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REVIEW 3 major objections 6 minor 19 references

Impute With Confidence: A Framework for Uncertainty Aware Multivariate Time Series Imputation

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read The paper's central claim is that Monte Carlo dropout variance measures imputation confidence well enough that a threshold-based selective imputation framework can reduce imputation error and, in some cases, improve downstream mortality…

desk verdict MC dropout uncertainty correlates cleanly with imputation error on ICU data, but the selective-imputation downstream claim rests entirely on validation-set AUPRC with thresholds chosen on that same set, so the benefit is not yet established. read the letter →

arxiv 2507.09353 v1 pith:ZMRDIDFV submitted 2025-07-12 cs.LG cs.AIstat.ML

classification cs.LGcs.AIstat.ML
keywords timeseriesimputationMonteCarlodropoutuncertaintyestimationselectiveelectronichealthrecordsmissingdatamortalityprediction
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 sets out to give deep time series imputation models a practical confidence measure. It claims that the standard deviation of Monte Carlo dropout forward passes tracks the model's actual imputation error, so that the values the model is least sure about are the values it is most likely to get wrong. On that basis it proposes a selective imputation framework: calibrate an uncertainty threshold on a validation set with synthetic masks, then impute only the missing values whose uncertainty falls below the threshold. The authors show that this lowers imputation error across three EHR datasets and five missingness types, and that in some configurations it also improves a downstream 24-hour mortality prediction task. A sympathetic reader would care because the approach offers a way to decide when to trust an imputation rather than blindly filling every gap.

What carries the argument

The central object is the Monte Carlo dropout uncertainty estimate: after training, the model runs $F$ forward passes with dropout enabled, and the standard deviation of the predicted values at each time step and variable is taken as the uncertainty $U \in \mathbb{R}^{T \times D}$. The threshold set $U$ is the collection of these uncertainties at positions that were synthetically masked during validation, and quantiles $t_{10}, t_{20}, \dots, t_{100}$ become the operating points for selective imputation. This object carries the argument because it links model confidence to observable error, and the calibration step is what turns the uncertainty measure into a decision rule.

What would settle it

Take a dataset with completely recorded ground truth, train an imputation model, then compare the uncertainty-to-error relationship for synthetically masked positions with the same relationship for positions that were genuinely missing but whose true values can later be recovered, for example from a redundant sensor; if the monotone increase of error with uncertainty disappears or flips on the genuine missing values, or if imputing only the lowest-uncertainty genuine missing values gives no error reduction over random selection, the framework's calibration does not transfer.

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Extended reading notes

Core claim

The central claim is that the elementwise standard deviation of Monte Carlo dropout forward passes is a faithful uncertainty measure for deep time series imputation models, and that this uncertainty can be used to impute selectively. Across MIMIC-IV, eICU, and HiRID, and across five synthetic missingness patterns, the paper shows that mean absolute error on imputed values increases with the uncertainty threshold, typically in a near-linear fashion, so that the model's least certain imputations are its least accurate. The framework calibrates thresholds t10, t20, ..., t100 on synthetically masked validation positions, then at inference time imputes only missing values whose uncertainty falls below the chosen threshold. The paper reports that in the clearest experiments (block blackout on eICU, MCAR on HiRID) the downstream 24-hour mortality classifier performs best with selective imputation rather than full imputation, and states more generally that choosing not to impute highly uncertain values can improve downstream performance in certain cases.

Load-bearing premise

The thresholds chosen from synthetically masked validation values are assumed to stay meaningful when the model imputes genuinely missing values, so that uncertainty and error remain coupled on the real missingness at inference.

Editorial extensions

If this is right

  • Any deep imputation model with dropout layers can obtain an uncertainty map at inference time by running $F$ forward passes and taking the standard deviation, without changing the architecture or the loss.
  • Setting an uncertainty threshold turns the imputer into a selective imputer: values above the threshold are left missing, which reduces mean absolute error on the values actually imputed.
  • In configurations where the synthetic training missingness resembles the real missingness, such as block blackout on eICU, a mid-range threshold like the 60th percentile can give better downstream AUPRC than either full imputation or no imputation.
  • Because the uncertainty measure is calibrated with quantiles $t_{10}, t_{20}, \dots, t_{100}$, the framework gives practitioners a simple knob to trade imputation coverage against imputation reliability.

