{"id":"c54bde32-54b1-4777-a6c4-652fa1147c4c","arxiv_id":"2411.08587","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"On simple toy data, both DE and DER scale their predicted noise with the injected level, but miscalibration appears in half of DE experiments and nearly all DER experiments.","lead":"This study compares how two deep learning methods, Deep Ensembles and Deep Evidential Regression, report their own aleatoric uncertainty when trained on simple tabular and image data with known injected noise. It shows the methods sense the noise level but often give miscalibrated uncertainty values, which matters for scientific fields that treat uncertainty as a measurable physical quantity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The paper's headline calibration counts (7/12 DE, 2/12 DER) rest on a non-standard criterion, 'within one std(σal) of the true uncertainty,' which for homoskedastic data gives a perfect model zero tolerance while rewarding overdispersed σal predictions; a coverage-based recalculation is needed…","rationale":"Read in good faith, the paper is a careful toy-study comparing two UQ methods with known ground-truth noise, and it is appropriately cautious about generalization. The central empirical claim is the set of calibration counts. The weakest link is the calibration definition: it compares a point estimate (true σy) to the distribution of predicted σal using one standard deviation of that distribution as the tolerance. This is not a proper calibration measure, and for homoskedastic data it is actively counterproductive: a perfect model would have zero spread, hence zero tolerance, whereas an unstable model gets more slack. This makes the 7/12 and 2/12 counts hard to interpret as evidence of miscalibration. The suggested coverage/PIT check would settle whether the qualitative conclusion is an artifact of the metric. The reader identified the same criterion as the weakest assumption; my concern strengthens it by pointing out the metric's variance-rewarding pathology. The verdict should remain conditional: the paper's conclusion is plausible but not quantitatively supported until the calibration metric is validated. No change to reader's CONDITIONAL verdict.","tokens_in":9291,"tokens_out":5035,"duration_ms":44978,"concrete_test":"Recompute the calibration pass/fail classification for all 24 model/noise/experiment runs using a standard coverage test: for each test point, form the predictive interval μ_i ± 1.0·σ_al,i and compute the empirical coverage rate; declare an experiment well-calibrated only if the coverage lies within [0.62, 0.74] (or, alternatively, if the PIT values z_i = Φ((y_i - μ_i)/σ_al,i) pass a Kolmogorov-Smirnov uniformity test at α=0.05). If the new pass counts are materially different from 7/12 (DE) and 2/12 (DER), the original criterion is the load-bearing element and the headline should be re-scoped. If the same qualitative ranking (DE better than DER, 2D-input worst) emerges, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3 and the desiderata in Section 1 define a model as well-calibrated when the true σy lies within one standard deviation of the distribution of predicted σal values over the test set. This is not a calibration metric in the standard sense, and it has a pathological property for homoskedastic data: if the model were perfectly calibrated, it would predict the same σal = σy for every test point, so std(σal) = 0 and the pass condition would require exact equality. A model that outputs noisy, overdispersed σal values gets a larger tolerance and can pass even with substantial bias. Thus the criterion rewards variance in the uncertainty estimates, which is the opposite of what good calibration should require. Since the headline counts (7/12 and 2/12 in Section 4) are computed from this criterion, they may reflect the metric's leniency rather than genuine miscalibration. In addition, each of the 12 experimental conditions is run with a single training initialization (no repeated seeds are reported), so the counts carry no statistical uncertainty. A standard diagnostic, such as empirical coverage of the central 68% predictive interval or a PIT-based uniformity test, would provide an unbiased check of whether the qualitative conclusion survives.