Energy-Constrained Information Storage on Memristive Devices in the Presence of Resistive Drift

Christos Papavassiliou; Deniz G\"und\"uz; Waleed El-Geresy

REVIEW 4 major objections 3 minor 35 references

Energy-Constrained Information Storage on Memristive Devices in the Presence of Resistive Drift

T0 review · 4 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A delay-conditioned DeepJSCC encoder/decoder pair beats delay-agnostic storage coding under equal average energy budgets.

desk verdict A solid algorithmic contribution—delay-conditioned DeepJSCC with cGDN—but the energy-constraint enforcement is loose, and the channel model is entirely the authors' own simulation. read the letter →

arxiv 2501.10376 v1 pith:BAOFDT5Q submitted 2024-12-16 cs.ET cs.ITcs.LGeess.SPmath.IT

Waleed El-Geresy , Christos Papavassiliou , Deniz Gündüz This is my paper · ORCID

classification cs.ETcs.ITcs.LGeess.SPmath.IT

keywords memristorsresistivedriftdeepjointsource-channelcodinganalogueinformationstorageconditionalGDNenergy-constrainedgenerativeadversarialnetworkchannelmodeldelayconditioning

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

The paper treats storing an image on an array of memristors as communication through time, where the channel is the delay-dependent resistive drift that degrades stored resistances between write and read. Its central claim is that a single deep joint source-channel coding (DeepJSCC) encoder/decoder pair, conditioned on the storage delay, learns an energy-aware analogue coding scheme that reconstructs natural images at higher and more balanced peak signal-to-noise ratio across delays than delay-agnostic coding under the same average energy budget, with the largest margin at the tightest budget studied, 0.01 J. To make this work, the paper derives a parametric energy cost $E(R)=|A\ln(B/R)|$ from published device measurements, linking the energy needed to program a memristor to the resistance state reached, and uses it as a regulariser during end-to-end training against a generative model of resistive drift. A sympathetic reader would care because this points to a practical way to use the analogue density of memristors while managing their main weakness, the slow stochastic drift of stored values, under a hard energy constraint.

What carries the argument

The load-bearing machinery is the combination of four components. First, the energy cost function $E(R)=|A\ln(B/R)|$ derived from published pulse-programming measurements: it turns the physical observation that lower resistance states are more stable but more expensive to program into a differentiable regulariser. Second, conditional GDN (cGDN), a modified form of generalised divisive normalisation in which the per-channel normalisation parameters $\beta$ are shifted by a learned, fully-connected embedding of the normalised delay; the inverse transform, icGDN, is used in the decoder, so delay information modulates every convolutional layer. Third, a delay- and initial-resistance-conditioned cGAN trained on an event-based drift model serves as a differentiable channel model for end-to-end gradient flow. Fourth, a delay-specialised batch schedule enforces the average energy constraint over a fixed set of delays, letting the network trade energy across delay conditions.

What would settle it

Take a real memristor array, program it with the resistance distributions produced by the delay-conditioned encoder at 0.01 J for short and long delays, wait each delay, read back, and compare reconstruction PSNR against the unconditioned encoder under identical conditions; if the conditioned scheme stops outperforming on hardware, the simulated drift model was the load-bearing assumption rather than the coding scheme.

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Extended reading notes

Core claim

The central claim is that the delay itself is usable side information for storage, not just a nuisance: an encoder/decoder pair that both know the delay at write and read time learns an energy-aware analogue coding scheme that outperforms delay-agnostic coding under the same average energy budget. The paper supports this with CIFAR-10 experiments over delays from 0 to 1000 seconds, showing the conditioned pair achieves higher and more balanced PSNR than unconditioned, encoder-only, and decoder-only baselines, with the biggest improvement at 0.01 J, where the unconditioned network degrades sharply. The authors also claim a new trade-off between programming energy and information retention, captured by $E(R)=|A\ln(B/R)|$, with $B=R(0)$ the equilibrium resistance and $A=\tau_{\mathrm{final}}K^2(1/R(\tau_{\mathrm{final}})-1/R(0))$; this function becomes the energy regulariser in the training loss. They implement conditioning through a modified divisive normalisation layer, conditional GDN (cGDN), which shifts the normalisation parameters by a learned embedding of the delay. The paper's own ground-truth evaluation against the event-based model shows the learned scheme transfers for most delays, with some drops where the surrogate statistics were not perfectly matched.

