State Characterisation of Self-Directed Channel Memristive Devices

D\'aniel Hajt\'o; Deniz G\"und\"uz; Gy\"orgy Cserey; Waleed El-Geresy

REVIEW 4 major objections 7 minor 22 references

State Characterisation of Self-Directed Channel Memristive Devices

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A diode-aware model recovers SDC memristor state from noisy data

desk verdict A plausible incremental state model for SDC memristors, but the missing held-out validation and single-device data keep the central claim conditional. read the letter →

arxiv 2505.15757 v1 pith:LGRTIC4M submitted 2025-05-21 cs.ET physics.app-ph

Dániel Hajtó , Waleed El-Geresy , Deniz Gündüz , György Cserey This is my paper · ORCID

classification cs.ETphysics.app-ph

keywords memristorself-directedchannelstatecharacterisationestimationSchottkydiodemodelGeneralisedMetastableSwitchminimum-varianceresistiveswitching

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper aims to establish a physics-inspired way to characterize the resistive state of self-directed channel (SDC) memristors, a type of redox-based resistive memory. The central proposal is Eq. (5), in which a single scalar state $x$ multiplies both an ohmic term and a corrected, zero-crossing Schottky diode term: $i = x(G_m v + \alpha_1(e^{\beta_1 v}-1)+\alpha_2(1-e^{-\beta_2 v}))$. The authors report that this state-dependent diode form fits measured current–voltage data better than the Generalised Metastable Switch Model and a modified version, and they derive a minimum-variance estimator that recovers $x$ from noisy voltage and current pairs. If correct, this gives a practical readout procedure for tracking the state of SDC memristors in memory and neuromorphic applications.

What carries the argument

The central object is the state-parameterised current–voltage relation of Eq. (5), $$i = x\,(G_m v + \alpha_1($e^{{\beta_1 v}}$-1) + \alpha_2(1-$e^{{-\beta_2 v}}$)),$$ in which the scalar state $x$ multiplies both an ohmic conductance $G_m v$ and a corrected diode component. The diode correction replaces the two independent exponentials of the original Generalised MSS form with two zero-crossing exponential terms, forcing zero current at zero voltage while allowing different forward and reverse parameters. The inverse of this relation, $x = g(v,i)$, is then linearised in the measurement noise to compute per-sample variances, and the minimum-variance state estimate is formed by weighting each sample inversely to its variance (Eq. 29).

What would settle it

A direct falsifying experiment would be to program a single SDC device into several distinct states, record full IV curves for each, and check whether the ratio of the diode contribution to the ohmic contribution, $I_d(v)/G_m v$, is exactly constant across states for every voltage; any state-dependent change in that ratio (beyond the common multiplier $x$) would violate Eq. (5). Equivalently, if the fitted diode parameters $\alpha_1,\alpha_2,\beta_1,\beta_2$ must be re-fit per state to maintain good agreement, the linear multiplier assumption fails.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that the conduction of SDC memristors is not captured by treating the device as a resistor with memory, nor by a linear ohmic term plus state-independent diode exponentials. Instead, the authors propose and fit a model where the resistive state $x$ acts as a common multiplier on both the ohmic conductance and the two Schottky diode conduction components, with the diode terms written in a zero-crossing form that lets forward and reverse exponential parameters be independent. Fitting this form to measurements yields lower error on all four reported metrics (MSE, MAE, MRE, MRSE) than the Generalised MSS and a modified Generalised MSS baseline, and the inverse of the model, combined with a minimum-variance weighting of multiple noisy measurements, provides a state estimate whose uncertainty is quantified and whose dynamics can be tracked over time.

Load-bearing premise

The model assumes that a single scalar state multiplies both the ohmic and the diode conduction terms linearly, motivated by the picture that more hopping sites shrink the Schottky barrier width; if this linear relation does not hold for SDC devices, the improved fit is an artifact of the chosen functional form rather than a physical state characterisation.

