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REVIEW 3 major objections 5 minor 70 references

Machine learning delta-T noise for temperature bias estimation

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A neural network trained on synthetic data can estimate the temperature bias of atomic-scale junctions from delta-T shot noise, with mean bias below one kelvin.

desk verdict Useful proof-of-concept with a real validation gap: the synthetic channel-opening model is calibrated on the same experimental data used for testing, so the <1 K mean bias is not yet a fair out-of-sample claim. read the letter →

arxiv 2412.00288 v1 pith:6ADXH2AX submitted 2024-11-29 cond-mat.mes-hall

Matthew Gerry , Jonathan J. Wang , Joanna Li , Ofir Shein-Lumbroso , Oren Tal , Dvira Segal This is my paper · ORCID
classification cond-mat.mes-hall
keywords delta-Tnoiseshotthermometryatomic-scalejunctionstemperaturebiasestimationmachinelearningneuralnetworksyntheticdatagenerationnoisychannel-openingprotocol
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

Temperature-biased atomic-scale junctions emit a telltale excess current noise, the delta-T noise, whose strength grows quadratically with the temperature difference across the junction. The paper asks whether that noise can be turned around to measure the temperature bias itself, which is hard to do directly at the nanoscale. Because each junction's noise also depends on how its quantized conduction channels open, the mapping is non-unique, so the authors train a feedforward neural network on synthetic datasets generated from the analytic delta-T noise formula plus a noisy channel-opening protocol. Applied to real break-junction data, the network predicts the applied temperature difference with a mean bias below 1 K for junctions up to 4 G$_0$, provided predictions are averaged over an ensemble of junctions. The result matters because it offers a non-invasive way to infer local temperature biases in nanoscale conductors and, more broadly, a template for extracting transport stimuli from noise measurements.

What carries the argument

The load-bearing object is the delta-T noise formula $$S_{\$\Delta$ T} = \frac{G_0 k_B}{\bar{T}}\left(\frac{\$pi^{2}$}{9}-\frac{2}{3}\right)(\$\Delta$ T)^2 \sum_i \tau_i(1-\tau_i),$$ which makes the excess noise quadratic in the temperature bias and proportional to the partition-noise sum of partially open transmission channels. Since the conductance $G = G_0\sum_i \tau_i$ fixes only the sum of transmissions, many channel configurations produce the same $G$ with different noise, so the inversion is not unique. The paper supplies the missing information with a noisy channel-opening protocol: the channel-opening parameter $x$ is sampled from an exponential distribution fit to low-conductance experimental data, channel transmissions are capped below full opening, and uniform noise is added to every $\tau_i$, generating synthetic $(G, S_{\Delta T}, \bar{T})$ triples that reproduce experimental scatter. A feedforward neural network with three hidden layers of 20 neurons, dropout, ReLU activation, and mean-absolute-error training is then trained on these triples to output $\Delta T/\bar{T}$. The decisive role of the protocol is shown by its deterministic counterpart, which trains successfully on synthetic data yet fails on experiments, whereas the noisy protocol yields mean biases under 1 K.

What would settle it

Measure fresh break-junction ensembles at conductance up to 4 $G_0$ with thermometers imposing $\Delta T$ values well away from the $\Delta T \approx \bar{T}$ line used in the original data (for example $\Delta T = 5$ K at $\bar{T} = 25$ K) and, without retuning any protocol parameters, check whether the ensemble-averaged mean bias stays below 1 K; a bias above 1 K would show the synthetic channel-opening distribution does not capture real junctions.

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Extended reading notes

Core claim

The paper's central claim is that the delta-T contribution to current shot noise, $S_{\Delta T}$, together with the measured conductance $G$ and average temperature $\bar{T}$, determines the applied temperature difference $\Delta T$ well enough for a supervised neural network to invert the relation on real experimental junctions, even though the network has only ever seen synthetic training data. Concretely, the network reports a mean bias---the signed deviation of predicted $\Delta T$ from the true value, averaged over the ensemble---below 1 K for junctions with conductance up to 4 $G_0$, comparable to the experimental uncertainty of roughly 0.5 K. A single junction's noise reading is dominated by other sources and cannot fix $\Delta T$ reliably; only the ensemble average of predictions becomes accurate. The paper further claims that this success validates the analytic delta-T noise expression Eq. (1) beyond the $G < 1\,G_0$ range in which it was originally tested, and that the same synthetic-data-plus-machine-learning workflow can be repurposed to estimate other transport stimuli.

