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REVIEW 4 major objections 5 minor 2 cited by

Bayesian Neural Networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials

T0 review · 4 major / 5 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Deep ensembles outperform variational Bayesian neural networks for uncertainty in machine learning interatomic potentials, across both high- and low-data regimes on a 7,815-structure TiO2 dataset.

desk verdict Useful open-source benchmark for UQ in MLIPs, but the headline claim is contradicted by the paper's own low-data tables; the NLL objection in the reader report is a red herring. read the letter →

arxiv 2509.19180 v2 pith:G5PK2V2Q submitted 2025-09-23 physics.chem-ph cond-mat.mtrl-sci

Riccardo Farris , Emanuele Telari , Nongnuch Artrith , Konstantin Neyman , Albert Bruix This is my paper
classification physics.chem-phcond-mat.mtrl-sci
keywords Bayesianneuralnetworksdeepensemblesuncertaintyquantificationmachinelearninginteratomicpotentialsvariationalinferencetitaniumdioxidenegativelog-likelihoodcalibration
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

Variational Bayesian neural networks are a principled but costly way to add uncertainty estimates to machine learning interatomic potentials. This paper asks whether they actually beat the simpler deep-ensemble approach in practice. On a dataset of 7,815 TiO2 structures, in both a full-data and a 20%-data regime, ten-member deep ensembles achieved the lowest MAE and RMSE, the most negative NLL, and the strongest correlation between predicted uncertainty and actual error among all methods tested. The three Bayesian guides (LRT, Flipout, Radial) were more expensive to train and more sensitive to random initialization, and only the Flipout/LRT variants came close to ensembling on accuracy. The result matters because a practitioner choosing a UQ method for MLIPs would want to know whether the extra complexity of Bayesian inference buys better trustworthiness; on this evidence, it does not.

What carries the argument

The comparison is carried out by wrapping the aenet neural-network architecture in three variational guides (AutoNormal mean-field with LRT or Flipout, and a Radial guide) trained by ELBO maximization via Bayes-by-Backprop, and comparing them against a ten-member deep ensemble. The evaluation uses NLL based on a Gaussian predictive distribution (Eq. 10), calibration curves with RMSCE, sharpness, a coefficient of determination between predicted sigma and absolute error, and a quartile-based overlap score between high-uncertainty and high-error predictions.

What would settle it

Recompute NLL from the reported RMSE and per-point predictive variances, enforcing the Gaussian lower bound; if DE's NLL is not actually below the value implied by its RMSE, the NLL comparison is invalid. Alternatively, re-train one DE and one Flipout network from identical seeds and inspect whether DE's advantage persists.

Watch

Extended reading notes

Core claim

The central claim is that, in the tested aenet-style MLIP setting, deep ensembles outperform variational Bayesian neural networks on both predictive accuracy and uncertainty quality, across data regimes. The paper reports DE achieving MAE 0.005 eV/atom and RMSE 0.012 on the high-data test set versus 0.014–0.019 MAE for the Bayesian methods, with DE also giving the most negative NLL (-4.65) and the lowest RMSCE (0.05). In the low-data regime, DE retains the lowest MAE and highest R2/overlap, though the Radial guide shows better calibration there. The authors further note that the Bayesian models take roughly 3–10x longer to train on a single CPU and are more sensitive to the random seed.

Load-bearing premise

The quantitative uncertainty ranking rests on the assumption in Eq. 10 that each method's predictive distribution is Gaussian with a known, comparable per-point variance; if that assumption fails, the NLL-based ordering is not reliable.

Editorial extensions

If this is right

  • If DE is the default, MLIP users can obtain well-calibrated uncertainty with a simple, cheap procedure, and NLL/RMSCE-based active learning can rely on ensemble variance.
  • Flipout and LRT, while slightly less accurate, remain the only Bayesian variants with competitive performance, and they show less sensitivity to outliers (lower RMSE variance) than DE in low-data settings.
  • The Radial guide underperformed in both regimes and is not recommended without further tuning.
  • The bayesaenet implementation makes these VBNN methods available for future MLIP studies, with the caveat of substantially higher training time.

Reading between the lines

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

  • The paper's NLL-based ranking assumes a Gaussian likelihood with known variance; if a reader enforces the Gaussian lower bound on NLL given the reported RMSE, the absolute NLL differences would shrink, although the ordinal ranking likely survives.
  • These results are tied to a small two-layer architecture; larger or graph-neural-network interatomic potentials might change the relative cost-benefit of Bayesian inference.
  • The overlap score is based on a single 75th-percentile threshold; a sensitivity analysis on thresholds would tell whether DE's active-learning advantage is robust.
  • GPU acceleration could narrow the training-time gap between DE and VBNN, but the seed-sensitivity of VBNN would remain a practical obstacle.
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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

4 major / 5 minor

Summary. The paper introduces a variational Bayesian neural network (VBNN) implementation in the aenet-PyTorch framework and compares it with deep ensembles (DE) for uncertainty quantification in machine-learning interatomic potentials. The comparison is carried out on a TiO2 dataset (7,815 structures) under two data regimes (100% and 20% training data) using accuracy metrics (MAE, RMSE, NLL) and UQ metrics (RMSCE, sharpness, R^2, overlap score). The authors report that DE consistently outperforms LRT, Flipout, and RAD guides on most metrics, with lower computational cost, and conclude that ensembles are more practical for UQ in this setting.