Load-bearing premise

The load-bearing assumption is that the computer model of resistive drift used for both training and testing faithfully matches real memristor behaviour; if real devices drift differently, the reported image-quality gains may shrink or disappear.

Editorial extensions

If this is right

A single trained delay-conditioned pair covers the whole delay range, so storage systems need not train or store a separate codec per expected readout time.
Under a tight energy budget, delay conditioning becomes necessary: the unconditioned baseline's reconstruction collapses at 0.01 J, while the conditioned pair maintains usable PSNR.
The network allocates the energy budget across delays, shifting more of it to long, noisy delays and using sparser, higher-resistance encodings for short delays.
The scheme transfers from the differentiable cGAN surrogate to the event-based ground-truth model for most delays, indicating the learned coding strategy is not merely fitted to the surrogate.

Reading between the lines

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

Because the energy regulariser is only a soft constraint, the exact PSNR at 0.01 J should depend on the weighting of the energy term; tightening that weighting could change the delay-energy allocation and is a direct ablation to run.
The derived cost function rests on a linear-conductance approximation and could be tested directly on fabricated devices by measuring pulse energy versus retained resistance, since the paper validates it only through the simulated channel.
cGDN is a generic conditioning mechanism: the same idea could condition a JSCC codec on channel signal-to-noise ratio in wireless fading or on battery state, because it only requires a differentiable scalar condition.

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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

The genuinely new piece here is the cGDN conditioning mechanism: a single encoder/decoder pair that takes the storage delay as a continuous side input, plus the energy-regularized JSCC formulation. That is a fair increment over the prior DeepJSCC storage papers [14], [19], [20], which did not condition on delay or budget. The paper also deserves credit for evaluating on the ground-truth event-based sim (Fig. 10), which shows real effort to check the cGAN surrogate, and for clearly separating encoder-only, decoder-only, and joint conditioning. The architecture work looks competent.

The soft spots are real but not fatal to the core algorithmic claim. First, the energy constraint is not the upper bound stated in Eq. (1). The regularizer in Eq. (18) is an equality penalty, and Section V.A openly admits that "energy constraints are violated" for some delays. That means the headline PSNR gains at low budgets could be partly an energy artifact, not a pure coding gain. The stress-test note is right about this internal mismatch. Still, the paper does report normalized energy curves, and the gains are larger at low budgets where the constraint binds, so the direction is plausible—but the numbers in Figs. 6 and 8 should be re-plotted with actual average energy held equal before you trust the magnitude.

Second, external validity is thin: the channel and ground truth are both the authors' own preprints [29], [30], no code or data are released, and there are no error bars. That is a serious limitation for a hype-prone field, but it does not invalidate the comparison within the simulation. The cGAN/event-based mismatch in Fig. 10 shows some PSNR drops at certain delays, so the surrogate is not perfect.

The "fundamental trade-off" language for Eq. (12) is overblown—it is a simplified first-order derivation, not a fundamental bound—but the energy cost function itself is a reasonable closed-form parameterization. The citation pattern is fine; self-citations are to the actual channel models used. The math is internally consistent.

Who this is for: people working on analog storage on memristive devices, or on conditioning DeepJSCC for time-varying channels. A serious referee should see it, mainly to force a cleaner constraint-satisfaction analysis and ideally a code/data release. I would not cite it within the next year without independently checking the energy accounting, but it deserves peer review.