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper compares aleatoric uncertainty estimates from Deep Ensembles (DE) and Deep Evidential Regression (DER) on two toy datasets—0D linear regression and 2D galaxy images—with noise injected on either the output or input variables and three noise levels. The authors propose three desiderata: predicted uncertainty should scale with injected noise, should be calibrated to the true uncertainty within one standard deviation of the predicted σal distribution, and should satisfy both properties across data dimensionality and injection type. They report that scaling holds across all models, but only 7 of 12 DE experiments and 2 of 12 DER experiments pass the calibration criterion, with the worst performance in the 2D input-uncertainty high-noise setting. They conclude that post-hoc calibration deserves further study and explicitly limit their claims to their toy, homoskedastic Gaussian setting.","tokens_in":9468,"tokens_out":5546,"duration_ms":49286,"significance":"The paper's main strength is its construction of benchmarks with known ground-truth aleatoric uncertainty, including a clear propagation of input noise to output uncertainty, and its explicit statement of limitations. The scaling result (desideratum i) is plausible and visually supported by Figure 2. The release of the DeepUQ code and notebooks is a useful community resource. However, the central calibration claim, expressed as the 7/12 and 2/12 counts, rests on a non-standard metric whose properties are problematic for homoskedastic data, and the quantitative values behind those counts are not reported. If the requested reanalysis with standard calibration diagnostics confirms the qualitative trend, the paper would provide a useful cautionary benchmarking result; without it, the headline conclusion is not yet established.","major_comments":[{"comment":"The calibration criterion used to produce the headline counts—that the true uncertainty σy lies within one standard deviation of the distribution of predicted σal values over the test set—is not a standard calibration measure and is pathological for the homoskedastic data studied here. A perfectly calibrated model would predict a constant σal = σy, giving std(σal) = 0 and requiring exact equality; a model that outputs overdispersed σal values gets a larger tolerance and can pass despite substantial bias. Because the 7/12 and 2/12 counts in Section 4 are computed from this criterion, they may reflect the width of the predicted σal distribution rather than actual calibration. Please redo the analysis with a standard diagnostic such as empirical coverage of the central 68% predictive interval or a PIT-based uniformity test.","section":"Section 3, desideratum (ii)"},{"comment":"The quantitative basis for the 7/12 and 2/12 counts is not reported. Figure 2 shows distributions of predicted σal values, but the text does not give the per-condition values of mean σal, std(σal), or the pass/fail determination, so the counts cannot be independently checked or reproduced from the paper. A table listing these quantities for each of the 12 conditions per method would make the central claim verifiable.","section":"Section 4, Figure 2 and Tables 1–2"},{"comment":"Each of the 12 experimental conditions per method appears to be run with a single training initialization. Since the comparison between DE and DER rests on the discrete counts 7/12 versus 2/12, the absence of repeated seeds means the headline difference has no statistical uncertainty and could be within run-to-run variability. Please report results across multiple seeds (e.g., mean and standard deviation of the calibration metrics) or at least confirm that the qualitative miscalibration pattern is stable across seeds.","section":"Section 3, experimental design"}],"minor_comments":[{"comment":"References [22] and [23] are the same paper (Seitzer et al., arXiv:2203.09168); they should be consolidated into a single citation.","section":"References"},{"comment":"Appendix D mentions several β schedules that were experimented with, but only the final choice β = 0.5 is presented in the main text; please state whether the other schedules are omitted for space or documented in the accompanying repository.","section":"Appendix D"},{"comment":"The phrase \"miscalibrated to std(σal)\" is awkward and unclear; suggest rewording to something like \"miscalibrated relative to the true uncertainty when judged by the std(σal) criterion.\"","section":"Abstract and Section 4"},{"comment":"The sentence \"the 0D experiments are calibrated for the medium- and high-noise models\" is ambiguous because it does not specify whether both output- and input-injection 0D experiments are included; please clarify which of the four 0D conditions pass.","section":"Section 4"},{"comment":"The DeepUQ-neurIPS-WS-2024 repository is mentioned, but no URL or DOI is provided; please include an availability statement so the code can be located.","section":"Appendix F"}],"recommendation":"major_revision","confidential_remarks":"This is a workshop-style empirical study with a sensible benchmark design and a clear statement of limitations. The central issue is that the headline calibration counts depend on a non-standard metric with pathological behavior for homoskedastic data, and the quantitative per-condition values are not reported. The requested reanalysis with standard calibration metrics and multiple seeds is feasible within the manuscript's scope, so I recommend major revision rather than rejection. The paper's fit to the journal is acceptable if the empirical analysis is strengthened."