Reading between the lines

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

  • The paper leaves open whether the thresholds chosen on synthetically masked validation values still separate good from bad imputations when the model faces genuinely missing values at inference, since no experiment compares uncertainty distributions or optimal thresholds between the two settings.
  • A natural extension would be to amortize the multiple forward passes or study how small $F$ can become before the uncertainty ranking degrades, which would address the inference-time cost the paper identifies as a limitation.
  • The 'certain cases' phrasing implies selective imputation is not always beneficial; a practical rule for when to expect gains would need to connect the benefit to the similarity between the training missingness type and the real missingness, which the paper flags as a possible explanation but does not establish.
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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 / 6 minor

Summary. The paper proposes a framework for uncertainty-aware multivariate time series imputation based on Monte Carlo dropout. For a given imputation model, the standard deviation across stochastic forward passes is used as an uncertainty estimate, thresholds are calibrated on synthetically masked validation values, and only missing values with uncertainty below a threshold are imputed. Experiments on MIMIC-IV, eICU, and HiRID with two architectures and five synthetic missingness mechanisms show a monotone relationship between uncertainty and imputation error, and selected downstream mortality-prediction experiments suggest that selective imputation can improve AUPRC.

Significance. If the claims are supported, the framework would be practically valuable because it applies to a broad class of deep imputation models without altering the architecture and does not fit the uncertainty measure to the downstream outcome, so the core uncertainty-error correlation claim is not circular. The breadth of the empirical sweep—three EHR datasets, two model families, and five missingness mechanisms—is a strength. However, the downstream benefit is currently established only on validation data with thresholds selected on the same data, and the transfer of synthetic-mask thresholds to genuine missingness is assumed rather than tested; these gaps are central to the paper's stated practical contribution.

major comments (3)
  1. [§5.3, Figures 3–4; §4 data split] The downstream claim that selective imputation improves mortality prediction is supported only by validation-set AUPRC, and the uncertainty threshold is selected on that same validation set. The manuscript explicitly reserves 50% of each dataset as test in §4, yet no test-set AUPRC is reported anywhere, and Figures 3 and 4 appear to be validation curves. With 11 thresholds, 2 models, 3 datasets, and 5 missingness types, the apparent gains at t60 (Figure 3) and t20 (Figure 4) may be artifacts of selection on the validation set. Please report test-set AUPRC for every threshold, and ideally choose thresholds using validation data and evaluate once on the held-out test set, with confidence intervals or multiple seeds.
  2. [§3.4 and §5.3] The calibration step computes thresholds t10–t100 as quantiles of the uncertainty distribution U gathered only from synthetically masked positions in the validation set, yet §5.3 applies selective imputation to Xobs samples with genuine missingness. No experiment compares uncertainty values or optimal thresholds between synthetic and genuine missing positions, so the paper assumes that thresholds calibrated on synthetic masks transfer to genuine missingness. This assumption is load-bearing for the selective-imputation results and should be tested, for example by plotting the uncertainty distribution on synthetic versus genuine missing positions for a held-out fold or by calibrating on genuine missingness when a small labeled set is available.
  3. [§5.2, Figures 1–2] The central uncertainty-error relationship is described qualitatively as 'very clear and consistent' but is not quantified. The paper reports no correlation coefficient, confidence interval, variance across random seeds, or statistical test, and the plotted MAE values are computed on the same validation set used to derive the thresholds. Since this relationship is the foundation for all subsequent selective-imputation experiments, please provide a numeric summary (e.g., Spearman or Pearson correlation between threshold and MAE per model/dataset/missingness condition, with uncertainty intervals) and report variability across independent training runs. Without this, the reader cannot assess the strength or generality of the claimed monotone trend.
minor comments (6)
  1. [§5.3] The text contains an unresolved cross-reference 'Appendix ??' when referring to the full set of AUPRC plots; please insert the correct appendix number.
  2. [Appendix A] Several figure captions are duplicated or contain typos, such as 'miiv' instead of 'MIMIC IV' (Figures 5–14) and 'hirid' lowercase (Figures 24–32); please standardize dataset names and captions.
  3. [§3.2] In the MAR definition, the claim that missingness 'depends solely on variables that remain observed' is weakened by the implementation note that genuinely missing values are filled with the mean before the logistic regression; please clarify whether this mean imputation introduces dependence on unobserved values and, if so, how the mechanism is still strictly MAR.
  4. [§3.4] The notation 't10, t20, ..., t100' is ambiguous: it is unclear whether these are quantile indices or actual uncertainty values at those quantiles. Since later text speaks of '60% most confident missing values', please define the threshold construction explicitly, including the mapping from quantile to threshold value.
  5. [§5.1 and Appendix B] The statement that the authors 'reproduce their benchmark comparison' is supported only by figures without numerical tables or reported errors; please add a table with MAE values and baseline comparisons so the reader can verify the claim.
  6. [Figures 3 and 4] The figures lack axis labels in the manuscript text and the '0.0' threshold (no imputation) is referenced but not clearly marked; please add labeled axes, legends, and error bars or confidence intervals.