Referee Report

4 major / 3 minor

Summary. This paper studies analogue information storage on memristive devices as a delay-dependent communication problem. The authors derive an energy cost function E(R)=|A ln(B/R)| from a simplified model of programming pulses, formulate the storage problem as an energy-constrained joint source-channel coding (JSCC) problem, and train a DeepJSCC autoencoder with a conditional GDN (cGDN) architecture so that the encoder and/or decoder can be conditioned on the storage delay. The channel is represented by a cGAN trained on a simulated event-based resistive-drift dataset from the authors' prior work. Experiments on CIFAR-10 compare unconditioned, encoder-conditioned, decoder-conditioned, and jointly conditioned settings under energy budgets from 1.0 J to 0.01 J, with reconstruction quality measured in PSNR, and include a ground-truth evaluation on the event-based simulator. The central claim is that the jointly delay-conditioned scheme achieves higher and more balanced PSNR across delays under equal average energy budgets.

Significance. If the central comparison holds, this is a useful step for analogue storage: it demonstrates a practical way to adapt a single JSCC codebook to a time-varying storage channel and an explicit energy-regularised training objective. The cGDN conditioning layer and the separate energy regularisation on a fixed delay grid are interesting architectural ideas, and the ground-truth evaluation in Section V.D is a good sanity check that is often missing in deep-learning-for-channels papers. However, the paper's 'fundamental' energy-retention trade-off is not established beyond a phenomenological model, and the experimental support is entirely internal to a simulation chain in which the cGAN and the ground-truth simulator are both from the authors' prior preprints; the headline energy-constrained comparison is also weakened by the admitted energy-constraint violations and by the equality-form regulariser.

major comments (4)

[IV.C, Eq. (18); V.A] The energy regulariser in Eq. (18) does not implement the constraint in Eq. (1). Eq. (18) penalises (1 - E(M_i)/e_b)^2, which is minimised when every encoded resistance costs exactly e_b; spending less than the budget is penalised as heavily as spending more. This is an equality target, not an upper bound. Section V.A then states that 'Energy constraints are violated in order to ensure that enough information is retained...', so the compared schemes may operate at different actual average energies at the delays used for the PSNR comparison. The reported PSNR advantage of the conditioned scheme could therefore partly reflect higher energy expenditure rather than better coding. Please report the achieved average energy for each setting and delay, and either enforce the constraint during evaluation or compare at equalised average energy.
[IV.A, IV.H, V.D] The entire experimental chain is validated only against the authors' own simulation. The cGAN channel model of [29] is trained on the event-based simulator of [30], and Section V.D evaluates the trained autoencoder on that same event-based simulator; there is no independent physical measurement anywhere in the loop. Figure 10 shows visible PSNR drops when switching from the cGAN to the event-based model at several delays, so the generative model is not perfect even within the simulated family. In the absence of device data or at least a broader family of simulators, the results should be presented as valid for the simulated drift model, not for memristive devices in general.
[III.A] The abstract and contributions describe Eq. (12) as a 'novel, fundamental trade-off' between energy and information lifetime. The derivation rests on several unvalidated simplifying assumptions: constant compliance current throughout the pulse, conductance linearly proportional to pulse duration, symmetric switching energy, and the specific form of Eq. (9). The constants A and B are set to illustrative values in Figure 2, and no measurement is provided. This is a plausible phenomenological model, but 'fundamental' is an overclaim. I recommend re-scoping the claim and stating explicitly that Eq. (12) is an illustrative first-order model.
[V.A, V.B, V.D] None of the PSNR results in Figures 6, 8, or 10 include error bars, multiple seeds, or significance tests, and the main claim of 'higher and more balanced reconstruction quality' rests on differences between single curves. Given the energy-constraint issue above, it is important to know whether the advantage of the jointly conditioned scheme is stable across training runs and statistically distinguishable from the unconditioned baseline.

minor comments (3)

[II] There is a typo in the paragraph following Eq. (2): 'mehtods' should be 'methods'.
[IV.C, Eq. (19)] The notation for the regularisation weights is inconsistent: the text defines lambda_res and lambda_energy, while Eq. (19) uses lambda_resistance and lambda_energy; in addition, the loss in Eq. (19) is written with a square root and calls the distortion MSE, although l was defined as a Frobenius norm in Eq. (2). Please align these definitions.
[IV.H, V.A] Section IV.H says the networks are trained for delays d in [0,1000], but Figure 6 reports results up to 1400 s; the recurrent cGAN extension with n=4 makes this possible, but the discrepancy should be stated explicitly in the text.

