GEM-FI: Gated Evidential Mixtures with Fisher Modulation

Fatemeh Daneshfar; Marco Mustafa Mohammed; Pietro Li\`o

arxiv: 2605.03750 · v1 · submitted 2026-05-05 · 💻 cs.LG

GEM-FI: Gated Evidential Mixtures with Fisher Modulation

Marco Mustafa Mohammed , Fatemeh Daneshfar , Pietro Li\`o This is my paper

Pith reviewed 2026-05-07 16:49 UTC · model grok-4.3

classification 💻 cs.LG

keywords evidential deep learninguncertainty estimationout-of-distribution detectionmixture modelscalibrationimage classificationFisher regularizationgated networks

0 comments

The pith

Gated evidential mixtures with Fisher modulation let models suppress evidence on low-support inputs while stabilizing multi-head uncertainty in a single forward pass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces GEM-FI as an extension of evidential deep learning that learns an internal energy signal to gate Dirichlet evidence outputs according to input support. It further adds a lightweight mixture of evidential heads with learned routing and applies a Fisher-informed regularizer to reduce head collapse. The central goal is to fix overconfidence, poor calibration, and limited representation of multi-modal epistemic uncertainty that standard EDL exhibits on image tasks. If the approach holds, single-pass inference could deliver both higher accuracy and stronger separation of in-distribution and out-of-distribution examples without ensembles.

Core claim

GEM-FI learns a feature-level energy signal that is mapped to a bounded gate to smoothly suppress evidence when support is low, combines this with a mixture of evidential heads that preserve single-pass inference, and stabilizes the mixture allocations through a Fisher-informed regularizer that reduces head collapse and yields smoother boundary uncertainty.

What carries the argument

The gated evidential mixture, which routes evidence across heads via a learned energy signal and Fisher regularizer to control suppression and allocation.

If this is right

Accuracy on CIFAR-10 rises from 91.11 to 93.75 while Brier score drops from 14.27 to 6.81.
Misclassification detection AUPR improves from 99.08 to 99.94 on the same dataset.
Epistemic OOD AUPR/AUROC reaches 92.59/95.09 on CIFAR-10-to-SVHN and 90.20/89.06 on CIFAR-10-to-CIFAR-100.
All gains occur with single-pass inference and no ensemble overhead.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The energy signal may act as a general density estimator in feature space that could transfer to non-image modalities.
Fisher modulation could be combined with other mixture regularizers to further control head diversity on long-tailed data.
If the gate remains stable under distribution shift, the method offers a lightweight path to safer deployment in settings that require uncertainty without extra compute.

Load-bearing premise

The learned energy signal and Fisher regularizer will keep suppressing evidence and preventing head collapse on data distributions outside the reported image-classification benchmarks without introducing new calibration artifacts.

What would settle it

On a fresh benchmark such as ImageNet subsets or medical imaging data, GEM-FI produces higher Brier scores or lower epistemic OOD AUPR than a plain evidential baseline.

Figures

Figures reproduced from arXiv: 2605.03750 by Fatemeh Daneshfar, Marco Mustafa Mohammed, Pietro Li\`o.

**Figure 1.** Figure 1: Two-moons setup with an additional OOD cluster. Panels show predictive entropy (brighter = higher uncertainty). 2024)) or apply post hoc score adjustments (e.g., temperature scaling (TS), energy scoring) (Guo et al., 2017; Romero et al., 2024). Consequently, there is a need for an in-model, learnable support signal that (i) directly gates evidential outputs, (ii) preserves single-pass inference, and (iii… view at source ↗

**Figure 3.** Figure 3: Architecture of the proposed method. (a) DAEDL: a spectrally normalized backbone with a single evidential head that outputs Dirichlet evidence, augmented with an offline feature-space density model (GDA) whose normalized likelihood rescales evidential outputs before computing uncertainty. (b) GEM-FI: extends the same backbone with an energy head Eψ that maps features z to a scalar energy E(x) and a bounded… view at source ↗