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a well-scoped empirical benchmark, not a breakthrough. What's new is that they evaluate both Deep Ensembles and Deep Evidential Regression on identical toy tasks, with Gaussian noise injected on either output or input, and use analytic error propagation to get a true sigma_y for the input-noise cases. That is a legitimate extension of Bramlage et al. and Egele et al., and the setup lets them check absolute calibration rather than only relative scaling. The paper does the basics right: external ground truth, no fitted-to-test hyperparameters, clear statements that conclusions are limited to toy homoskedastic Gaussian data, and loss/MSE tables so you can see both methods fit the means comparably. The finding that predicted sigma_al scales with injected noise across all 24 runs is solid and consistent with prior work.\n\nThe soft spots are real but not fatal. The calibration criterion—true sigma_y within one std(sigma_al) of the predicted distribution—is non-standard and has a pathological property for homoskedastic data. A perfectly calibrated model would output a constant sigma_al = sigma_y, so std(sigma_al) = 0 and the criterion demands exact equality; a model with noisy, overdispersed uncertainty estimates gets a wider tolerance and can pass despite bias. The 7/12 and 2/12 counts therefore partly reward variance in the uncertainty estimates. The stress-test note is right, and it lands on the paper's own definition in Section 3. The qualitative trend—worse calibration for 2D input-uncertainty and high noise—is plausible from Figure 2, but the exact proportions are criterion-dependent. Also, the 12 conditions per method appear to be single training runs each; no seeds are reported, so the counts carry no statistical uncertainty. I'd want a coverage-based check (e.g., central 68% interval coverage or PIT) before trusting the quantitative claim. Minor: the companion repo is named but not linked, and the 2D generator DeepBench is described as in prep and not public, so the 2D experiments are not independently reproducible right now. There's also a duplicated reference (Seitzer et al. appears as [22] and [23]).\n\nWho is this for? People doing UQ benchmarking on simple regression problems, and anyone relying on DE/DER in high-noise image regression. It is a legitimate workshop-level contribution. I would send it to a referee rather than desk reject—the comparison is useful and the limitations are honestly stated—but I would ask for a standard calibration diagnostic and seed variability before relying on the miscalibration rates.\n\nRecommendation: engage, but referee with revision expectations.","headline":"A transparent toy-data comparison of DE and DER aleatoric uncertainties, whose headline miscalibration counts rest on a non-standard tolerance criterion and no seed variability.","tokens_in":10117,"tokens_out":2049,"would_cite":false,"duration_ms":18738,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Deep learning uncertainty estimates—Deep Ensembles and Deep Evidential Regression—scale with injected noise but are miscalibrated on toy regression tasks, with only 7 of 12 DE and 2 of 12 DER experiments meeting the paper's calibration…","keywords":["aleatoric uncertainty","uncertainty calibration","deep ensembles","deep evidential regression","input uncertainty propagation","regression benchmarks","uncertainty quantification","neural network regression"],"falsifier":"Recompute the paper's 24 experiments but score calibration by the empirical coverage of the predicted $\\pm 1\\sigma$ (or $\\pm 2\\sigma$) intervals on held-out data, or by the probability integral transform of the true values under each model's predictive distribution; if most experiments then look calibrated, the paper's miscalibration conclusion is an artifact of the $\\mathrm{std}(\\sigma_{\\rm al})$ criterion rather than a property of DE and DER.","tokens_in":8988,"feed_emoji":"📉","tokens_out":10742,"duration_ms":84029,"temperature":0.7,"pith_summary":"The paper builds a benchmark for checking whether deep learning uncertainty estimates return the correct aleatoric (data-inherent) uncertainty, using deliberately simple regression tasks where the truth is