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Robust Evidential Learning Through Latent Consistency

Charmaine Barker, Daniel Bethell, Simos Gerasimou

arXiv:2610.01384v1cs.LG

TL;DR

OOD and adversarial inputs can elicit confident but unreliable predictions, while evidential models can assign strong evidence to poorly supported inputs. CLEAR calibrates group-conditioned latent geometry and uses conflict among latent perturbation views to adjust evidence post-hoc. Across classification, regression, and object detection, it improves uncertainty quality while preserving predictive performance, with modest additional inference overhead.

  • Problem

    OOD and adversarial inputs can produce confident but unreliable predictions, and evidential models can assign strong evidence to poorly supported inputs.

    Source: §1 · p. 1

  • Method

    CLEAR calibrates group-conditioned latent geometry from held-out data and uses conflict among latent perturbation views to selectively adjust evidence without retraining or changing the base prediction.

    Source: §1 · p. 2, §4 · p. 3, §4.1 · p. 4

  • Results

    Across classification, regression, and object detection, CLEAR consistently improves uncertainty quality while preserving predictive performance and adding modest inference overhead.

    Source: §6 · pp. 9–10

  • Takeaways & Limitations

    Latent conflict provides a practical, broadly applicable signal for identifying unsupported evidential confidence across varied distributional and adversarial challenges.

    Source: §6 · pp. 9–10

    CLEAR requires an evidential model; using a conventional pretrained model may require retraining or an Evidential Meta Model to provide evidential outputs.

    Source: D ADDITIONAL DISCUSSION · p. 28

Abstract

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Reliable uncertainty quantification is essential for deploying deep learning models in high-stakes settings, where out-of-distribution and adversarial inputs can induce confident but unreliable predictions. Evidential Deep Learning provides efficient uncertainty estimates in a single forward pass, but can still assign high evidential strength to inputs that are poorly supported by the learned representation, such as adversarial inputs. We introduce CLEAR, a lightweight, task-agnostic post-hoc method that improves evidential robustness without retraining or altering the base prediction. Using held-out calibration data, CLEAR characterises the group-conditioned geometry of the model's latent space. At inference, it efficiently generates perturbation views directly in the latent space and measures their conflict relative to the calibrated geometry of the predicted group. High latent conflict indicates unsupported evidence, which CLEAR uses to selectively reduce evidential strength while retaining evidence for latent-consistent inputs. On ImageNet$\rightarrow$CUB, CLEAR improves OOD and adversarial AUROC by $+8.29$ and $+5.01$ while running 17.4$\times$ faster than competing post-hoc methods while preserving predictive performance across classification, regression, and object detection benchmarks.

1 INTRODUCTION

In safety-critical settings, OOD and adversarial inputs can elicit confident but unreliable predictions. Evidential methods are efficient, but post-hoc robustness approaches can add computation or suppress evidence for valid in-distribution inputs.

1 INTRODUCTION

  • OOD and adversarial inputs can leave models highly confident beyond their training conditions, making unreliable predictions a safety-critical concern.Identifying unreliable predictions is described as fundamental to safe deployment.Source: §1 · p. 1
  • Evidential methods estimate uncertainty in one deterministic pass, yet can assign strong evidence to poorly supported OOD and adversarial inputs.EDL models class probabilities with a Dirichlet distribution; DER uses a Normal-Inverse-Gamma distribution for continuous predictions.Source: §1 · p. 1
  • Existing post-hoc methods can improve evidential robustness without retraining, but may require repeated evaluations or transformed inputs and reduce valid ID evidence retention.The cited approaches are described as potentially suppressing evidence even when ID predictions are correct.Source: §1 · pp. 1–2
  • CLEAR uses held-out ID data to calibrate output-group latent geometry, then tests latent perturbation conflict and selectively reduces unsupported evidence without retraining or changing the base prediction.Evidence is retained for inputs whose latent behaviour is consistent with calibrated ID structure.Source: §1 · p. 2

2 RELATED WORK

Prior uncertainty-quantification approaches differ in what uncertainty they capture and in their computational and calibration requirements. Evidential post-hoc methods address robustness, but can sacrifice single-pass efficiency or task generality.