Circularity Check

1 steps flagged · score 4.0 of 10

Downstream benefit is validation AUPRC with the threshold selected on that same validation set; no held-out test AUPRC breaks the loop, while the core uncertainty–error correlation is non-circular.

  1. fitted input called prediction [Section 5.3 (Downstream Task Impact); data split in Section 4; conclusion in Section 6]
    "For each threshold, we selectively impute according to that threshold (note imputation for the classification task is performed on Xobs samples with no synthetic missing values) using the now pre-trained imputation model, then train and test a Light Gradient-Boosting Machine (LGBM) Ke et al. (2017) mortality classifier. From there we obtain validation set AUPRC to measure model performance. In Figure 3 we can see a clear case of the downstream task performing better when imputation is only performed on the 60% most confident missing values."

    The thresholds t10..t100 are fixed quantiles of validation-set uncertainty, but the 'clear case' (t60) is identified by inspecting the AUPRC curve computed on the same validation split, and no test-set AUPRC is reported despite the 50% test split defined in Section 4. The claimed downstream gain is therefore the validation-curve value used to select the threshold: it is a selected maximum, not an independent out-of-sample prediction. The evidence for selective-imputation benefit reduces to the selection criterion itself.

full rationale

The central uncertainty–error claim is not circular: the Monte Carlo dropout standard deviation is defined from forward-pass variance, not from imputation error, and the observed monotone MAE-versus-threshold relationship is an empirical correlation tested across datasets, models, and missingness types. There is no self-citation chain or imported uniqueness argument; the Gal and Ghahramani citation is an external, standard result. The partial circularity is confined to the downstream evaluation: thresholds are calibrated on validation uncertainty, the same validation set supplies the AUPRC used to identify a peak, and the conclusion that selective imputation 'in certain cases' improves downstream performance is defended with that same validation AUPRC rather than a held-out test result. This is a self-fitting loop in the downstream claim, but it does not infect the independently meaningful uncertainty–error correlation, so the score is moderate rather than high.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claim relies on the MC dropout uncertainty assumption, the synthetic-to-genuine transfer assumption, the representativeness of synthetic missingness, and the chosen variable subset. No novel entities are introduced; blockBO is a data corruption scheme, not a postulated entity.