Editorial extensions

If this is right

The state of an SDC memristor can be estimated from ordinary noisy voltage and current readouts, with an explicit variance for the estimate, instead of assuming noiseless measurements.
Multilevel storage and drift monitoring become practical: the estimated state trajectory over time can reveal metastability and resistive drift in the device.
The improved fit suggests that programming protocols should account for the state's effect on the Schottky barrier, not just the ohmic resistance.
The model's state variable $x$ is not an instantaneous resistance (since the VI relation is nonlinear), so it provides a more faithful readout quantity for applications.
The minimum-variance weighting procedure is general and could be applied to other nonlinear memristor models with a similar scalar state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the linear multiplier relation holds across a wider range of states and devices, the same scalar state could serve as a single readout for both ohmic and barrier-limited conduction, simplifying circuit-level state tracking.
A natural testable extension is to compare this model on the same device at different temperatures, since Schottky barrier width and hopping-site density change with temperature; the model predicts the same functional form with re-scaled $x$ only if the linear multiplier is physical.
The paper's correction to the diode form suggests that previously published memristor models using non-zero-crossing exponentials may have over-parameterised fits; re-examining them with the zero-crossing constraint could change reported state estimates.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know: this paper does not break new physical ground, but it offers a genuinely useful, physics-inspired state model for SDC memristors. The two modifications to the Generalized MSS framework—state-dependent diode scaling (Eq. 5) and the zero-crossing-corrected diode form (Eq. 6)—are new in this combination, and the weighted minimum-variance estimator (Eq. 29) is a sensible adaptation of a standard result. The authors are also honest about their assumptions: Markovian state, linear state scaling, and additive correlated noise are all flagged explicitly.

The soft spot is real: the central physical claim—that the scalar state x linearly multiplies both the ohmic and diode conduction terms—is supported only by in-sample fits on a single device. The proposed model is strictly more flexible than the baselines, so a lower training error is expected even if the specific multiplicative structure is wrong. There is no held-out validation, no cross-validation, no error bars, and Figure 7 re-uses the same fitted model to compute the state estimates, so it does not independently confirm the state variable. The manuscript also has mechanical problems: placeholder values like “X”, “min”, and “max” in the experimental section, and a garbled figure caption. These are sloppy but not fatal.

That said, the math holds up. The estimator derivation is coherent, the fitting comparison, while weak, is not contradicted by the presented data, and the physical motivation is plausible. This is a solid engineering paper, not a breakthrough. It would benefit from a major revision: add held-out validation or at least error bars, report the actual experimental parameters, clean up the placeholders, and either justify the linear scaling with more data or soften the physical interpretation.

The paper is aimed at researchers working on memristor characterization for memory and neuromorphic applications. It deserves a serious referee and, with revision, could be a useful contribution. I would not recommend rejecting it outright, but acceptance should be conditional on addressing the validation gap.

Referee Report

4 major / 7 minor

Summary. This paper addresses state characterisation of self-directed channel (SDC) memristors. It proposes a physics-inspired conduction model in Eq. (5), i = x(Gm v + alpha1(e^{beta1 v} - 1) + alpha2(1 - e^{-beta2 v})), in which a scalar state x multiplies both the ohmic and diode branches, together with a corrected zero-crossing diode form. Using data from a single Knowm SDC device, the authors fit model parameters by grid search and per-measurement Levenberg-Marquardt state values, then compare fitting errors against the Generalised MSS and a modified version. They invert the fitted model to obtain a state estimate from noisy voltage and current pairs and derive minimum-variance weights (Eq. 29) under a correlated additive noise model. The estimator is demonstrated on 60-minute resistive drift measurements for two initial states.

Significance. If the model and estimator were validated, the work would provide a practical state characterisation protocol for SDC memristors, with a physically motivated nonlinear IV family and an uncertainty-aware state estimate. The paper deserves credit for identifying the zero-crossing defect in the GMSS diode form, for explicitly deriving the variance-proportional weights in Eq. (29), and for demonstrating that a state-dependent diode branch reduces in-sample fitting error. However, the empirical support is currently limited because all model comparisons are in-sample on a single device and the state estimator is the inverse of the same fitted model; the central claims therefore need additional validation before the results can be considered established.

major comments (4)