Load-bearing premise

Everything rests on the noisy channel-opening protocol mirroring how transmission channels really open in hydrogen-containing gold junctions up to 4 $G_0$: the distribution of $x$ is fit to the same experimental data used for testing, and the piecewise slopes are chosen by hand, so if real junctions open differently the synthetic training distribution is wrong and the network's accuracy on experiments collapses.

Editorial extensions

If this is right

  • Ensemble-averaged delta-T noise becomes a viable nanoscale thermometer for atomic-scale junctions, with mean signed errors below 1 K for conductance up to 4 $G_0$.
  • The analytic quadratic delta-T noise formula, previously checked only below 1 $G_0$, is supported at higher conductance and at temperature differences approaching the physical maximum $\Delta T = 2\bar{T}$.
  • Single-junction noise readings cannot determine $\Delta T$; experiments must record ensembles of junctions, which changes how thermometry data should be collected.
  • Networks trained at low conductance can extrapolate to higher conductance (up to 8 $G_0$ in the paper's test), but they resist extrapolating outside the trained $\Delta T$ range, so training sets must span the expected temperature biases.

Reading between the lines

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

  • The same synthetic-training-plus-ensemble-averaging recipe should extend to other stimuli, such as voltage bias, magnetic-field-tuned transmission, or local heating, wherever the noise has a known functional dependence on the stimulus.
  • The protocol's hand-chosen piecewise slopes are a bottleneck; an ab initio or transferable version of the synthetic data generator would reveal how much accuracy depends on the specific channel-opening model.
  • The ensemble-averaging requirement means the method measures a statistical temperature bias across junction configurations rather than an instantaneous local temperature; tracking fast thermal dynamics would require time-resolved noise or repeated rapid break-junction cycles.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper trains a feedforward neural network on synthetic conductance, delta-T noise, and mean-temperature data to predict the temperature difference across atomic-scale junctions, and then applies the trained network to experimental data. Two synthetic generation schemes are considered: a deterministic channel-opening protocol with a fixed parameter x, and a noisy protocol in which x is sampled from an exponential distribution, additional piecewise channel-opening functions are used, and transmission noise is added. The network trained on the noisy protocol yields a mean signed error below 1 K on the experimental set for junctions with conductance up to 4 G0, which the authors interpret as demonstrating ensemble-level temperature-bias estimation and as supporting the delta-T noise formula beyond the previously tested 1 G0 range.

Significance. If the central claim survives scrutiny, the paper offers a useful demonstration of machine learning for an inverse transport problem: extracting a thermal stimulus from noise and conductance data without knowing the channel-resolved transmission coefficients. The manuscript is transparent about its architecture, reports metrics averaged over 10 retrained models, includes a deterministic-versus-noisy protocol comparison, and checks the quadratic delta-T formula against the full integral expression in Appendix C. However, the experimental validation is currently undermined by the calibration of the noisy channel-opening protocol to the same experimental dataset that is later used as the test set, and by the small, highly correlated set of nine experimental (Tbar, dT) pairs. These issues affect the load-bearing claim of a sub-Kelvin mean bias, so the significance is conditional on an out-of-sample validation.