Circularity Check

2 steps flagged · score 6.0 of 10

The headline PSNR gain is partly an artefact of admitted energy-budget violations, and the 'ground truth' channel is the authors' own simulator; both load-bearing steps are self-referential.

other [Section IV.C.2, Eq. (18); Section V.A]
"renergy(M ) = 1/n Σ_i (1 − E(M_i)/e_b)^2 ... Energy constraints are violated in order to ensure that enough information is retained, following storage and recovery, to reconstruct the image to a reasonable degree. The violation of the energy constraints demonstrates that the trade-off that the network has learnt between energy consumption and storage reliability generalises to larger delays."

The optimization constraint stated in Eq. (1) is EM[E(m)] ≤ B, but the regularizer actually used in training, Eq. (18), is an equality penalty: it is minimized when each device spends exactly e_b and penalizes under-spending as much as over-spending. Section V.A then explicitly admits that energy constraints are violated during evaluation, and Figure 6(e) shows normalized energy above 1 for conditioned schemes at large delays. The claimed advantage of delay conditioning 'while still respecting the average energy budget' therefore may be driven by unequal energy over-spend rather than by the coding scheme.
self citation load bearing [Section IV.A (Dataset); Section V.D (Ground Truth Model Evaluation)]
"We use a resistive drift dataset based on an event-based model of memristive devices [30], introduced in [29]... we evaluate the autoencoder on the ground truth, event-based model, as a measure of its ability to generalise to the statistics of a real device... (in this case, the event-based model developed in [30])."

The 'ground truth' is not an external measurement of real memristors: [30] is the authors' own event-based simulator, and the cGAN channel model [29] was trained on that same simulator. The evaluation in Section V.D therefore only checks consistency between two self-authored models; it does not anchor the autoencoder's performance to actual device statistics. Since the central claim is about storing images on memristive devices, the entire experimental chain rests on these self-citations, making the channel model load-bearing and unverified outside the authors' own simulator.

full rationale

The paper's physical energy-cost derivation in Section III is not circular: it follows from stated simplifying assumptions (linear conductance change, compliance current inversely proportional to final resistance, constant current during programming) and external literature, and the resulting E(R) in Eq. (12) is not obtained by equating it to the target distortion. The cGDN contribution is also a legitimate architectural extension of the known GDN transform, not a renamed version of the result. However, two load-bearing steps create partial circularity. First, the energy regularizer in Eq. (18) is an equality penalty, not the upper-bound constraint of Eq. (1), and Section V.A admits the constraint is violated so that the conditioned networks can retain information at large delays. The headline 'higher and more balanced reconstruction quality ... while still satisfying average power constraints' is thus not established: the PSNR gain at long delays may be purchased by exceeding the budget, and the energy values reported in Figure 6 are computed from the same regularizer's cost function, so the comparison is self-referential. Second, both the training channel (cGAN, [29]) and the 'ground truth' evaluation model (event-based, [30]) are prior preprints by the same authors, so the validation is an internal consistency check between two self-authored simulators rather than external anchoring to real memristive device behavior. These issues do not make the algorithmic comparison among delay-conditioning variants meaningless, but they prevent the paper's central claim from being independently supported. Overall score 6: one or more predictions reduce by construction or by self-citation chain, though the architecture contributions retain independent algorithmic content.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central energy cost function rests on two hand-set constants (A and B) derived from simplifying assumptions about pulse dynamics, and the storage channel is a cGAN trained on the authors' own event-based simulator. No external benchmark anchors the channel model, and no real-device measurements are included. The cGDN conditioning itself introduces no new physical entity.

free parameters (6)