2 RELATED WORK

  • Uncertainty methods include Bayesian inference, dropout, ensembles, distance-aware models, test-time augmentation, and conformal prediction, with differing computational and calibration requirements.The passage distinguishes approaches to aleatoric and epistemic uncertainty and notes that conformal sets or intervals can indicate uncertainty.Source: §2 · p. 2
  • EDL uses a Dirichlet distribution for single-pass epistemic and aleatoric uncertainty, but deterministic inference lacks the multiple perspectives of dropout or ensembles.The passage notes that overconfident errors are particularly evident under adversarial perturbations.Source: §2 · p. 2
  • Many post-hoc EDL methods use multiple forward passes or stochastic sampling, while task-specific approaches such as classification methods limit generality.These limitations motivate seeking robustness while retaining efficiency and task flexibility.Source: §2 · p. 2

3 PRELIMINARIES

The preliminaries set a supervised-learning framework with a latent representation and introduce evidential formulations for classification and regression. CLEAR then uses latent consistency to adjust evidential strength while leaving the base prediction unchanged.

3 PRELIMINARIES

  • The setting assumes input-output samples drawn i.i.d. from an underlying distribution and seeks a latent representation that captures their relationship and generalizes to unseen samples.Inputs and task-dependent outputs are denoted by X and Y.Source: §3 · p. 2
  • EDL replaces softmax with a Dirichlet distribution over class probabilities, using non-negative evidence to define its parameters.The Dirichlet predictive variance and a KL penalty to the uniform prior are part of the standard objective; evidence strength indicates concentration around the predicted class.Source: §3 · pp. 2–3
  • DER models continuous targets with a Normal-Inverse-Gamma distribution and trains with its negative log-likelihood plus an evidence regulariser.The formulation’s parameters determine evidential strength and uncertainty.Source: §3 · p. 3
  • Both EDL and DER encode confidence through evidential strength, which CLEAR recalibrates using latent consistency without changing the base prediction.The passage identifies Dirichlet concentration for classification and NIG strength for regression.Source: §3 · p. 3

4 CONFLICT-AWARE LATENT EVIDENCE ADJUSTMENT FOR ADVERSARIAL ROBUSTNESS

CLEAR calibrates output-group latent geometry from held-out data, then measures conflict among perturbed latent views relative to that geometry. It uses conflict to reduce unsupported evidence while preserving the base prediction.

4 CONFLICT-AWARE LATENT EVIDENCE ADJUSTMENT FOR ADVERSARIAL ROBUSTNESS

  • CLEAR characterises pretrained-model ID latent structure, generates perturbation views, and down-weights evidence when their conflict with the predicted group’s calibrated geometry is high.Compatible ID inputs retain evidence; the workflow does not retrain or modify the predictor.Source: §4 · p. 3, Figure 1 · p. 4

4.1 LATENT CALIBRATION

  • Held-out examples are assigned to output groups by class labels or, for regression, calibration-set quantile bins with approximately equal group sizes.CLEAR estimates each group’s latent mean and covariance; its characteristic scale adapts perturbation magnitude to that geometry.Source: §4.1 · p. 4

4.2 LATENT PERTURBATION VIEWS

  • At inference, CLEAR samples latent views around the penultimate representation using a perturbation magnitude scaled to the predicted group.The views are compared as unordered pairs rather than evaluated independently.Source: §4.2 · p. 5
  • The views are centred and whitened by the predicted group’s calibrated statistics, and their pairwise cross-dimensional interactions yield a raw conflict score.Large interactions indicate that local latent behaviour is inconsistent with the predicted group’s calibrated structure.Source: §4.2 · p. 5
  • A calibration-derived reference conflict bounds the raw score, leaving low-conflict inputs unchanged while increasing the score toward one as conflict grows.The resulting scale is near one for latent-consistent inputs and reduces evidence for high-conflict inputs.Source: §4.2 · p. 5
  • The same conflict mechanism serves classification and regression, but the final evidence adjustment differs and leaves each base prediction unchanged.Classification rescales evidence; regression preserves its predictive mean and scale while down-weighting evidence-related parameters.Source: §4.2 · p. 6

