by introducing aphysical masking (PM) strategy into LiCoO2 channel-basedRedox-IGRs.38) Specifically, the drain voltage used to probethe channel current (reservoir state) is replaced from aconstant bias to a periodic triangular waveform. Thismaintains the device in a transient regime and inducesmore complex responses. Unlike conventional digitalmasking,48) which requires preprocessing of the input signalsby multiplication with mask matrices, PM requires no suchpreprocessing and is therefore advantageous for edge im-plementation. While the basic concept of PM was previouslyreported at the 2025 International Conference on Solid StateDevices and Materials (SSDM 2025),49) the present studyfurther demonstrates that combining PM with the invertedinput method leads to a substantial improvement in compu-tational performance. We evaluate the impact of PM on theinformation processing capacity (IPC) of Redox-IGRs—atask-independent metric that quantitatively assesses nonli-nearity, memory, and dimensionality—and reveal the originof the performance enhancement.50,51) Furthermore, wedemonstrate that combining PM with inversion pulse inputmethod substantially improves computational performance.To quantitatively evaluate this improvement, we employedthe second-order NARMA2 task—a standard benchmarktask in PRC that assesses the ability of a reservoir to predictthe behavior of nonlinear dynamical systems. In theNARMA2 task, our redox-IGR without PM exhibits anormalized mean squared error (NMSE) of 0.21, whereasapplying PM reduces the NMSE to 0.033 at an operationalfrequency of 50 mHz, representing state-of-the-art perfor-mance among PRC systems operating below1 Hz.33,34,37,43,46,52,53) In addition, the total IPC increasesfrom 11 (without PM) to 20 (with PM), primarily due toenhanced nonlinear capacity, indicating that PM effectivelydoubles the dimensionality of the system. These resultsestablish PM as a powerful strategy for extending thecomputational performance of PRC into previously inacces-sible low-frequency regimes, opening pathways for edge-AIdevices capable of processing slow temporal dynamics.2. MethodA schematic illustration of the LiCoO2 Redox-IGR used inthis study is shown in Fig. 1(a). Ti (5 nm)/Pt (35 nm) sourceand drain electrodes were deposited by electron-beamevaporation on SrTiO3 (100) substrates. A (104)-orientedLiCoO2 (LCO) channel layer with a thickness of approxi-mately 100 nm was deposited by pulsed laser depositionusing a 266 nm Nd:YAG laser under an oxygen atmosphere,with the substrate temperature maintained at 600 °C. As thesolid electrolyte, an amorphous Li3PO4 film (~300 nm) wasdeposited by RF sputtering in Ar atmosphere. A Si layer(~20 nm) was deposited as the gate electrode, followed by aPt current collector (50 nm) by electron-beam evaporation.The device geometry consisted of one source and two drainelectrodes, defining channel lengths of 5 and 20 μm, and achannel width of 500 μm. Further details of the fabricationprocess are described in our previous report.38) Electricalcharacterization of the devices and measurements for in-formation processing tasks were performed using a semi-conductor parameter analyzer (4200A-SCS, Keithley)equipped with source–measure units. During the measure-ments, the devices were placed in a vacuum chamberevacuated by a turbomolecular pump and maintained atroom temperature. Electrical contact was made using tung-sten probes. Gate voltages (VG) were applied to drive ionicmotion within the solid electrolyte, while the drain currents(ID) were monitored to obtain the reservoir states. Inexperiments with PM, the drain voltage (VD) was suppliedas a periodic triangular waveform, whereas control measure-ments were performed under a constant drain bias.3. Results3.1. Concept of physical maskingThe Redox-IGR used in this study has a multi-terminaltransistor structure composed of two drain terminals, onecommon gate, and one common source, as schematicallyshown in Fig. 1(a). The input information is applied as asequence of pulsed gate voltages. Upon application of theseinputs, lithium-ion transport within the solid electrolyte andsubsequent insertion and extraction of lithium ions into andfrom the LCO channel occur, leading to redox reactions thatmodulate both the hole concentration and hole mobility ofthe channel.54) The resulting conductance variations of theLCO channel are monitored as the drain current, whichserves as the reservoir states representing the nonlinearresponses of the system to the input signals. In conventionalIGR