A (energy cost scale) = A = tau_final * K^2 * (1/R(tau_final) - 1/R(0)); with tau_final=1.0 s, K=2.0, R(tau_final)=0.1 kOhm, R(0)=500 kOhm in…
Scale parameter in the derived energy cost E(R)=|A ln(B/R)|; chosen for illustration, not fitted to device measurements (Section III.A, Fig. 2).
B = R(0) (reference resistance) = 500 kOhm (equilibrium resistance)
Sets the zero-energy reference state in Eq. (11); chosen rather than measured (Section III.A).
energy budget e_b = 1.0, 0.5, 0.1, 0.05, 0.01 J
Constraint parameter in energy regularization Eq. (18); varied by hand across experiments.
regularization weights lambda_res, lambda_energy = 1.0
Balance reconstruction error against resistance range and energy terms in Eq. (19); stated as design choices (Section IV.C).
soft resistance limits R_high, R_low = 750 kOhm, 0.1 kOhm
Regularization boundaries for encoder outputs (Eqs. 16-17); chosen to match dataset range (Section IV.C).
cGAN recurrence steps n = 4
Extends cGAN delay validity to 2000 s, chosen conservatively for computational cost (Section IV.H).

assumptions (4)

domain assumption Linear approximation of conductance change during programming pulse (Eq. 5): G(tau) increases linearly with time from G(0) to G(tau_final).
Used to derive the time-resistance relation and energy cost in Section III.A; not validated against device measurements in this paper.
domain assumption The programming current is constant at its maximum compliance value during the entire pulse, and the energy cost is symmetric under reversing the transition (Section III.A).
Both simplify the integral in Eq. (10); the symmetric transition assumption is particularly strong and not tested.
ad hoc to paper The cGAN trained in [29] faithfully models the conditional drift distribution, including for delays up to 2000 s via recurrent evaluation with n=4.
The entire training and evaluation relies on this learned surrogate channel (Section IV.A, IV.H); ground truth check only compares to the authors' own event-based simulation [30].
ad hoc to paper The event-based simulation [30] is a valid substitute for real memristor drift statistics.
No real-device measurements appear anywhere; Section V.D claims validation but only against this simulation.

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Cite this review

Pith. "Pith review of Energy-Constrained Information Storage on Memristive Devices in the Presence of Resistive Drift." pith.science (2026). https://pith.science/paper/BAOFDT5Q

@misc{pith2026250110376,
  author       = {Pith},
  title        = {Pith review of: Energy-Constrained Information Storage on Memristive Devices in the Presence of Resistive Drift},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BAOFDT5Q}},
  note         = {Machine review of arXiv:2501.10376}
}

read the original abstract

In this paper, we examine the problem of information storage on memristors affected by resistive drift noise under energy constraints. We introduce a novel, fundamental trade-off between the information lifetime of memristive states and the energy that must be expended to bring the device into a particular state. We then treat the storage problem as one of communication over a noisy, energy-constrained channel, and propose a joint source-channel coding (JSCC) approach to storing images in an analogue fashion. To design an encoding scheme for natural images and to model the memristive channel, we make use of data-driven techniques from the field of deep learning for communications, namely deep joint source-channel coding (DeepJSCC), employing a generative model of resistive drift as a computationally tractable differentiable channel model for end-to-end optimisation. We introduce a modified version of generalised divisive normalisation (GDN), a biologically inspired form of normalisation, that we call conditional GDN (cGDN), allowing for conditioning on continuous channel characteristics, including the initial resistive state and the delay between storage and reading. Our results show that the delay-conditioned network is able to learn an energy-aware coding scheme that achieves a higher and more balanced reconstruction quality across a range of storage delays.

Figures

Figures reproduced from arXiv: 2501.10376 by the authors.

**Figure 2.** Costs associated with bringing the resistance of a memristor to a specified value, starting from [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Histogram of the normalised delays following the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: The cGDN transform for conditioning the encoder and/or decoder network on the delay, applied to the latent channels [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: The DeepJSCC autoencoder architecture for delay-conditioned data storage. To introduce delay conditioning, we replace [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: A comparison of the PSNRs for a variety of autoencoder experiments, demonstrating the impact of delay conditioning [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: Image reconstruction results for a range of delays ranging from 0s to 1000s, for two different energy budgets. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: Comparison of the encoder/decoder/encoder and de [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: A comparison of the input distributions for the different encoder/decoder conditioned settings, for two different energy [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Evaluation on the ground truth event-based model for [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]

Discussion (0). Continue with ORCID to comment.

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