[Section V-A, Table II] All fitting and evaluation are performed on the same single-device dataset, and the proposed model is strictly more flexible than modified GMSS: it allows the diode branch to scale with x while modified GMSS keeps the diode state-independent. The lower errors in Table II therefore do not, by themselves, establish that the linear multiplicative structure in Eq. (5) is the correct physical form. Please add held-out validation (for example, fitting on a subset of states or cycles and evaluating on the rest) or a model-selection criterion that penalises parameter count, and report parameter uncertainty from the grid-search procedure.
[Section VI-C, Eq. (16)] The state estimate used in the drift demonstration is the algebraic inverse of the fitted model evaluated with the Table I parameters, so the demonstration in Fig. 7 reuses the same fitted model that produced the data fit. Without an independent ground-truth state measurement or at least a held-out state prediction, the experiment cannot confirm that x corresponds to a physical device state; it only shows that the estimator produces a smooth curve. Please validate the estimator on states not used in fitting, or compare it against an independent conductance or resistance readout.
[Section IV-B, IV-C] The experimental section is incomplete and partly subjective: the number of state measurements is given as "X separate state measurements", the read amplitude is "Aread in [min, max]" with the actual values left blank, and the filtering criterion is a manual review of Lissajous figures. These gaps make the dataset non-reproducible and make it impossible to assess whether the state range and measurement conditions are representative. Please supply the missing values and an objective, reproducible filtering rule.
[Section VI-A, Eq. (20)] The minimum-variance derivation assumes that the additive noise N is perfectly correlated between the applied-voltage and resistor-voltage measurements, so that the noise cancels exactly in vmemristor. This assumption is stated but not tested, and the subsequent exclusion of low-magnitude measurements (below 30% of the maximum) is an ad hoc patch. If the correlation is imperfect, the variance expression in Eq. (27) and the weights in Eq. (29) are not minimum-variance. Please characterise the measurement noise empirically or justify the assumption from the instrument architecture.

minor comments (7)

[Section III, Eq. (2)] Equation (2) defines gx(i) = f(x) * i, but the readout is a function from voltage to current; this should be gx(v) = f(x) * v (or equivalent), otherwise the notation is inconsistent with Eq. (1).
[Section IV-D1] The text says "choose voltage regions" but the clustering is applied to currents; please align the terminology with the actual procedure.
[Figure 7] Figure 7 has unreadable axis labels made of embedded font tokens such as "/uni00000013"; the estimated-state axis and legend need to be rendered properly.
[Section VI-B] The sentence stating that multiplying by a constant multiplies noise power by the constant is inconsistent with Eq. (28); the noise power is multiplied by the square of the constant.
[Table II] Table II contains stray spaces in entries such as "3 .152" and "0 .2325"; please fix the formatting.
[Section II-A] There is a typo, "memrsitive", in the description of modulation of the memristive state.
[Section V-B] The discussion asserts that the results suggest the state-dependence is "approximately linear", but no statistical test or confidence interval is given to support this claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. 16 is the intended algebraic inverse of the proposed model, not a relabelled fitted prediction, and no load-bearing conclusion depends on a self-citation chain.

full rationale

The paper's derivation chain is self-contained rather than circular. Equation (5) defines the proposed model i = x(G_m v + I_d(v)), with x as the model-defined state; Equation (16) is the algebraic rearrangement of that same equation used as the state estimator. This inverse relationship is intentional and is not presented as an independent measurement of a pre-existing physical quantity, so the state estimate is a constructed latent variable rather than a fitted input renamed as a prediction. The fit comparison in Table II is an in-sample comparison, and the proposed model is more flexible than the modified GMSS baseline, so the lower training error is not strong independent confirmation of the linear state-scaling assumption; that is a model-selection and physical-interpretation risk, not a definitional circularity. The self-citations ([7], [8], [21]) are used for background, motivation, and prior framework; no uniqueness theorem or load-bearing mathematical conclusion is imported from them, and the baselines (Generalised MSS and modified GMSS) are external to the authors. The manuscript itself flags the need for further exploration of the connection between the Ohmic and diode components, consistent with the state-scaling assumption being a modelling hypothesis rather than a result forced by construction. No Eq. X equals Eq. Y beyond the intended model/inverse pair, and no prediction reduces to a fitted parameter by construction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central model rests on several fitted parameters obtained by grid search on a single dataset, plus one per-measurement state scalar. The physical and noise-model assumptions are stated as premises rather than derived, and the linear state multiplier is not independently validated.

free parameters (6)

Gm = 8.679e0
State-independent conductance scale fitted by grid search (Table I).
alpha1 = 2.622e-1
Forward diode amplitude fitted by grid search (Table I).
alpha2 = 6.597e-2
Reverse diode amplitude fitted by grid search (Table I).
beta1 = 1.370e1
Forward diode exponential coefficient fitted by grid search (Table I).
beta2 = 1.005e1
Reverse diode exponential coefficient fitted by grid search (Table I).
per-measurement state x_i = not reported; one per VI set
The state scalar for each measurement is obtained by Levenberg-Marquardt fitting against the model; these are nuisance parameters central to the state characterisation claim.