5 RESULTS

Across classification, regression, and object detection, CLEAR improves uncertainty performance under distribution shifts while preserving predictive performance. Further experiments report robustness under corruption and stronger attacks, alongside broadly stable behavior across hyperparameters and latent representations.

5.1 CORE RESULTS

  • 84.63% AUROC and 92.61% AAUROC on ImageNet→CUB accompany 80.54% ID coverage, while CLEAR is strongest or competitive across ID retention, OOD detection, and adversarial detection.It also reaches 98.54% AUROC and 97.66% AAUROC on MNIST→FashionMNIST, and 77.45% AAUROC on CIFAR10→SVHN.Source: Table 1 · p. 7, §5.1 · pp. 7–8

5.2 REGRESSION RESULTS

  • Across regression benchmarks, CLEAR improves OOD and adversarial separation while preserving comparable predictive error; on California Housing, OOD coverage falls from 91.60% to 26.34%.On Airfoil, where OOD samples are defined by extreme input-frequency values rather than target extremes, CLEAR retains 72.87% ID coverage while reducing OOD and adversarial coverage to 20.46% and 0.62%.Source: Table 2 · p. 8, §5.2 · pp. 8–9

5.3 OBJECT DETECTION RESULTS

  • On clean CelebA detections, CLEAR improves every evaluated uncertainty metric over EMM and raises uncertainty–localisation correlation from r = 0.003 to r = 0.168.Across five covariate shifts, the overall Pearson correlation rises from 0.010 to 0.049; Figure 3 qualitatively compares EMM and CLEAR uncertainty under Gaussian noise.Source: §5.3 · p. 9, Figure 3 · p. 9

5.4 FURTHER EXPERIMENTS AND ABLATION

  • Additional experiments report strong uncertainty performance under corruption and increasing attack strength, broad hyperparameter and thresholding stability, and consistent behavior across latent representations.The analyses include corrupted benchmarks, attack and threshold studies, validation of calibrated geometry, latent-depth sensitivity, and visualizations of latent perturbation views.Source: §5.4 · p. 9

6 CONCLUSIONS

CLEAR improves evidential uncertainty across classification, regression, and object detection while preserving predictive performance. It jointly improves complementary uncertainty objectives with modest inference overhead, and the authors identify denser structured prediction as future work.

6 CONCLUSIONS

  • Across classification, regression, and object detection, CLEAR improves uncertainty quality while preserving predictive performance.The evaluation spans diverse OOD settings, covariate shifts, adversarial attacks, and uncertainty thresholds.Source: §6 · p. 9
  • CLEAR jointly improves complementary uncertainty objectives, avoids pronounced trade-offs seen in several comparative methods, and adds only modest inference overhead.Source: §6 · p. 10
  • The authors identify evaluation on denser structured prediction tasks, such as semantic segmentation, as future work.Source: §6 · p. 10

A IMPLEMENTATION DETAILS

CLEAR calibrates group-conditioned latent statistics once using held-out data, then reuses them to adjust evidential outputs at inference. The appendix introduces theoretical analysis to complement the method’s presentation in Section 4.