major comments (3)
  1. [Sec. III B / Appendix A] The noisy channel-opening protocol is not independent of the test data used in Figs. 9-11. The distribution of x is extracted from the experimental G<1G0 data (Sec. III B and Fig. 7), and the piecewise slopes and saturation values in Appendix A are, in the authors' own words, 'obviously somewhat arbitrary' and chosen to mimic the experimental scatter. Since the same experimental set appears both as the calibration target for the generator and as the test set for the network, the sub-Kelvin mean bias is partly a measure of how well the generator reproduces its calibration data rather than a predictive test. The sensitivity shown in Sec. IV B, where the deterministic protocol gives a 4.5 K bias on the same experimental set while the noisy protocol gives under 1 K, confirms that the channel-opening model is load-bearing. I request an out-of-sample test: fit the protocol parameters using a subset of experimental junctions (or an independent experiment) and evaluate the trained network on the held-out junctions, together with a sensitivity analysis over plausible protocol parameters.
  2. [Sec. IV C / Figs. 3, 10, 11] The experimental demonstration rests on only nine (Tbar, dT) pairs, all clustered near dT approximately Tbar (Fig. 3), and the headline metric is a signed mean bias. A signed average can be below 1 K even when individual predictions are poor, because over- and under-predictions cancel; the histograms in Fig. 10 are indeed wide, and the mean absolute error reaches about 3.75 K in Fig. 11(a). Because Tbar is an input feature and dT is strongly correlated with Tbar in the experimental set, the network could exploit this correlation rather than a generalizable noise-to-temperature mapping. I ask the authors to report per-junction bias distributions, confidence intervals for the ensemble mean, and a metric such as median absolute error, and to test on experimental data spanning a wider range of dT/Tbar before claiming that the method estimates temperature bias within experimental uncertainties.
  3. [Sec. IV C / Sec. V] The paper states that the experimental agreement 'supports the theoretical expression (1)' beyond 1 G0, but this support is indirect and partially circular: the synthetic training data are generated from Eq. (1), so the network cannot detect an error in Eq. (1) unless the channel-opening protocol is independently validated. Appendix C shows that training with the integral formula (C2) gives similar metrics, but the comparison is made under the same noisy channel-opening protocol and therefore does not test the protocol itself. To support Eq. (1) beyond 1 G0, the authors should validate the channel-opening model against independent channel-resolved measurements, for example shot-noise-derived transmission histograms, or test on a dataset where a competing noise formula is distinguishable.
minor comments (5)
  1. [Sec. II B] The expression S_deltaT = S_I - 4 G k_B Tbar is consistent with Eq. (1) only after identifying G with G0 sum_i tau_i; this identification should be stated explicitly when the expression is introduced.
  2. [Sec. III A] The sentence 'there are exactly three partially open channels at any time' is only true within one conductance interval of the deterministic protocol; please rephrase to indicate that this holds for each interval between consecutive integer multiples of G0.
  3. [Appendix B] The learning rate is said to be constant, but its numerical value is not reported; please include it for reproducibility.
  4. [Sec. IV C] Figure 11 reports metrics averaged over 10 models; please also state the number of experimental junctions contributing to each max-G bin and whether the same junctions appear in multiple bins.
  5. [Throughout] There are several small language slips, such as 'As shown in Ref. 32, The second order expression' in Sec. II A; a careful proofread would improve presentation.

Circularity Check

1 steps flagged · score 6.0 of 10

Sub-K mean bias on experiments reflects calibration of the noisy channel-opening protocol to the same test data, so the experimental support for Eq. (1) beyond 1G0 is partially circular.

  1. fitted input called prediction [Introduction; Sec. III B (S1); Appendix A; evaluated in Sec. IV C / Figs. 9-11.]
    "The process of reducing prediction errors on real datasets provides valuable insights into the sequential channel-opening protocol, enabling the development of a model that reasonably aligns with the observed behavior in real junctions. ... The mean value of x determined in this way from the experimental data is 0.095. ... The protocol above is obviously somewhat arbitrary in that the slopes chosen and the residual opening before saturation could have been constructed with different numbers to mimic experiments."

    The noisy channel-opening protocol is not independent: the exponential x-distribution is fit to the same experimental data (mean 0.095, rounded to 0.1), and Appendix A admits the higher-G slopes and caps are arbitrary choices made 'to mimic experiments.' The Introduction states the protocol was developed by reducing prediction errors on real datasets, which are the same datasets later used as the test set in Sec. IV C. The NN trained on synthetic data from this calibrated generator then reports mean bias <1 K on those experiments. Thus the low bias mainly confirms that the generator matches the test set's SΔT-vs-G scatter, especially above 1G0; it is not an out-of-sample test of the inverse mapping.

full rationale

The central derivation chain is: Eq. (1) (from Ref. 32 and re-derived in App. C) -> synthetic SΔT generated with a channel-opening protocol -> NN trained on synthetic data -> prediction on experimental data. The main circularity is that the channel-opening protocol is calibrated to the same experimental dataset that is later used as the test set. Sec. III B fits the x-distribution mean to the experimental G<1G0 data, and Appendix A admits the slopes and saturation caps are arbitrary choices made to mimic experiments; the Introduction explicitly says the protocol was developed by reducing prediction errors on real datasets. Consequently, the Sec. IV C result of <1 K mean bias on experimental junctions is not an independent out-of-sample test: the generator was tuned so that synthetic (G, SΔT) pairs occupy the same region of feature space as the experimental test points, and Eq. (1) then supplies the ΔT labels. The paper's claim that this supports Eq. (1) beyond 1G0 is therefore partially circular. No load-bearing self-citation is found: Eq. (1) is re-derived in Appendix C from standard full-counting-statistics references, and the experimental data of Ref. 32 are real published data. The deterministic-protocol failure is a useful control, but it only shows that a badly mismatched generator fails, not that the calibrated generator's success is an independent validation. Overall, the partial circularity in the experimental validation warrants a score of 6.