**Figure 4.** Figure 4: PR and ROC curves for OOD detection on CIFAR-10 (ID) vs. SVHN (OOD). provided in Appendix F.2 and F.3. As an additional stress test, we evaluate GEM under common distribution-shift and corruption benchmarks (Section F.4). 4.2. Image Classification and Confidence Calibration To address Q2, we report ID test accuracy, misclassificationdetection AUPR, and the Brier score on CIFAR-10. Table 2 summarizes th… view at source ↗

**Figure 5.** Figure 5: Comparison of three GEM variants on CIFAR-10 test images. The input is shown at the top of each column, and the induced Dirichlet distribution is visualized on the probability simplex below. Annotations S (total evidence) and Vac (vacuity) summarize the resulting uncertainty geometry. (a) Before Norm. (b) After Norm. ID Far-OOD Near-OOD (c) ID vs OOD view at source ↗

**Figure 6.** Figure 6: t-SNE visualization of feature embeddings for GEM-FI. Limitations and future work. GEM uses learned energy as an internal control signal for evidence gating, not as a calibrated estimator of representation-level support. Accordingly, alignment between energy and any support proxy (e.g., kNN distance) is empirical and may vary across regimes, architectures, and datasets; we provide no monotonicity guarant… view at source ↗

**Figure 7.** Figure 7: shows Precision–Recall curves for OOD detection (SVHN vs. CIFAR-10) using different uncertainty scores. GEM-FI achieves the highest AUPR across all metrics, indicating a better ranking that preserves precision as recall increases. In particular, mutual information (MI) provides the cleanest separation (93.06%), suggesting that mixturecomponent disagreement is highly informative for far-OOD detection. By c… view at source ↗

**Figure 8.** Figure 8: ROC curves for OOD detection with different uncertainty scores view at source ↗

**Figure 9.** Figure 9: reports ID reliability diagrams on CIFAR-10 (test set) for GEM-CORE, GEM-MIX, and GEM-FI using the final post-gating probabilities (before any post-hoc calibration). This qualitative view complements view at source ↗

**Figure 10.** Figure 10: Confidence on correct vs. incorrect predictions (CIFAR10 test, ID). Mean max-confidence for correct and incorrect predictions for GEM-CORE, GEM-MIX, and GEM-FI. Discussion. Across models, reliability curves remain close to the diagonal on ID data, consistent with the low ECE values in view at source ↗

**Figure 11.** Figure 11: Uncertainty distributions measured by (top) maximum probability, (middle) entropy, and (bottom) MI for GEM-FI. Blue = ID samples; Red = OOD samples. MI achieves the best separation, especially for far-OOD pairs. High MI indicates between-head disagreement, which is particularly useful for OOD detection. F.10. Score Comparison Boxplots view at source ↗

**Figure 12.** Figure 12: Entropy (aleatoric) vs. MI (epistemic) scatter plots for GEM-FI. Top row: MNIST shifts; bottom row: CIFAR-10 shifts. Panels (d) and (h) show Correct vs Misclass for MNIST and CIFAR-10, respectively. ID samples (blue) cluster in the low-entropy, low-MI region, while OOD and corrupted samples (red) exhibit higher values, enabling effective threshold-based OOD detection view at source ↗

**Figure 13.** Figure 13: Box plots comparing uncertainty scores for ID (CIFAR10), Near-OOD (CIFAR-100), and Far-OOD (SVHN). MI and α0 show the clearest separation between ID and OOD samples. G. Sensitivity Analysis G.1. Qualitative Comparison with Baselines view at source ↗

**Figure 14.** Figure 14: Qualitative comparison of feature spaces across methods. Rows: GEM-CORE (top), GEM-MIX (middle), GEM-FI (bottom). Columns: Before Normalization, After Normalization, ID (Blue) vs OOD (Red/Orange). resulting in vertical gradients dominated by Cinter. As λ increases, the influence of intra-class conflict becomes more pronounced, leading to smoother diagonal transitions across the conflict landscape. At λ = … view at source ↗