A IMPLEMENTATION DETAILS

  • Calibration uses held-out examples to estimate group statistics and a global reference conflict, which are reused for subsequent inputs.Class labels or target-quantile bins define groups; each calibration example receives independent perturbation draws and its raw conflict scores are averaged before the calibration median is computed.Source: A IMPLEMENTATION DETAILS · p. 14
  • At inference, CLEAR obtains the latent representation and evidential output in one forward pass, generates latent views without further backbone or head evaluations, and preserves the predicted class or regression mean.Whitening uses triangular solves with the stored Cholesky factor, and vector reductions avoid constructing cross-dimensional interaction matrices.Source: A IMPLEMENTATION DETAILS · p. 14

B THEORETICAL ANALYSIS

B.1 PROPOSITION 1

The proposition establishes that CLEAR preserves the base prediction while reducing evidential strength as latent conflict rises. The accompanying evaluations report results on corrupted inputs and show that confidence separation varies with latent-space separation.

B.1 PROPOSITION 1

  • CLEAR preserves the predicted class while reducing total evidential strength, so scalar uncertainty increases or remains unchanged; increasing conflict contracts predictive probabilities toward uniform without changing their ordering.Source: §B.1 · pp. 16–17
  • In regression, CLEAR leaves the predictive mean unchanged while monotonically increasing aleatoric and epistemic uncertainty as latent conflict increases.Source: §B.1 · p. 17

C.1 CORRUPTED BENCHMARKS

  • On MNIST→MNIST-C, CLEAR achieves OOD and adversarial coverage of 19.26% and 3.34%, and AUROC and ID-Adv. AUROC of 89.85% and 96.51%, respectively.On CIFAR-10-C, it achieves ID-Adv. AUROC of 69.90% at severity 1 and 66.32% at severity 5, while I-EDL has the highest ID-OOD AUROC at severity 5.Source: §C.1 · p. 17, Table 3 · p. 18

C.2 EXTRA METRICS ANALYSIS

  • CLEAR produces larger confidence reductions for OOD and adversarial inputs across MNIST and CIFAR settings, with weaker distinctions on Oxford Flowers and ImageNet.NLL and ECE assess ID predictive-distribution calibration, which CLEAR does not explicitly optimize.Source: §C.2 · p. 18

C.3 ABLATION ANALYSIS

CLEAR’s sensitivity analysis varies latent-view count, perturbation magnitude, evidence down-weighting, reference quantile, and regression-bin granularity. The reported choices balance stable performance, separation, and calibration reliability.

C.3 ABLATION ANALYSIS

  • Performance changes only marginally across evaluated perturbation magnitudes τ, consistent with interpreting conflict relative to a reference calibrated using the same perturbation mechanism.The authors use τ = 0.05, within the broad region of stable performance.Source: §C.3 · pp. 18–19, Figure 4 · p. 19
  • Increasing latent views V leaves metrics almost unchanged, while increasing pairwise comparisons quadratically; the authors select V = 3 as a low-cost setting with multiple comparisons.Source: §C.3 · p. 19, Figure 5 · p. 20
  • Increasing δ strengthens down-weighting: larger values improve adversarial rejection on challenging datasets, but eventually reduce ID coverage and ID-OOD AUROC; δ = 10 is selected as an intermediate setting.Source: §C.3 · pp. 19–20, Figure 6 · p. 20
  • Intermediate reference quantiles perform best in the reported analysis: low quantiles can reduce discrimination, while high quantiles make CLEAR more permissive; the median lies in a stable region.Source: §C.3 · pp. 20–21, Figure 7 · p. 20
  • For regression, larger bin counts B tend to weaken separation on several datasets as per-bin estimates become less reliable; B = 10 balances output specificity with populated calibration groups.ID coverage remains broadly stable, while very small B may obscure local latent-geometry changes.Source: §C.3 · p. 21, Figure 8 · p. 21

C.4 THRESHOLD ANALYSIS

CLEAR remains effective across threshold statistics and varied adversarial attacks, with differential entropy providing the strongest balance of ID retention and unreliable-input rejection. Its attack performance remains strong as perturbations intensify.