free parameters (5)
  • patient filtering thresholds = LOS >= 30 hours, no death in first 30 hours, >= 4 measurements, no >12h contiguous missingness per variable, age >=…
    Adopted from the YAIB pipeline (van de Water et al., 2024) in Sec. 4; these arbitrary choices shape the datasets and therefore the measured performance.
  • uncertainty threshold quantile = varies by model/dataset/missingness type, e.g., t60 for eICU blockBO and t20 for HiRID MCAR
    Selected in Sec. 3.4 and Sec. 5.3 as the quantile that maximizes validation AUPRC; downstream gains are reported on that same validation set.
  • Monte Carlo forward pass count F = 16
    Chosen by the authors in Sec. 5.2 to estimate uncertainty; no sensitivity analysis on F is reported.
  • logistic regression intercept for MAR and MNAR missingness generation = chosen to achieve 30% missingness
    Used in Sec. 3.2 to set the synthetic missingness rate for the logistic-regression-based masking; fitted to each dataset.
  • imputation model hyperparameters = learning rate in {0.001, 0.005}, layers in {2, 4}, d_model in {64, 128}, d_inner in {64, 128}, heads in {4, 8}…
    Selected by randomized grid search on validation MAE per model, dataset, and missingness type, as described in Sec. 5.1 and Table 1.
assumptions (4)
  • domain assumption Monte Carlo dropout approximates Bayesian inference in a deep Gaussian process, so sample standard deviation is a predictive uncertainty measure (Gal and Ghahramani, 2016).
    Invoked in Sec. 3.3 as the basis for U_cor; this is a transferred theoretical result, not re-derived in this paper.
  • domain assumption Uncertainty values and thresholds computed on synthetically masked positions are representative of genuine missing values at inference.
    Sec. 3.4 constructs U only from synthetic masks, while Sec. 5.3 applies those thresholds to Xobs with genuine missingness; no transfer check is provided.
  • domain assumption Synthetic missingness patterns (MCAR, MAR, MNAR, BO, blockBO) represent real ICU missingness well enough to train and calibrate models that transfer.
    Used throughout Sec. 3.2 and Sec. 5.1 to train all imputation models; no validation on naturally occurring missingness is performed.
  • domain assumption The six most observed dynamic variables are sufficient for the imputation and mortality prediction tasks.
    Sec. 4 restricts all experiments to Heart Rate, Mean Arterial Pressure, Systolic and Diastolic Blood Pressure, Respiratory Rate, and Blood Oxygen Saturation; if other variables carry critical signal, the results may not transfer.

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Cite this review

Pith. "Pith review of Impute With Confidence: A Framework for Uncertainty Aware Multivariate Time Series Imputation." pith.science (2026). https://pith.science/paper/ZMRDIDFV

@misc{pith2026250709353,
  author       = {Pith},
  title        = {Pith review of: Impute With Confidence: A Framework for Uncertainty Aware Multivariate Time Series Imputation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZMRDIDFV}},
  note         = {Machine review of arXiv:2507.09353}
}
read the original abstract

Time series data with missing values is common across many domains. Healthcare presents special challenges due to prolonged periods of sensor disconnection. In such cases, having a confidence measure for imputed values is critical. Most existing methods either overlook model uncertainty or lack mechanisms to estimate it. To address this gap, we introduce a general framework that quantifies and leverages uncertainty for selective imputation. By focusing on values the model is most confident in, highly unreliable imputations are avoided. Our experiments on multiple EHR datasets, covering diverse types of missingness, demonstrate that selectively imputing less-uncertain values not only reduces imputation errors but also improves downstream tasks. Specifically, we show performance gains in a 24-hour mortality prediction task, underscoring the practical benefit of incorporating uncertainty into time series imputation.

Figures

Figures reproduced from arXiv: 2507.09353 by the authors.