**Figure 15.** Figure 15: Effect of the mixing coefficient λ on the conflict score C in GEM-FI. Each panel shows C as a function of inter-class conflict Cinter and intra-class conflict Cintra for a fixed value of λ (from left to right: λ ∈ 0, 0.25, 0.5, 0.75, 1.0). Larger values of C indicate stronger disagreement between evidential components view at source ↗

**Figure 16.** Figure 16: Uncertainty vs. support (entropy / 1 − max p). 0.2 0.4 0.6 0.00 0.25 0.50 0.75 1.00 1.25 NLL ID (CIFAR-10) 0.2 0.4 0.6 0.8 1 2 3 4 5 6 near-OOD (CIFAR-100) 0.4 0.6 0.8 1.0 0.5 1.0 1.5 2.0 2.5 3.0 far-OOD (SVHN) Baseline GEM-CORE GEM-FI 0.2 0.4 0.6 kNN Distance (Support Proxy) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Brier Score 0.2 0.4 0.6 0.8 kNN Distance (Support Proxy) 0.0 0.1 0.2 0.3 0.4 0.5 0.4 0.6 0.8 1.0 kNN Di… view at source ↗

**Figure 17.** Figure 17: Calibration vs. support (NLL, Brier; ↓ better). 0.2 0.4 0.6 kNN Distance (Support Proxy) 0.0 0.2 0.4 0.6 0.8 1.0 Accuracy ID (CIFAR-10) 0.2 0.4 0.6 0.8 kNN Distance (Support Proxy) 0.0 0.2 0.4 0.6 0.8 1.0 Max Confidence near-OOD (CIFAR-100) 0.4 0.6 0.8 1.0 kNN Distance (Support Proxy) 0.0 0.2 0.4 0.6 0.8 1.0 Max Confidence far-OOD (SVHN) Baseline GEM-CORE GEM-FI view at source ↗

**Figure 18.** Figure 18: Accuracy (ID; ↑ better) and confidence (OOD; ↓ better) vs. support view at source ↗

**Figure 19.** Figure 19: Normalized energy vs. support. While the relationship is broadly increasing on average, local non-monotonicity can appear in transition regimes near class boundaries or mixed-support regions; this does not materially affect the bulk OOD detection behavior, where energy still serves as a distance-informed support signal. ing and mixture design still retain substantial performance without structured synthe… view at source ↗

read the original abstract

Evidential Deep Learning (EDL) enables single-pass uncertainty estimation by predicting Dirichlet evidence, but it can remain overconfident and poorly calibrated, and it often fails to represent multi-modal epistemic uncertainty. We introduce Gated Evidential Mixtures (GEM), a family of models that learns an in-model energy signal and uses it to gate evidential outputs end-to-end in a distance-informed manner. GEM-CORE learns a feature-level energy and maps it to a bounded gate that smoothly suppresses evidence when support is low. To capture epistemic multi-modality without multi-pass ensembling, GEM-MIX adds a lightweight mixture of evidential heads with learned routing weights while preserving single-pass inference. Finally, GEM-FI stabilizes mixture allocations via a Fisher-informed regularizer, reducing head collapse and producing smoother boundary uncertainty. Across image classification and OOD detection benchmarks, GEM improves calibration and ID/OOD separation with single-pass inference. On CIFAR-10, GEM-FI vs. DAEDL improves accuracy from 91.11 to 93.75 (+2.64 pp), reduces Brier x100 from 14.27 to 6.81 (-7.46), and also improves misclassification-detection AUPR from 99.08 to 99.94 (+0.86). For epistemic OOD detection, GEM-FI achieves AUPR/AUROC of 92.59/95.09 on CIFAR-10 to SVHN and 90.20/89.06 on CIFAR-10 to CIFAR-100, compared with 85.54/89.30 and 88.19/86.10 for DAEDL.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

GEM-FI adds energy gating and Fisher regularization to evidential mixtures for measurable gains in calibration and OOD detection on image benchmarks, though verification needs the full methods.