C.4 THRESHOLD ANALYSIS

  • Differential entropy retains 94.83% of ID samples while reducing OOD and adversarial coverage to 1.84% and 7.21%, with ID-OOD AUROC of 98.54% and ID-Adv. AUROC of 97.66%.It provides the strongest overall balance among the four evaluated uncertainty measures.Source: §C.4 · p. 21, Table 5 · p. 22
  • CLEAR remains effective across all four threshold measures, while differential entropy is the most favourable default for retaining ID predictions and rejecting OOD and adversarial inputs.Comparative methods vary more across threshold types, and CLEAR’s performance remains comparatively stable.Source: §C.4 · p. 21

C.5 ADVERSARIAL ATTACK ANALYSIS

  • At L2-PGD strength 1.0, CLEAR achieves 7.21% adversarial coverage and 97.66% AAUROC; at FGSM strength 1.0, it has near-zero coverage and 97.88% AAUROC.CLEAR has the lowest coverage in all but one evaluated attack setting and the highest AAUROC in all but the weakest L2-PGD setting, where it matches PostNet closely.Source: §C.5 · p. 22
  • At strength 1.0, CLEAR reaches 96.14% AAUROC under AutoAttack and 98.63% AAUROC under Salt and Pepper, while retaining 23.79% and 1.28% adversarial coverage, respectively.Across the evaluated strengths, CLEAR has the highest AutoAttack AAUROC; under Salt and Pepper it has the lowest coverage and highest AAUROC.Source: §C.5 · p. 22

C.6 FULL OBJECT DETECTION RESULTS

On CelebA detection, CLEAR adjusts evidential uncertainty without changing the detector or its bounding-box predictions. Its uncertainty better reflects localisation quality on clean detections and under the evaluated corruptions.

C.6 FULL OBJECT DETECTION RESULTS

  • On clean CelebA detections, CLEAR raises AUROC from 0.503 to 0.585 and AUPRC from 0.125 to 0.211, while reducing FPR95 from 0.907 to 0.824 and ECE from 0.844 to 0.750.The Pearson correlation between uncertainty and localisation error rises from r = 0.003 with EMM to r = 0.168 with CLEAR.Source: Table 7 · p. 23, §C.6 · p. 23
  • The CelebA setup freezes YOLO11n and EMM before applying CLEAR to held-out detections, so the comparison adjusts uncertainty while leaving the detector and box predictions unchanged.Localisation error is defined as 1−IoU; evaluation includes AUROC, AUPRC, FPR95, calibration error, and uncertainty–error correlation.Source: §C.6 · p. 23
  • Across brightness, blur, noise, compression, and resize/crop shifts, CLEAR raises overall Pearson correlation between uncertainty and localisation error from 0.010 to 0.049.The increase occurs for every evaluated corruption, with the largest gains for compression and blur.Source: Table 8 · p. 23, §C.6 · p. 24
  • Across corruption types and severities, CLEAR generally maintains a stronger uncertainty–localisation relationship than EMM, although the absolute correlations remain modest.The figure presents Pearson correlation between predictive uncertainty and localisation error; higher values indicate that detections with larger localisation error receive greater uncertainty.Source: Figure 9 · p. 24, §C.6 · p. 24
  • The object-detection results extend CLEAR’s latent-conflict approach to structured prediction, where uncertainty can reflect the reliability of individual detections’ localisation.The evaluation uses YOLO11n on CelebA with an evidential meta-model trained on intermediate features.Source: §C.6 · pp. 22, 24

C.7 HELD-OUT ANALYSIS OF THE LATENT WHITENING GEOMETRY

Held-out analyses indicate that CLEAR’s fitted latent geometry captures useful second-order structure, though not an exact Gaussian distribution. Performance remains strong across representation depths, and visualized latent views show greater conflict for the illustrated OOD inputs.