Significance. If the central claim is upheld, the paper offers useful practical guidance for choosing UQ methods in MLIPs and provides an open-source VBNN implementation. The systematic comparison across two data regimes, five random seeds, and multiple complementary UQ metrics is a genuine strength. However, the paper's own tables contain several contradictions with the stated central claim, and key details of the NLL computation and data splitting are missing, so the conclusions as written are not fully supported.

major comments (4)
  1. [§4.1, §5, Tables 4 and 6] The central claim that 'DE consistently achieved the lowest values across all evaluated metrics' is contradicted by the paper's own tables. In the low-data regime, Table 4 reports DE RMSE = 0.082 ± 0.012, while FO and LRT both achieve 0.075. In Table 6, DE has RMSCE = 0.10, worse than RAD's 0.06, and DE has the highest sharpness (0.16), indicating the least sharp predictions. The conclusion (§5) repeats 'lowest MAE and RMSE' and 'most calibrated uncertainty estimates', which are not supported by the low-data results. The narrative must be revised to acknowledge regime-dependent trade-offs.
  2. [§4.2, Figure 5, Tables 5 and 6] Textual statements about sharpness directly contradict the reported numbers. The text says RAD 'exhibits one of the highest sharpness values' in the low-data regime, but Table 6 shows RAD has the lowest sharpness (0.09) while DE has the highest (0.16). It also states that 'DE produc[es] the sharpest distributions in both cases', but in the high-data regime RAD has SHARP = 0.022 versus DE's 0.027, and in the low-data regime DE is the least sharp. These contradictions undermine the qualitative UQ discussion and need correction.
  3. [§3.1, §3.3] The low-data split is described inconsistently. Section 3.1 says the reduced subset is '20% of the joint training and validation set (1265, 141)', but 20% of 7034 (6330+704) is about 1407, and an 80/20 split of that would be about 1125/282, not 1265/141 (which is a 90/10 split). Section 3.3 says 'only 20% of the entire dataset' is used for training and validation, which would be about 1563 structures. Since all low-data comparisons depend on this split, the exact procedure must be clarified.
  4. [Eq. (10), Tables 3 and 4] The NLL computation is insufficiently specified. The manuscript does not state how sigma_i in Eq. (10) is obtained for each method: is it the ensemble standard deviation for DE, the posterior predictive standard deviation for VBNNs, and is the tuned likelihood variance included? Because the Gaussian NLL with per-point variances is unbounded below, small variances can drive very negative NLL values, so the reported NLL differences are not self-explanatory without reporting the predictive-variance distribution or pairing NLL with calibration metrics. Please clarify and, if possible, report NLL alongside the variance statistics.
minor comments (5)
  1. [Eq. (1)] The denominator in Bayes' theorem should be p(Y|X), not p(X|Y).
  2. [§4.2, Figure 5] The text refers to 'Table 4' when discussing calibration/sharpness trade-offs; this should be Table 6.
  3. [§3.5, Tables 1 and 2] Hyperparameters are reported only for the VBNN models; the DE hyperparameters (learning rate, batch size, etc.) are not given, making it unclear whether the comparison is fully controlled. Please add the DE configurations or state that they follow the same defaults.
  4. [General] No statistical significance tests are reported. With only five runs and overlapping standard deviations (e.g., low-data RMSE for DE vs FO/LRT), qualitative claims such as 'significantly outperform' should be tempered or supported by confidence intervals or a significance test.
  5. [§2.2] Minor typo: 'explicity' should be 'explicitly'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the accuracy/UQ comparison is an empirical benchmark with held-out test set; self-citations are tooling references only.

full rationale

The paper's central claim is an empirical comparison of deep ensembles versus variational Bayesian neural networks on a fixed TiO2 dataset. The derivation chain is standard: ensemble moments (Eqs. 3-4), variational inference/ELBO (Eqs. 5-6), and evaluation metrics (Eqs. 8-13) are all definitions, not results derived from the target conclusion. Hyperparameters, including the likelihood variance, were selected by validation MSE (Sec. 3.5), and all reported MAE/RMSE/NLL/RMSCE/sharpness/R2/overlap values are evaluated on a held-out test set (781 structures) that was not used for hyperparameter optimization. No fitted parameter is renamed as a prediction. The self-citations (Refs. [32], [33]) cite the underlying aenet framework and aenet-PyTorch implementation; they are infrastructure references and do not carry the conclusion. There is no invoked uniqueness theorem and no ansatz smuggled in via self-citation. The paper even acknowledges that DE's empirical superiority is not new ('it is not new that DE empirically outperforms BNNs'), citing external work. Thus no derivation step reduces to its own inputs by construction. Note: the summary statement that DE 'consistently achieved the lowest values across all evaluated metrics' is contradicted by some entries in Tables 4 and 6 (e.g., FO/LRT lower RMSE in low-data; RAD lower RMSCE and sharpness), but that is an internal-consistency/correctness concern, not circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on standard variational inference and several domain modeling choices. No new physical entities are introduced. The main free parameters are the Optuna-tuned hyperparameters, some of which directly enter the uncertainty metrics.