read the letter

The main point is that this paper builds on evidential deep learning by adding a learned feature-level energy signal to gate evidence outputs and a Fisher regularizer on a mixture of heads to stabilize allocations and capture multi-modal epistemic uncertainty in one pass. The combination is presented as a new family of models that avoids ensembles while addressing overconfidence and poor calibration in standard EDL. What the work does well is deliver specific empirical improvements on public benchmarks. On CIFAR-10 it lifts accuracy from 91.11 to 93.75, cuts Brier score from 14.27 to 6.81, and raises epistemic OOD AUPR/AUROC on shifts to SVHN and CIFAR-100 versus the DAEDL baseline. These are measured on held-out sets, so the numbers are at least externally falsifiable. The soft spots are the absence of ablation tables, error bars, or training details for the energy-to-gate mapping and the Fisher term. Without those it is hard to tell how much each piece drives the gains or whether the results are sensitive to initialization and hyperparameters. Generalization beyond the reported image-classification and OOD setups is also untested, which matches the reader's note on external validity. This paper is aimed at researchers who need practical single-pass uncertainty for deep models in computer vision and reliable deployment. A reader already working on evidential or Dirichlet-based methods would find the routing and stabilization ideas worth examining. The approach shows clear engagement with the EDL literature and no obvious internal contradictions in the equations or claims. It deserves a serious referee to check the full implementation, run the missing controls, and confirm whether the reported lifts hold under scrutiny. I would send it to peer review rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Gated Evidential Mixtures (GEM) to address limitations in Evidential Deep Learning (EDL) such as overconfidence and poor representation of multi-modal epistemic uncertainty. GEM-CORE learns a feature-level energy signal mapped to a bounded gate that suppresses evidence for low-support inputs; GEM-MIX adds a lightweight mixture of evidential heads with learned routing weights for single-pass multi-modal uncertainty; GEM-FI further stabilizes the mixture via a Fisher-informed regularizer to reduce head collapse. Empirical results on CIFAR-10, SVHN, and CIFAR-100 show gains over DAEDL, including CIFAR-10 accuracy rising from 91.11 to 93.75, Brier score (x100) falling from 14.27 to 6.81, and improved epistemic OOD AUPR/AUROC on CIFAR-10-to-SVHN and CIFAR-10-to-CIFAR-100 shifts.

Significance. If the reported gains prove robust, the work supplies a practical single-pass framework for calibrated uncertainty in EDL that avoids multi-pass ensembling while capturing multi-modal epistemic uncertainty. The concrete metric improvements on standard image-classification and OOD benchmarks indicate potential value for reliable deep learning in safety-critical settings; the energy-gating and Fisher-regularization ideas are modular enough to be adopted more broadly.

major comments (2)

[§4] §4 (Experiments): The central performance claims (accuracy +2.64 pp, Brier reduction of 7.46, OOD AUPR/AUROC lifts) are presented without ablation tables, error bars, or statistical significance tests that isolate the contribution of the energy gate, mixture routing, and Fisher regularizer; this absence prevents verification that the gains are attributable to the proposed components rather than implementation details or hyperparameter tuning.
[§3.3] §3.3 (GEM-FI): The Fisher-informed regularizer is introduced to prevent head collapse, yet the manuscript provides no derivation or explicit loss term showing how the regularizer is added to the evidence objective, nor any analysis of whether it introduces new calibration artifacts on the reported benchmarks.

minor comments (2)

[Abstract] The abstract and §4 would be clearer if the computational overhead (forward-pass cost of the mixture) were quantified relative to DAEDL.
[§3.1] Notation for the energy-to-gate mapping function should be defined explicitly (e.g., as an equation) to support reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful and constructive review of our manuscript. We address each of the major comments below and outline the revisions we will make to improve the clarity and rigor of the presentation.

read point-by-point responses

Referee: [§4] §4 (Experiments): The central performance claims (accuracy +2.64 pp, Brier reduction of 7.46, OOD AUPR/AUROC lifts) are presented without ablation tables, error bars, or statistical significance tests that isolate the contribution of the energy gate, mixture routing, and Fisher regularizer; this absence prevents verification that the gains are attributable to the proposed components rather than implementation details or hyperparameter tuning.