Figure 1
Figure 1. Impact of Uncertainty on MAE for eICU (left) and MIMIC IV (right). [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Impact of Uncertainty on MAE for HiRID 5.3. Downstream Task Impact We utilize the thresholds t10, t20, ..., t100 as well as an initial t0, which is equivalent to not imputing at all. For each threshold, we selectively impute according to that threshold (note imputation for the classification task is performed on Xobs samples with no synthetic missing values) using the now pre-trained imputation model, then train and… view at source ↗
Figure 3
Figure 3. Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on eICU 6. Discussion This work highlights the importance of uncertainty estimation towards thoughtful imputa￾tion for real world time series datasets. We demonstrate that in certain cases the down￾stream model performs better when only selective imputation is applied.… view at source ↗
Figures from the paper (32 more)
Figure 4
Figure 4. Figure 4: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on HiRID study the stability of the uncertainty value as one decreases F. Additionally, we evaluate our models on a very c…
Figure 5
Figure 5. Figure 5: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on miiv 13 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on miiv [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on miiv 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on miiv [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on miiv 15 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on miiv [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]
Figure 11
Figure 11. Figure 11: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on miiv 16 [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on miiv [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]
Figure 13
Figure 13. Figure 13: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on miiv 17 [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on miiv [PITH_FULL_IMAGE:figures/full_fig_p018_14.png]
Figure 15
Figure 15. Figure 15: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on eicu 18 [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on eicu [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]
Figure 17
Figure 17. Figure 17: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on eicu 19 [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]
Figure 18
Figure 18. Figure 18: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on eicu [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]
Figure 19
Figure 19. Figure 19: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on eicu 20 [PITH_FULL_IMAGE:figures/full_fig_p020_19.png]
Figure 20
Figure 20. Figure 20: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on eicu [PITH_FULL_IMAGE:figures/full_fig_p021_20.png]
Figure 21
Figure 21. Figure 21: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on eicu 21 [PITH_FULL_IMAGE:figures/full_fig_p021_21.png]
Figure 22
Figure 22. Figure 22: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on eicu [PITH_FULL_IMAGE:figures/full_fig_p022_22.png]
Figure 23
Figure 23. Figure 23: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on eicu 22 [PITH_FULL_IMAGE:figures/full_fig_p022_23.png]
Figure 24
Figure 24. Figure 24: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MCAR missingness on hirid [PITH_FULL_IMAGE:figures/full_fig_p023_24.png]
Figure 25
Figure 25. Figure 25: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on hirid 23 [PITH_FULL_IMAGE:figures/full_fig_p023_25.png]
Figure 26
Figure 26. Figure 26: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MAR missingness on hirid [PITH_FULL_IMAGE:figures/full_fig_p024_26.png]
Figure 27
Figure 27. Figure 27: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on hirid 24 [PITH_FULL_IMAGE:figures/full_fig_p024_27.png]
Figure 28
Figure 28. Figure 28: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for MNAR missingness on hirid [PITH_FULL_IMAGE:figures/full_fig_p025_28.png]
Figure 29
Figure 29. Figure 29: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on hirid 25 [PITH_FULL_IMAGE:figures/full_fig_p025_29.png]
Figure 30
Figure 30. Figure 30: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for BO missingness on hirid [PITH_FULL_IMAGE:figures/full_fig_p026_30.png]
Figure 31
Figure 31. Figure 31: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on hirid 26 [PITH_FULL_IMAGE:figures/full_fig_p026_31.png]
Figure 32
Figure 32. Figure 32: Impact of Uncertainty on AUPRC for a classifier trained for mortality prediction, using a pretrained imputation model trained for blockBO missingness on hirid 27 [PITH_FULL_IMAGE:figures/full_fig_p027_32.png]
Figure 33
Figure 33. Figure 33: Imputation baseline comparison on the eicu dataset. Note that the ’Attention’ method is a vanilla Transformer encoder. 28 [PITH_FULL_IMAGE:figures/full_fig_p028_33.png]
Figure 34
Figure 34. Figure 34: Imputation baseline comparison on the MIMIC IV dataset. Note that the ’At￾tention’ method is a vanilla Transformer encoder [PITH_FULL_IMAGE:figures/full_fig_p029_34.png]
Figure 35
Figure 35. Figure 35: Imputation baseline comparison on the HiRID dataset. Note that the ’Attention’ method is a vanilla Transformer encoder. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_35.png]

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Reviewed August 6, 2026 · model on record in the stance chip above.