Assumptions & free parameters 4 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the synthetic data generator. The generator uses the previously derived delta-T noise formula and a channel-opening protocol whose parameters are either fitted to the same experimental data used for testing or selected by hand to reproduce experimental trends. No new physical entities are introduced.

free parameters (4)
  • mean of x (channel-opening rate distribution) = 0.1 (from experimental mean 0.095)
    Sampled from an exponential distribution in the noisy protocol; the mean is taken from the experimental x histogram for G<1G0, calibrating the training distribution to the test data.
  • x rejection cutoff = 0.4
    Values above 0.4 are rejected because the experimental histogram shows suppression; this truncation changes the training distribution.
  • transmission noise amplitude = uniform in [0, 0.05]
    Added to each tau_i in step (S3) to mimic run-to-run variations; the magnitude is chosen by hand.
  • piecewise channel-opening slopes and saturation values = e.g., 0.95 saturation for channel 2; slopes 20/19, 0.6, 0.4-x, 0.07, 0.38-x, 0.35 across regimes
    Defines how channels open above 1 G0. The paper admits this parametrization is somewhat arbitrary and was chosen to mimic experimental trends.
assumptions (3)
  • domain assumption Coherent, noninteracting Landauer transport with energy-independent transmissions (Eq. C2) and a quadratic expansion in deltaT/Tbar (Eq. 1).
    Underlies all synthetic data generation. Eq. (1) was previously tested only below 1 G0 (Ref. 32), but here it is used up to 4 G0 and for deltaT up to 2Tbar.
  • domain assumption Hydrogen-contaminated gold junctions exhibit the same qualitative channel-opening statistics as the gold nanowire simulations of Refs. [49,64] plus the paper's modifications.
    The noisy protocol is guided by gold-only studies even though the experimental junctions contain hydrogen, an acknowledged mismatch in Sec. III B.
  • ad hoc to paper The arbitrary piecewise channel-opening functions in Appendix A accurately represent real junction evolution.
    The slopes and saturation values are not derived from a microscopic model but chosen to make synthetic data resemble the experimental scatter.

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Pith. "Pith review of Machine learning delta-T noise for temperature bias estimation." pith.science (2026). https://pith.science/paper/6ADXH2AX

@misc{pith2026241200288,
  author       = {Pith},
  title        = {Pith review of: Machine learning delta-T noise for temperature bias estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6ADXH2AX}},
  note         = {Machine review of arXiv:2412.00288}
}
abstract

Delta-T shot noise is activated in temperature-biased electronic junctions, down to the atomic scale. It is characterized by a quadratic dependence on the temperature difference and a nonlinear relationship with the transmission coefficients of partially opened conduction channels. In this work, we demonstrate that delta-T noise, measured across an ensemble of atomic-scale junctions, can be utilized to estimate the temperature bias in these systems. Our approach employs a supervised machine learning algorithm to train a neural network with input features being the scaled electrical conductance, the delta-T noise, and the mean temperature. Due to limited experimental data, we generate synthetic datasets, designed to mimic experiments. The neural network, trained on these synthetic data, was subsequently applied to predict temperature biases from experimental datasets. Using performance metrics, we demonstrate that the mean bias -- the deviation of predicted temperature differences from their true value -- is less than 1 K for junctions with conductance up to 4$G_0$. Our study highlights that, while a single delta-T noise measurement is insufficient for accurately estimating the applied temperature bias due to noise contributions from other sources, averaging over an ensemble of junctions enables predictions within experimental uncertainties. This demonstrates that machine learning approaches can be utilized for estimation of temperature biases, and similarly other stimuli in electronic junctions.

Figures

Figures reproduced from arXiv: 2412.00288 by the authors.

Figure 1
Figure 1. FIG. 1. A schematic diagram of a single-molecule atomic [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Visual representation of experimental measurements. (a) Scaled shot noise [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Pairs of ∆ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The transmission probability [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Visualization of synthetic dataset generated by the deterministic channel-opening protocol with [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Histogram of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Synthetic datasets with 0 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Neural network predicted ∆ [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Histograms of single chosen true ∆ [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Metrics of (a) mean absolute error and (b) mean bias of neural network ∆ [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Extrapolation tasks. Neural network predictions [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Neural network architecture: Performance evaluation in terms of the mean absolute error and mean bias metrics of [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Training and testing the ML model on synthetic data. We present the NN predicted ∆ [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Predictions based on training with the integral formula for delta-T noise, Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Predictions based on training with the integral formula for delta-T noise. Histograms of particular ∆ [PITH_FULL_IMAGE:figures/full_fig_p016_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17. Metrics when training with the integral formula for delta-T noise: (a) mean absolute error and (b) mean bias. Results [PITH_FULL_IMAGE:figures/full_fig_p016_17.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.