Authors: We agree that the experimental section would be strengthened by including ablations that isolate the contributions of the energy gate (GEM-CORE), the mixture routing (GEM-MIX), and the Fisher regularizer (GEM-FI). In the revised version, we will add ablation tables demonstrating the incremental performance gains from each component. We will also report mean and standard deviation over multiple random seeds (e.g., 5 runs) to provide error bars, and include statistical significance tests such as paired t-tests or Wilcoxon tests to confirm that the improvements are statistically significant and not due to hyperparameter tuning or implementation specifics. revision: yes
Referee: [§3.3] §3.3 (GEM-FI): The Fisher-informed regularizer is introduced to prevent head collapse, yet the manuscript provides no derivation or explicit loss term showing how the regularizer is added to the evidence objective, nor any analysis of whether it introduces new calibration artifacts on the reported benchmarks.

Authors: We acknowledge that the presentation of the Fisher-informed regularizer in Section 3.3 could be more explicit. The regularizer is added as an additional term to the standard evidential loss to penalize inconsistencies in the Fisher information across mixture heads. In the revision, we will provide a full derivation of this term, explicitly state the combined objective function, and include an analysis of its effects on calibration metrics (e.g., Brier score and ECE) to verify that it does not introduce new artifacts. This will clarify how the regularizer stabilizes the mixture without compromising calibration. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces architectural innovations (gated energy signals in GEM-CORE, mixture heads in GEM-MIX, and a Fisher-informed regularizer in GEM-FI) to address limitations in evidential deep learning, then validates them via empirical results on held-out test sets (CIFAR-10 accuracy/Brier, OOD AUPR/AUROC on SVHN/CIFAR-100). These metrics are measured externally rather than derived by construction from fitted parameters or self-referential equations. No self-definitional loops, fitted-input predictions, or load-bearing self-citation chains appear in the method description; the central claims rest on standard benchmark comparisons without reducing to the inputs by definition.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 2 invented entities

The central claim rests on the standard EDL assumption that Dirichlet evidence parameters capture epistemic uncertainty, plus two new invented mechanisms (energy gate and Fisher regularizer) whose independent evidence is only the reported benchmark gains.

free parameters (2)

energy-to-gate mapping parameters
Learned mapping from feature energy to bounded gate values; fitted during end-to-end training.
mixture routing weights
Learned weights that allocate inputs across evidential heads.

axioms (1)

domain assumption Dirichlet distribution parameters can represent both aleatoric and epistemic uncertainty in classification
Inherited from prior EDL work and invoked to justify the base evidential heads.

invented entities (2)

in-model energy signal no independent evidence
purpose: Feature-level scalar used to gate evidence suppression in low-support regions
New construct introduced to modulate evidential outputs in a distance-informed way.
Fisher-informed regularizer no independent evidence
purpose: Term that stabilizes mixture head allocations and reduces collapse
New regularizer added to the training objective.

pith-pipeline@v0.9.0 · 5612 in / 1498 out tokens · 44318 ms · 2026-05-07T16:49:18.028256+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

12 extracted references · 3 canonical work pages

[1]

Cheng, Z

to appear; also available as arXiv:2410.00393. Cheng, Z. et al. Semi-supervised prior networks for OOD-robust calibration.arXiv,

work page arXiv
[2]

doi: 10.1007/s11263-024- 02117-4. Yoon, T. and Kim, H. Uncertainty estimation by density aware evi- dential deep learning. InProceedings of the 41st International Conference on Machine Learning, volume 235 ofProceedings of Machine Learning Research, pp. 57217–57243. PMLR,

work page doi:10.1007/s11263-024-
[3]

Code and Reproducibility Code and reproduction instructions are available at:https: //github.com/Marcorazhan/GEM-FI

A. Code and Reproducibility Code and reproduction instructions are available at:https: //github.com/Marcorazhan/GEM-FI. B. Notation Summary Table 4 collects the main symbols used in Sections 2.1– 2.3 and fixes the distinction between single-head, per-head, gating, and routing quantities. 10 GEM-FI: Gated Evidential Mixtures with Fisher Modulation Table 4....