free parameters (8)
  • Network architecture = Two hidden layers, 15 units each, tanh activation
    Chosen by hand and shared across all models; affects capacity and all results.
  • Ensemble size = 10 networks
    Chosen by hand for deep ensembles; the uncertainty estimate depends on this number.
  • Learning rate = FO: 3.25e-4 (20%), 1.24e-4 (100%); LRT: 5.40e-4, 4.9e-5; RAD: 1.37e-4, 5.36e-4
    Tuned via Optuna over [1e-5, 1e-3] on validation set.
  • Batch size = FO: 64/256; LRT: 64/64; RAD: 32/64
    Tuned via Optuna from [32, 64, 128, 256].
  • MC samples = 2 for all models
    Tuned via Optuna from [1, 2]; affects ELBO gradient stability and training cost.
  • Gaussian prior scale = FO: 0.175/0.206; LRT: 0.358/0.209; RAD: 0.115/0.108
    Tuned via Optuna from [0.1, 1.5]; controls regularization strength.
  • Gaussian q_theta scale = FO: 0.001832/0.000605; LRT: 0.001246/0.000227; RAD: 0.000172/0.000800
    Tuned via Optuna from [1e-4, 0.1]; initial variational posterior variance.
  • Likelihood variance = FO: 0.260/0.893; LRT: 0.282/0.132; RAD: 0.793/0.294
    Tuned via Optuna from [0.1, 2.0]; enter NLL and calibration calculations directly.
assumptions (5)
  • standard math Bayes theorem and ELBO variational inference
    Used in Sec. 2.2, Eqs. (5)-(6); standard probabilistic formalism.
  • domain assumption Mean-field factorization of the variational posterior
    Sec. 2.2, Eq. (7); assumes independent Gaussian weights, which may miss posterior correlations.
  • domain assumption Homoscedastic Gaussian likelihood for energies
    Sec. 3.4, Eq. (10); used to define NLL and calibration. The reported NLL values contradict this assumption if computed literally.
  • domain assumption Ensemble standard deviation is a valid predictive uncertainty
    Sec. 2.1, Eq. (4); heuristic epistemic uncertainty without a probabilistic derivation.
  • domain assumption The 20% subset represents a meaningful low-data regime
    Sec. 3.1; the subsetting procedure is stated inconsistently, so representativeness cannot be assessed from the text.

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Cite this review

Pith. "Pith review of Bayesian Neural Networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials." pith.science (2026). https://pith.science/paper/G5PK2V2Q

@misc{pith2026250919180,
  author       = {Pith},
  title        = {Pith review of: Bayesian Neural Networks versus deep ensembles for uncertainty quantification in machine learning interatomic potentials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G5PK2V2Q}},
  note         = {Machine review of arXiv:2509.19180}
}
abstract

Neural-network-based machine learning interatomic potentials have emerged as powerful tools for predicting atomic energies and forces, enabling accurate and efficient simulations in atomistic modeling. A key limitation of traditional deep learning approaches, however, is their inability to provide reliable estimates of predictive uncertainty. Such uncertainty quantification is critical for assessing model reliability, especially in materials science, where often the model is applied on out-of-distribution data. Different strategies have been proposed to address this challenge, with deep ensembles and Bayesian neural networks being among the most widely used. In this work, we introduce an implementation of Bayesian neural networks with variational inference in the aenet-PyTorch framework. To evaluate their applicability to machine learning interatomic potentials, we systematically compare the performance of variational BNNs and deep ensembles on a dataset of 7,815 TiO$_{2}$ structures. The models are trained on both the full dataset and a subset to assess how variations in data representation influence predictive accuracy and uncertainty estimation. This analysis provides insights into the strengths and limitations of each approach, offering practical guidance for the development of uncertainty-aware machine learning interatomic potentials.

Figures

Figures reproduced from arXiv: 2509.19180 by the authors.

Figure 1
Figure 1. Illustration of uncertainty calibration behavior in three types of models. Top: predicted values ordered by [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Illustration of the overlap metric. Each dot is a prediction with its uncertainty (x-axis) and absolute error [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Predictive performance metrics (MAE, RMSE, NLL) for all models across high-data (100% of the dataset) [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Root mean squared calibration error (RMSCE) and sharpness (SHARP) of the predicted uncertainty distribu [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Calibration curves (top) and sharpness distributions (bottom) for the best-performing models in each data [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Quality of uncertainty estimation as assessed by coefficient of determination ( [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

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Forward citations

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.