C.7 HELD-OUT ANALYSIS OF THE LATENT WHITENING GEOMETRY

  • For the illustrated MNIST geometry, held-out class clusters broadly align with training-estimated covariance contours, while whitened coordinates are centered and approximately bell-shaped with heavier tails than a standard normal.The fitted statistics are used as local second-order geometry, not as an exact generative model.Source: §C.7 · p. 24, Figure 10 · p. 25
  • On held-out ID samples, whitening yields a normalized mean norm of 0.072, mean absolute off-diagonal covariance of 0.071, and mean diagonal covariance of 1.286, indicating approximate centering and decorrelation with moderate variance deviation.The table reports per-class held-out whitening diagnostics using geometry estimated from training data.Source: Table 9 · p. 25, §C.7 · p. 25
  • Whitened latents do not follow an exact multivariate standard normal: the nominal 95% Gaussian region contains 63.4% of held-out samples and the radial Kolmogorov-Smirnov statistic is 0.358.The fitted Gaussian geometry captures central structure more faithfully than the tails; the task objective does not constrain class-conditional latents to be Gaussian.Source: §C.7 · p. 25
  • Variance-matched Uniform and Rademacher perturbations produce conflict scores with Spearman rank correlations of 0.99998 against the Gaussian baseline.The results indicate that the conflict mechanism relies on stable local second-order geometry rather than an exact Gaussian perturbation law.Source: §C.7 · p. 25

C.8 SENSITIVITY TO LATENT REPRESENTATION DEPTH

  • On MNIST→FashionMNIST, layer 1 gives the highest ID coverage at 98.98% and lowest OOD coverage at 0.41%, while layer 2 gives the highest ID-OOD AUROC of 99.91% and AAUROC of 99.93%.The penultimate representation remains effective, with AUROC of 98.42% and AAUROC of 98.29%; the same trained model is used across representations.Source: Table 10 · p. 26, §C.8 · p. 26

C.9 QUALITATIVE ANALYSIS OF LATENT PERTURBATION VIEWS

  • Feature-inverted latent views preserve dominant image semantics, yet shown DeepWeeds OOD inputs have raw conflict scores of 976.11–2459.20 versus 54.51–323.75 for Oxford Flowers ID inputs.The perturbation magnitude is enlarged for visualization, so these conflict values are qualitative rather than operating scores.Source: Figure 11 · p. 26, §C.9 · p. 27

C.8 SENSITIVITY TO LATENT REPRESENTATION DEPTH

  • CLEAR’s default penultimate representation is the feature representation consumed by the evidential head; shallower layers can perform better on this dataset pair, but the default gives a consistent definition across models and tasks.The tested representations are residual-layer outputs 1–3 and the penultimate representation, with dimensions 64, 128, 256, and 512.Source: §C.8 · p. 26

D ADDITIONAL DISCUSSION

The discussion emphasizes evaluating uncertainty methods across ID retention, OOD detection, and adversarial detection together. It also describes benchmark-specific trade-offs, regression coverage boundaries, and the setup for reproducible experiments.

D ADDITIONAL DISCUSSION

  • On MNIST→KMNIST and CIFAR10→CIFAR100, CLEAR’s losses on individual metrics are comparatively small while some alternatives sacrifice substantially on complementary objectives, supporting joint evaluation of ID retention, OOD detection, and adversarial detection.On CIFAR10→CIFAR100, CLEAR’s AAUROC is 71.93%, compared with 12.22% for C-EDL, which has the highest OOD AUROC.Source: D ADDITIONAL DISCUSSION · p. 27
  • On Oxford Flowers→DeepWeeds, R-EDL has the highest OOD AUROC but weaker adversarial separation, while PostNet’s near-zero adversarial coverage coincides with ID accuracy of 5.92% and ID coverage of 14.30%.The low-shot setting likely makes class-conditioned density estimation difficult, so coverage should be interpreted together with predictive performance.Source: D ADDITIONAL DISCUSSION · p. 27
  • On ImageNet→CUB, CLEAR avoids the near-total acceptance or rejection seen with some alternatives, retaining substantial ID coverage while achieving the highest OOD and adversarial AUROC.The comparison retains common method-specific settings across datasets rather than tuning each method separately for every benchmark.Source: D ADDITIONAL DISCUSSION · pp. 27–28
  • Applying CLEAR to a conventional pretrained model requires evidential outputs; directly obtaining them may entail computationally prohibitive evidential retraining for large models or datasets.An Evidential Meta Model over frozen features is a lightweight alternative that leaves the original predictor unchanged.Source: D ADDITIONAL DISCUSSION · p. 28
  • On some regression benchmarks, weakly geometry-supported atypical ID samples can receive increased uncertainty, and the ID–OOD separation threshold does not enforce a fixed ID retention rate.The underlying regression prediction remains unchanged, so reduced coverage reflects selective uncertainty rather than degraded predictive accuracy.Source: D ADDITIONAL DISCUSSION · p. 28