assumptions (6)

domain assumption For a fixed state x, the VI relation i = g_x(v) is one-to-one.
Section III states that each voltage input yields a unique current output and that the state can theoretically be determined from any noiseless (v,i) pair; this underpins the invertibility used in Eq. 16.
domain assumption The memristor state evolves as a Markovian process.
Section V-B states that the approach relies on the assumption that the state is Markovian.
ad hoc to paper State x scales both the Ohmic and diode conduction terms linearly (Eq. 5).
Motivated by a hypothesized linear relation between hopping-site density and Schottky barrier width, but no independent physical measurement or derivation supports this linearity.
domain assumption Measurement noise is constant additive Gaussian, common to the applied and resistor voltage readings (Eqs. 17-19).
Section VI-A; this noise structure makes the memristor voltage noise cancel and reduces current noise to N/R_series, which drives the estimator weights.
domain assumption Fitting error is approximately proportional to output current magnitude.
Section IV-D1; used to construct the loss function and error metrics, but the assumption is asserted rather than empirically validated.
standard math First-order Taylor expansion of g is accurate for small noise.
Section VI-A; relies on small noise and an accurate partial derivative with respect to current, which for this model is a function of voltage only.

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Cite this review

Pith. "Pith review of State Characterisation of Self-Directed Channel Memristive Devices." pith.science (2026). https://pith.science/paper/LGRTIC4M

@misc{pith2026250515757,
  author       = {Pith},
  title        = {Pith review of: State Characterisation of Self-Directed Channel Memristive Devices},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LGRTIC4M}},
  note         = {Machine review of arXiv:2505.15757}
}

read the original abstract

Knowing how to reliably use memristors as information storage devices is crucial not only to their role as emerging memories, but also for their application in neural network acceleration and as components of novel neuromorphic systems. In order to better understand the dynamics of information storage on memristors, it is essential to be able to characterise and measure their state. To this end, in this paper we propose a general, physics-inspired modelling approach for characterising the state of self-directed channel (SDC) memristors. Additionally, to enable the identification of the proposed state from device data, we introduce a noise-aware approach to the minimum-variance estimation of the state from voltage and current pairs.

Figures

Figures reproduced from arXiv: 2505.15757 by the authors.

**Figure 2.** Each state of the memristor parameterises a VI characteristic, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Proposed physical model explaining the SDC memristor’s [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Illustrative figures showing the READ, SET, and RESET waveforms used to measure and set/reset the memristors as part of our [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: The measurement circuit for the memristor. [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: Fitting results for our proposed model (Figure [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: State estimation using the proposed model and the associated [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Memristor -The missing circuit element,

L. Chua, “Memristor -The missing circuit element,” IEEE Transactions on Circuit Theory , vol. 18, no. 5, pp. 507–519, 1971

work page 1971

[2] [2]

The missing memristor found,

D. B. Strukov, G. S. Snider, D. R. Stewart, and R. S. Williams, “The missing memristor found,” Nature, vol. 453, pp. 80–83, May 2008

work page 2008

[3] [3]

Memristive devices and systems,

L. Chua and Sung Mo Kang, “Memristive devices and systems,” Proceedings of the IEEE , vol. 64, no. 2, pp. 209–223, 1976

work page 1976

[4] [4]

Resistance switching memories are memristors,

L. Chua, “Resistance switching memories are memristors,” Applied Physics A, vol. 102, pp. 765–783, Mar. 2011

work page 2011

[5] [5]

First draft of a report on the EDV AC,

J. von Neumann, “First draft of a report on the EDV AC,” IEEE Annals of the History of Computing , vol. 15, no. 4, pp. 27–75, 1993

work page 1993

[6] [6]

Accounting for Memristor I-V Non-Linearity in Low Power Memristive Amplifiers,

J. Wang, A. Serb, C. Papavassiliou, and T. Prodromakis, “Accounting for Memristor I-V Non-Linearity in Low Power Memristive Amplifiers,” in 2021 IEEE International Symposium on Circuits and Systems (ISCAS) , pp. 1–5, May 2021

work page 2021

[7] [7]

Event-Based Simula- tion of Stochastic Memristive Devices for Neuromorphic Computing,

W. El-Geresy, C. Papavassiliou, and D. G ¨und¨uz, “Event-Based Simula- tion of Stochastic Memristive Devices for Neuromorphic Computing,” arXiv:2407.04718 [physics], June 2024

work page arXiv 2024

[8] [8]

Delay Conditioned Generative Modelling of Resistive Drift in Memristors

W. El-Geresy, C. Papavassiliou, and D. G ¨und¨uz, “Delay Con- ditioned Generative Modelling of Resistive Drift in Memristors,” arXiv:2408.01539 [cs, eess] , Aug. 2024

work page Pith review arXiv 2024