2018
[4]

parameterize target Dirichlet distributions. Density-aware variants rescale evidential outputs using feature-space likelihoods; DAEDL employs an offline Gaussian surrogate such as GDA (Mur- phy, 2012; Bishop, 2006), which improves calibration under shift but leaves the density term decoupled from end-to-end learning. Mixture-style evidential models (Ryu et al.,

2012
[5]

FI-informed evi- dential training has also been explored (Deng et al., 2023)

report calibration gains by explicitly modulating evidential outputs. FI-informed evi- dential training has also been explored (Deng et al., 2023). Table 5 summarizes how GEM-FI differs from closely related single-pass evidential and density-aware methods along key architectural and algorithmic dimensions. GEM- FI integrates in-model support gating, multi...

2023
[6]

Method End-to-enddensity Single-pass Multi-modalepistemicIn-modelgating FIfor routing DAEDL (Yoon & Kim, 2024)✗ ✓ ✗ ✗ ✗ Ryu et al

with input perturbations and Table 5.Comparison of GEM-FI with closely related single-pass evidential and density-aware methods. Method End-to-enddensity Single-pass Multi-modalepistemicIn-modelgating FIfor routing DAEDL (Yoon & Kim, 2024)✗ ✓ ✗ ✗ ✗ Ryu et al. (Ryu et al., 2024)✓ ✓ ✓ ✗ ✗ Deng et al. (Deng et al., 2023)✓ ✓ ✗ ✗ ✓ Zhang et al. (Zhang et al., ...

2024
[7]

Energy-based views (Grathwohl et al., 2020; Liu et al.,

in feature space. Energy-based views (Grathwohl et al., 2020; Liu et al.,

2020
[8]

reinterpret discriminative classifiers as implicit energy models and have reported improved separability in some settings between ID and OOD examples than softmax confidence. Follow-ups analyze theoretical conditions for energy-based separability (Morteza & Li, 2022), explore ar- chitectural variants such as masked energy models (He et al., 2023), and stu...

2022
[9]

MNIST contains 60,000 training and 10,000 test grayscale images of size 28×28 , and CIFAR-10 consists of 50,000 training and 10,000 test RGB images of size 32×32

and CIFAR-10 (Krizhevsky, 2009). MNIST contains 60,000 training and 10,000 test grayscale images of size 28×28 , and CIFAR-10 consists of 50,000 training and 10,000 test RGB images of size 32×32 . For OOD evaluation, we use FashionMNIST (Xiao et al.,

2009
[10]

and CIFAR-10-C (Hendrycks & Dietterich, 2019). MNIST-C consists of 15 corruption types with a fixed (tuned) severity 12 GEM-FI: Gated Evidential Mixtures with Fisher Modulation Table 6.Comparison of the per-component Dirichlet concentration α(k) c and final predictive mean ˆpc between the DAEDL baseline and the proposed GEM-FI method. Here uc and u(k) c d...

2019
[11]

need not increase reliably at mild severities: the model can still extract sufficient class evidence and maintain high-confidence predictions even when inputs are corrupted. Since our approach primarily targets epistemic support esti- mation and ID/OOD separation–i.e., suppressing evidence when representation support is low and stabilizing mixture allocat...

work page arXiv 2017
[12]

Overall, these diagnostics support that GEM achieves strong ID cali- bration intrinsically, while maintaining substantially lower confidence on incorrect predictions

Since TS optimizes NLL rather than ECE, applying TS may slightly improve or slightly worsen ECE depending on the model (Table 11). Overall, these diagnostics support that GEM achieves strong ID cali- bration intrinsically, while maintaining substantially lower confidence on incorrect predictions. F.8. Uncertainty Distributions (ID vs OOD) Figure 11 visual...