operation, the drain current is measured under aconstant drain bias, as in standard ion-gated transistors[Fig. 1(b)].37,55) This configuration corresponds to the casewithout PM. When the internal device dynamics are suffi-ciently complex—such as in EDL-IGRs composed of hy-drogen-terminated diamond channels and Li+ solid electro-lytes—the coupled ion–electron dynamics at the electrolyte/channel interface can exhibit edge-of-chaos behavior, re-sulting in high computational performance.36) However, intypical redox-type transistors composed of oxide channelssuch as WO3 and Li+ solid electrolytes, the conductancemodulation follows relatively simple relaxation dynamicslimited by ion diffusion within the ion–electron mixedconductor channel. This diffusive and monotonic behavioris the primary reason for the lower computational perfor-mance observed in conventional redox-IGRs.37) To over-come this limitation, we introduce PM, in which the draincurrent is measured under a periodically varying triangulardrain voltage, as illustrated in Fig. 1(c). In this configuration,not only the gate input but also the dynamic variation of thedrain voltage contributes to the effective ion gating, therebymaintaining the system in a transient, non-equilibrium stateand enhancing the complexity of its response. As describedlater in detail, the use of triangular drain voltages withdifferent amplitudes and frequencies, as shown in Fig. 1(c),allows the PM conditions to coexist in each channel withdistinct transient behaviors, which is expected to enhance theoverall high dimensionality of the device. Unlike conven-tional digital masking, which applies a random or binarymask matrix to the input sequence as a preprocessing11SP25-2© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 64, 11SP25 (2025) D. Nishioka et al.step,24,25,48) PM requires no such external signal processingand is thus advantageous for hardware implementation inedge environments. Furthermore, because PM manipulatesthe intrinsic dynamics of the device itself rather than theinput data, this concept can be broadly applied to varioustypes of physical reservoir systems that can accept multipleinput channels, beyond the scope of IGRs.3.2. Effect of physical masking on conductancemodulation dynamicsFigure 2 illustrates the effect of PM on the temporalevolution of conductance modulation in the Redox-IGR.When a sequence of pulsed gate voltages, shown in the upperpanels of Figs. 2(a) and 2(b), is applied to the gate, the draincurrent is measured either under a constant drain bias[Fig. 2(a), middle] or under a triangular drain voltage (withPM) [Fig. 2(b), middle]. The channel conductance(G= ID/VD) calculated from these measurements exhibitsmarkedly different behaviors depending on the drain-biascondition. In the absence of PM, as shown in the lower panelof Fig. 2(a), the conductance responds to the gate-voltagepulses in a simple relaxation manner, reflecting the slowredox dynamics of lithium-ion diffusion and insertion/extraction within the LCO channel.54) Such monotonicrelaxation responses lead to high correlation between adja-cent temporal states in the virtual-node (time-multiplexing)representation commonly used in reservoir computing.48)Consequently, the effective reservoir dimensionality—i.e.the number of functionally independent virtual nodes—becomes significantly smaller than the nominal number ofsampled nodes. (Details of the virtual-node approach inIGR systems are discussed elsewhere.36,37)) By contrast,when a simple triangular drain voltage is applied duringmeasurement [Fig. 2(b)], the conductance response showsfar more diverse and intricate temporal behavior, as seen inthe lower panel. This enhanced complexity mitigates theaforementioned redundancy among adjacent virtual nodes,thereby increasing the effective dimensionality of the re-servoir state space.The origin of this behavior can be explained in terms of theeffective gate voltage, (VG,eff =VG −VD/2), acting on thechannel. As depicted in Fig. 2(c), under a constant VD, VG,effvaries solely with the externally applied gate voltage. Hence,for a given input pulse of VG, the conductance G simply relaxestoward its steady-state value on the master (G–VG) curve [insetof Fig. 2(c)], with a time constant determined by the ionicresistance of the electrolyte, the chemical capacitance and theelectronic resistance of the channel. In contrast, when atriangular VD is applied [Fig. 2(d)], VG,eff continuously oscil-lates with VD, resulting in dynamic modulation of G even at afixed