E EXPERIMENTAL SETUP

  • The experimental setup section introduces datasets, model architectures, comparative methods, training procedures, and task-specific configurations to clarify the evaluation protocol and support reproducibility.Source: E EXPERIMENTAL SETUP · p. 28

E.1 DATASETS

This section outlines the evaluation setup for CLEAR across classification, regression, and detection, including datasets, models, calibration, training, attacks, and comparison methods. It also describes CLEAR’s inference-time and latent-space computational costs relative to the frozen evidential model and more computationally expensive post-hoc methods.

E.1 DATASETS

  • CLEAR is evaluated on image, tabular, and detection benchmarks with near- and far-OOD, corruption, target-shift, and covariate-shift settings.Examples include ImageNet paired with CUB, extreme house prices in California Housing, and extreme input frequency in Airfoil Self-Noise; validation data calibrate ID–OOD thresholds before test evaluation.Source: §E.1 · pp. 30–31

E.2 MODELS

  • The evaluation uses task-specific frozen backbones, a tabular MLP, and YOLO11n, with CLEAR applied after model training.Models include ResNet-18, EfficientNet-B0, DenseNet-121, and ViT-B/16; the ImageNet ViT backbone is frozen while its task-specific head is trained.Source: §E.2 · pp. 31–32

E.3 ID-OOD THRESHOLDS

  • ID–OOD thresholds are selected on validation data by maximizing TPR − FPR on ROC curves, then fixed for test-time rejection.Scoring options include differential entropy, predictive entropy, mutual information, and maximum probability; differential entropy applies only to Dirichlet-based models.Source: §E.3 · p. 32

E.4 COMPARATIVE APPROACHES

E.5 ADVERSARIAL ATTACKS

E.6 TRAINING DETAILS

  • Training uses shared optimization settings across comparative approaches for each dataset, with method-specific parameters varying only when required.The common setup uses batch size 64, Adam, weight decay 10^-4, and dropout 0.25; ImageNet trains only the task-specific head while its pretrained ViT-B/16 backbone remains frozen.Source: §E.6 · p. 35

E.7 RUNTIME AND COMPLEXITY

  • One-time calibration costs O(|Dcal|d2 + Kd3 + |Dcal|T(Vd2 + V2d)) for classification, replacing K with B for regression.This combines latent covariance estimation, per-group Cholesky and scale computation, and reference-conflict estimation; the cost is incurred once after training.Source: §E.7 · pp. 35–36
  • CLEAR generates V perturbation views in latent space and evaluates their unordered pairs in O(V^2d) time after O(Vd^2) whitening.The pairwise conflict calculation sums over the d latent dimensions rather than explicitly evaluating all d(d−1) interactions.Source: §E.7 · p. 36
  • With the default V = 3, CLEAR adds O(d^2) computation per prediction.Source: §E.7 · p. 36
  • 18.69 s on Oxford Flowers for CLEAR versus 18.48 s for EDL, 74.46 s for C-EDL, and 660.19 s for S-EDL, illustrating near-single-pass timing.On MNIST→FashionMNIST, inference takes 2.36 s for CLEAR, 1.96 s for EDL, 13.15 s for C-EDL, and 57.56 s for S-EDL; on ImageNet, it takes 423.66 s for CLEAR, 397.02 s for EDL, and 7356.02 s for S-EDL.Source: §E.7 · p. 36

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