known exactly. Gaussian noise of known amplitude is injected on either the input or the output of a scalar-input linear regression and an image regression; input noise is propagated through the known map to obtain the true output uncertainty, and that truth is compared with the uncertainties predicted by Deep Ensembles and Deep Evidential Regression. Across all models and noise levels, the predicted uncertainties scale with the injected noise, so the methods capture the right trend. But under the paper's calibration criterion—the true uncertainty must lie within one standard deviation of the mean of the predicted-uncertainty distribution—only 7 of 12 Deep Ensemble experiments and 2 of 12 Deep Evidential Regression experiments are well calibrated, with the worst performance in the high-noise, input-uncertainty image experiment. This matters because in scientific applications aleatoric uncertainty is often physically meaningful, so a predicted value that misses the true noise level by a large factor would mislead interpretation.","feed_headline":"Deep-learning uncertainty estimates fail 15 of 24 calibration checks","feed_subtitle":"Deep Ensembles pass 7 of 12; evidential regression just 2 of 12, worst on 2D high-noise input","key_machinery":"The load-bearing mechanism is the benchmark's ability to know the true aleatoric uncertainty exactly. For output-uncertainty experiments, noise is injected directly on $y$ with known $\\sigma_y$; for input-uncertainty experiments, noise is injected on $x$ and propagated through the known map $y = mx$ (0D) or $y = \\sum_{i=1}^{32\\times32} x_i$ (2D) via standard error propagation, giving $\\sigma_y = |m|\\sigma_x$ and $\\sigma_y = 32\\sigma_x$. The predicted aleatoric uncertainty is then compared with that known value through the distribution of $\\sigma_{\\rm al}$ over the test set, using the paper's criterion that the true $\\sigma_y$ must fall inside the mean $\\pm$ one standard deviation of that distribution. The two methods define $\\sigma_{\\rm al}$ differently: Deep Ensembles average the predicted variances of $K=10$ mean-variance networks, while Deep Evidential Regression uses the width of the Student-$t$ distribution implied by its normal-inverse-gamma evidential priors. Training losses are modified—$\\beta$-NLL for the ensembles, and NIG with a $t$-width regularization term for evidential regression—to keep variance estimates from collapsing.","core_discovery":"On its own terms, the paper establishes that two popular uncertainty quantification methods do not return quantitatively trustworthy aleatoric uncertainty estimates, even on simple toy data. The central result is a calibration count: requiring the true output uncertainty $\\sigma_y$ to lie within one standard deviation of the mean of the distribution of predicted $\\sigma_{\\rm al}$ values on the test set, only seven of twelve Deep Ensemble experiments and two of twelve Deep Evidential Regression experiments are well calibrated. Deep Ensembles pass the criterion for the 0D medium- and high-noise experiments but deviate most on the 2D input-uncertainty setup; Deep Evidential Regression overestimates uncertainty at low noise and underestimates it at medium and high noise, with only the 0D output low-noise and 2D output medium-noise runs calibrated. Both methods satisfy the weaker requirement that predicted uncertainty scales with injected noise. The authors explicitly caution that these conclusions apply only to their toy, homoskedastic Gaussian datasets, not to real-world data.","pith_inferences":["Beyond the paper: because the calibration criterion uses the spread of the predicted-uncertainty distribution as its tolerance, a method that produces highly variable $\\sigma_{\\rm al}$ estimates can pass even when its typical estimate is far from the truth; the 7/12 and 2/12 counts are therefore not a general statement about which method is better calibrated in the standard probabilistic sense.","Beyond the paper: the same exact-truth benchmark could be applied to heteroskedastic and non-Gaussian noise, where the Normal-likelihood assumptions inside both methods are violated and calibration failures would likely be larger.","Beyond the paper: a direct testable extension is to score the same 24 configurations with a proper coverage-based metric—for instance, the fraction of test points inside the predicted $\\pm 1\\sigma$ band—to see whether the qualitative ordering (2D input high-noise worst, DER worse than DE) survives."],"forward_implications":["If the central claim is right, DE and DER uncertainty values should not be read as physical noise levels on these tasks without a calibration check, even though the underlying regressions fit well.","Because