gate-input level. Consequently, G is no longer uniquelydefined for each VG; instead, it fluctuates within a finite rangethat reflects the instantaneous VD variation. However, as shownin the lower panel of Fig. 2(b), the amplitude of this fluctuationis smaller than that induced directly by the gate voltage.Considering the relation G∝σ = μpe, (where σ is the electricalconductivity, μ is the hole mobility, p is the hole carrier density,and e is the elementary charge), it can be inferred that duringsuch small fluctuations, the mobility μ remains almost constant,and the variation in G mainly corresponds to a change in thecarrier density p. Since p in this device reflects the amount of Liinserted into the LCO channel, it is considered that, under PMoperation, Li+ are inserted into or extracted from the channel inresponse to the applied VG, while Li+ near the channel/electrolyte interface are further driven by the oscillating VD,Fig. 1. (a) Schematic illustration of the redox-type ion-gating reservoir used in this study. (b) Conventional operation scheme, in which inputinformation is applied as a pulsed gate-voltage sequence and the drain currents are measured under a constant drain voltage. (c) Device operation withphysical masking, where a periodic triangular drain-voltage waveform is applied instead of a constant bias for current measurement.11SP25-3© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 64, 11SP25 (2025) D. Nishioka et al.repeatedly undergoing insertion and extraction synchronizedwith VD. This analysis suggests that such interfacial Li+ motioncontributes to the complex conductance modulation observedunder PM operation. As illustrated in the inset of Fig. 2(d), thiscorresponds to sampling a broader portion of the nonlinear(G–VG,eff) characteristic, effectively activating a richer set ofnonlinear responses intrinsic to the device. These resultsindicate that PM enables the Redox-IGR to more efficientlyutilize its inherent nonlinearity for information processing bymaintaining the system in a dynamically perturbed state.3.3. Performance evaluation using a second-ordernonlinear dynamical system taskTo evaluate the effect of the triangular-wave drain voltage-basedPM on the computational performance of the Redox-IGR,we employed the NARMA2 task, which is widely used forassessing reservoir computing systems.27,29,33,34,36,37,47,56) TheNARMA2 system is defined as( ) ( ) ( ) ( )( ) ( )+ = ++ +y k y k y k y ku k1 0.4 0.4 10.6 0.1, 1tar tar tar tar3where u(k) is a random input uniformly distributed between0 and 0.5, and k denotes discrete time. The objective of thistask is to train the reservoir to reproduce the system outputytar(k) from the given input sequence u(k). Accurate predic-tion requires that the reservoir possesses nonlinear andmemory characteristics comparable to those inherent in theNARMA2 system.Figure 3(a) schematically illustrates the information-pro-cessing scheme used in the present work. The input signal u(k) was converted into a pulsed-voltage sequence (basevoltage = 0 V, maximum = +1 V, minimum = −3 V) witha frequency of 50 mHz and a duty cycle of 25%, and appliedto the gate terminal of the device. During operation, twodrain terminals were driven by triangular-wave voltagesserving as physical masks: one with an amplitude of±0.4 V at 250 mHz and the other with ±0.8 V at 100 mHz.For comparison, control experiments without PM wereperformed by applying constant drain biases of 0.4 V toboth terminals. The effect of these PM conditions on theprediction error in the NARMA2 task and on the informa-tion-processing capacity (IPC) is summarized in supplemen-tary Fig. 1, and the details of the IPC analysis are describedin a later section. Although larger amplitudes and higherfrequencies of the triangular drain voltages tend to improvethe computational performance of the IGR, the best perfor-mance was achieved when different voltages and frequencieswere applied simultaneously to the two drain terminals.Fig. 2. Input–output characteristics of the device (a) without and (b) with physical masking. Each panel shows the input gate-voltage sequence (top),the drain voltage (middle), and the corresponding conductance response (bottom). Schematic illustrations of the effective gate voltage for (c) operationwithout PM and (d) operation with PM.11SP25-4© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 64, 11SP25 (2025) D. Nishioka et al.Based on these observations, the PM conditions describedabove were adopted throughout this study. For each inputsequence, the gate current (IG) and two drain currents wererecorded as physical nodes, and twenty current values weresampled per input period (five points during the “pulse-on”phase and fifteen during the interval) at a sampling rate of1 Hz to generate virtual nodes at equal time intervals.Combining the three current responses and the twenty virtualnodes yielded a total of 60 reservoir states. An example ofthe current response and the corresponding sampling pointsfor the virtual nodes is shown in supplementary Fig. 2. Asnoted above, the two triangular drain voltages have frequen-cies different from that of the gate input; however, as shownin supplementary Fig. 2, all signals operate in the same phaseat each discrete time step. To ensure consistency among thevirtual nodes, the frequencies of the PM signals wereselected under this condition. To further enhance thecomputational performance, the inversion input methodwas also employed: an inverted signal (uinv(k) = umax −u(k), (umax = 0.5)) was created, and reservoir states weregenerated following the same procedure. Details of thisinversion method are described elsewhere.40) Consequently,a 120-dimensional reservoir state vector (x1(k), x2(k), …,x120(k)) was obtained for each input u(k), and the reservoiroutput was calculated as a linear combination of the statesand readout weights:( )=Y WX, 2where Y= (y(1), y(2), …) denotes the reservoir outputvector, X= (x(1), x(2), …) is the reservoir-state matrix, x(k) = (1, x1(k), x2(k), …, x120(k))T is the reservoir statevector, and W= (w0, w1, …,w120) is the readout-weightvector. The readout weights were trained by ridge regression(W= YtarXT(XXT+λI)−1, where Ytar = (ytar(1), ytar(2), …) isthe target vector, I is the identity matrix) with a regulariza-tion parameter ( = ×5 10 4), using 50 data for washout,1000 data for training, and 200 data for testing. Thecomputational performance was evaluated using the NMSEdefined as;[ ( ) ( )][ ( )]( )= =Ly k y ky kNMSE1var, 3kL1 tar2tarwhere var(⋅) denotes the variance, and L represents the datalength (1000 for training and 200 for testing).Figure 3(b) compares the target and reservoir outputs forthe cases without PM (top) and with PM (bottom). WithoutPM, the reservoir output shows limited agreement with thetarget, yielding NMSEs of 0.081 for training and 0.21 fortesting. When PM was applied, the reservoir output closelymatched the target, and the NMSEs decreased to 0.021(training) and 0.033 (testing), corresponding to an 85%reduction in test error. These results clearly demonstratethat PM significantly enhances the computational capabilityof the Redox-IGR. Supplementary Table 1 summarizes theNMSEs obtained under PM operation using six-fold cross-Fig. 3. (a) Schematic illustration of the information-processing scheme in the Redox-IGR. The input information was converted into a pulsed sequenceat 50 mHz and applied as the gate voltage. From the three measured current responses, 20 virtual nodes were extracted. The same procedure wasperformed for the inverted input, yielding 120 reservoir states in total. The reservoir output was computed as a linear combination of these states andthe trained readout weights. (b) Results of the NARMA2 task for operation (top) without and (bottom) with physical masking (PM). Gray lines representthe target sequence, while blue and red lines denote the reservoir-predicted waveforms during training and testing, respectively. (c) Comparison of theprediction error for the NARMA2 test data as a function of the device operating frequency with other PRC systems.27,29,33,34,36,37,47,56)11SP25-5© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 64, 11SP25 (2025) D. Nishioka et al.validation (with 1000 steps for training and 200 steps fortesting; the schematic procedure is illustrated in supplemen-tary Fig. 3). The NMSEs for the test datasets ranged from0.027 to 0.044, with an average of 0.034, indicatingconsistent and robust performance regardless of the specifictraining or testing dataset used. Figure 3(c) summarizes therelationship between the test error and operational frequencyfor various PRC systems. The PM-enhanced Redox-IGRsuccessfully overcomes the inherent low-performance lim-itation of conventional redox-type reservoirs and achievesstate-of-the-art accuracy in the sub-1 Hz regime. While high-performance PRCs—such as EDL-IGRs, spin-wave reser-voirs, and photonic circuits—are typically realized in high-frequency domains,14,24–27,36,45,47,56) few systems have ex-hibited comparable performance at such low