the predicted uncertainties scale with injected noise, the methods can still be used to rank relative noise levels across datasets.","Deep Evidential Regression would need calibration before use in downstream physics analyses, since it fails the paper's criterion in nearly all tested configurations.","The 2D input-uncertainty, high-noise regime is where both methods are least reliable, so applications with noisy image inputs and large noise should expect the largest errors.","Post-facto calibration (for example, training an auxiliary isotonic model on uncertainty values) is the natural next step, as the paper itself suggests."],"supporting_citations":[{"why":"Defines Deep Ensembles, the mean-variance ensemble method whose predicted aleatoric uncertainty the paper benchmarks.","marker":"[14]"},{"why":"Introduces Deep Evidential Regression and the evidential Gaussian-inverse-gamma formulation that underlies the DER uncertainty estimate.","marker":"[1]"},{"why":"Supplies the NIG loss and the definition of $\\sigma_{\\rm al}$ as the $t$-distribution width used to train and interpret the DER models.","marker":"[16]"},{"why":"Introduces the $\\beta$-NLL loss modification and the $\\beta = 0.5$ recommendation used to stabilize Deep Ensemble variance training.","marker":"[22]"},{"why":"Gives the error-propagation formulas used to convert injected input noise into true output uncertainty.","marker":"[13]"},{"why":"Provides the prior DER regression calibration study that this paper extends to input-uncertainty experiments.","marker":"[3]"},{"why":"Earlier automated Deep Ensemble result that predicted uncertainty scales with output-injected noise, confirmed here.","marker":"[8]"}],"fun_headline_variants":["Deep uncertainty methods fail 15 of 24 calibration checks","Aleatoric uncertainty miscalibrated in most deep UQ experiments","Deep Ensembles and evidential regression often miss true uncertainty","Only 9 of 24 deep-learning uncertainty estimates are calibrated","Calibration fails in deep UQ: uncertainty estimates often off"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The headline calibration counts depend on the study's definition of 'well-calibrated'—the true uncertainty lying within one standard deviation of the mean of the predicted-uncertainty distribution—rather than on a standard statistical calibration measure such as prediction-interval coverage or the probability integral transform; under a stricter criterion the 7/12 and 2/12 proportions would change.","fun_headline_variants_meta":{"raw":{"variants":["Deep uncertainty methods fail 15 of 24 calibration checks","Aleatoric uncertainty miscalibrated in most deep UQ experiments","Deep Ensembles and evidential regression often miss true uncertainty","Only 9 of 24 deep-learning uncertainty estimates are calibrated","Calibration fails in deep UQ: uncertainty estimates often off"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001174,"raw_usage":{"total_tokens":4878,"prompt_tokens":997,"completion_tokens":3881,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":613,"completion_tokens_details":{"reasoning_tokens":3795}},"tokens_in":613,"tokens_out":3881,"duration_ms":27258,"temperature":1.0,"reasoning_tokens":3795,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T21:31:16.315137+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the paper's 24 experiments but score calibration by the empirical coverage of the predicted $\\pm 1\\sigma$ (or $\\pm 2\\sigma$) intervals on held-out data, or by the probability integral transform of the true values under each model's predictive distribution; if most experiments then look calibrated, the paper's miscalibration conclusion is an artifact of the $\\mathrm{std}(\\sigma_{\\rm al})$ criterion rather than a property of DE and DER.","supporting_citations":[{"cited_title":"The Unreasonable Effectiveness of Deep Evidential Regression","cited_arxiv_id":"2205.10060","evidence_quote":"Supplies the NIG loss and the definition of $\\sigma_{\\rm al}$ as the $t$-distribution width used to train and interpret the DER models."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the error-propagation formulas used to convert injected input noise into true output uncertainty."},{"cited_title":"Plausible uncertainties for human pose regression","cited_arxiv_id":null,"evidence_quote":"Provides the prior DER regression calibration study that this paper extends to input-uncertainty experiments."},{"cited_title":"AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification","cited_arxiv_id":"2110.13511","evidence_quote":"Earlier automated Deep Ensemble result that predicted uncertainty scales with output-injected noise, confirmed here."}],"review_version":1}