operationspeeds. Thus, the PM-driven Redox-IGR represents a pro-mising class of low-frequency, high-performance physicalreservoirs, capable of processing slow dynamical signalssuch as low-frequency components of biological rhythms(heartbeat, respiration, glucose variation) or long-periodseismic waves, thereby paving the way for future edge-AIprocessors optimized for slow temporal dynamics.3.4. Information-processing-capacity analysisTo elucidate the origin of the performance enhancement inthe PM-assisted IGR, we evaluated the IPC of the device.The IPC provides a quantitative measure of a reservoir’scomputational ability, directly characterizing its memory andnonlinear transformation capabilities.50,51) In this analysis, arandom input sequence u(k) taking values between –1 and 1was applied to the reservoir, and the accuracy with which thereservoir reconstructed a set of orthogonal-polynomial targetfunctions zm(k)—generated from delayed versions of theinput—was used to compute the capacities. The targetfunctions were defined as( ) [ ( )] ( )==z k P u k d , 4mdDn0m d,where m is the target index, d is the delay step, D is themaximum delay, and nm,d denotes the polynomial ordercorresponding to each combination of m and d.Here, Pn’ represents a set of orthogonal polynomialsconstructed via Gram–Schmidt orthogonalization as[ ( )] ( ) [ ( )] ( )( )==P u k d u k d c P u k d 5nninini01[ ( )] ( )[ ( )]( )( ) = ==cP u k d u kP u k d6in kTinkTi112with P0 = 1. Thus, the degree of nonlinearity for each targetzm is defined as = =n ndDm d0 , . The component-wisecapacity (Cm), which represents the reservoir’s ability toreconstruct the target zm, was calculated from the reconstruc-tion accuracy as[ ( ) ( )][ ( )]( )=Cz k y kz k1 7mk mk m22and the total capacity was defined as the sum of all partialcapacities:( )=C C . 8mmtotTo avoid overestimation of the IPC, a surrogate analysiswas applied: the time order of each target sequence zm wasrandomly shuffled to obtain the surrogate capacity Csur, andany Cm values below 1.5 times the maximum of Csur were setto zero. This surrogate procedure serves as a safeguard againstspurious capacity contributions, as discussed elsewhere.11)The degree-specific capacity Cn, which characterizes a spe-cific degree of nonlinearity, is defined as follows.( )( )=C C . 9nm nmFig. 4. (a) Relationship between the component-wise capacity Cm and delay for targets representing linear nonlinearity. Cyan plots and gray dashedlines indicate the results with and without PM, respectively. (b) Relationship between Cm and delay for targets representing cubic nonlinearity. Greenplots and gray dashed lines indicate the results with and without PM, respectively. (c) Total capacity of the Redox-IGR, color-coded by degree-specificcapacity. The total capacity nearly doubles with the application of PM. Because the total capacity reflects the effective dimensionality of the reservoir-state matrix, the inset schematically illustrates how the IGR maps one-dimensional input information into a higher-dimensional space.11SP25-6© 2025 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdJpn. J. Appl. Phys. 64, 11SP25 (2025) D. Nishioka et al.Here, m(n) represents all indices of total degree n. Byexamining the capacities corresponding to each nonlinearcomponent, one can directly assess how effectively thereservoir performs nonlinear transformations of differentdegrees.For instance, when n= 1, ( [ ( )]=z P u k dm 1 ( ) ¯= u k d u); the corresponding capacity C1 represents the linear (memory)capacity that quantifies how accurately the reservoir can recallpast inputs. Figure 4(a) shows the delay-length dependence ofthe component-wise capacities for the cases with and withoutPM. As the delay increases, the Cm decreases, indicating thedecay of memory over time—the so-called forgetting curve.The integral of this curve corresponds to the linear capacity C1,which was found to be similar for both cases, suggesting thatPM has little effect on the short-term memory of the device. Incontrast, Fig. 4(b) presents the case for third-order nonlineartargets ( [ ( )]=z P u k dm 3 ), where the reservoir must recon-struct cubic transformations of past inputs. Here, the PM-assisted IGR exhibits significantly higher capacities than thenon-PM device, indicating improved nonlinear processingcapability. The total third-order capacity C3 was obtainedby summing all relevant partial capacities, including cross-terms such as [ ( )]P u k d1 1 [ ( )] ( )P u k d d d,2 2 1 2 and[ ( )] [ ( )]P u k d P u k d1 1 1 2 [ ( )] ( )<