2017

[1] [1]

Cheng, Z

to appear; also available as arXiv:2410.00393. Cheng, Z. et al. Semi-supervised prior networks for OOD-robust calibration.arXiv,

work page arXiv

[2] [2]

doi: 10.1007/s11263-024- 02117-4. Yoon, T. and Kim, H. Uncertainty estimation by density aware evi- dential deep learning. InProceedings of the 41st International Conference on Machine Learning, volume 235 ofProceedings of Machine Learning Research, pp. 57217–57243. PMLR,

work page doi:10.1007/s11263-024-

[3] [3]

Code and Reproducibility Code and reproduction instructions are available at:https: //github.com/Marcorazhan/GEM-FI

A. Code and Reproducibility Code and reproduction instructions are available at:https: //github.com/Marcorazhan/GEM-FI. B. Notation Summary Table 4 collects the main symbols used in Sections 2.1– 2.3 and fixes the distinction between single-head, per-head, gating, and routing quantities. 10 GEM-FI: Gated Evidential Mixtures with Fisher Modulation Table 4....

2018

[4] [4]

parameterize target Dirichlet distributions. Density-aware variants rescale evidential outputs using feature-space likelihoods; DAEDL employs an offline Gaussian surrogate such as GDA (Mur- phy, 2012; Bishop, 2006), which improves calibration under shift but leaves the density term decoupled from end-to-end learning. Mixture-style evidential models (Ryu et al.,

2012

[5] [5]

FI-informed evi- dential training has also been explored (Deng et al., 2023)

report calibration gains by explicitly modulating evidential outputs. FI-informed evi- dential training has also been explored (Deng et al., 2023). Table 5 summarizes how GEM-FI differs from closely related single-pass evidential and density-aware methods along key architectural and algorithmic dimensions. GEM- FI integrates in-model support gating, multi...

2023

[6] [6]

Method End-to-enddensity Single-pass Multi-modalepistemicIn-modelgating FIfor routing DAEDL (Yoon & Kim, 2024)✗ ✓ ✗ ✗ ✗ Ryu et al

with input perturbations and Table 5.Comparison of GEM-FI with closely related single-pass evidential and density-aware methods. Method End-to-enddensity Single-pass Multi-modalepistemicIn-modelgating FIfor routing DAEDL (Yoon & Kim, 2024)✗ ✓ ✗ ✗ ✗ Ryu et al. (Ryu et al., 2024)✓ ✓ ✓ ✗ ✗ Deng et al. (Deng et al., 2023)✓ ✓ ✗ ✗ ✓ Zhang et al. (Zhang et al., ...

2024

[7] [7]

Energy-based views (Grathwohl et al., 2020; Liu et al.,

in feature space. Energy-based views (Grathwohl et al., 2020; Liu et al.,

2020

[8] [8]

reinterpret discriminative classifiers as implicit energy models and have reported improved separability in some settings between ID and OOD examples than softmax confidence. Follow-ups analyze theoretical conditions for energy-based separability (Morteza & Li, 2022), explore ar- chitectural variants such as masked energy models (He et al., 2023), and stu...

2022

[9] [9]

MNIST contains 60,000 training and 10,000 test grayscale images of size 28×28 , and CIFAR-10 consists of 50,000 training and 10,000 test RGB images of size 32×32

and CIFAR-10 (Krizhevsky, 2009). MNIST contains 60,000 training and 10,000 test grayscale images of size 28×28 , and CIFAR-10 consists of 50,000 training and 10,000 test RGB images of size 32×32 . For OOD evaluation, we use FashionMNIST (Xiao et al.,

2009

[10] [10]

and CIFAR-10-C (Hendrycks & Dietterich, 2019). MNIST-C consists of 15 corruption types with a fixed (tuned) severity 12 GEM-FI: Gated Evidential Mixtures with Fisher Modulation Table 6.Comparison of the per-component Dirichlet concentration α(k) c and final predictive mean ˆpc between the DAEDL baseline and the proposed GEM-FI method. Here uc and u(k) c d...

2019

[11] [11]

need not increase reliably at mild severities: the model can still extract sufficient class evidence and maintain high-confidence predictions even when inputs are corrupted. Since our approach primarily targets epistemic support esti- mation and ID/OOD separation–i.e., suppressing evidence when representation support is low and stabilizing mixture allocat...

work page arXiv 2017

[12] [12]

Overall, these diagnostics support that GEM achieves strong ID cali- bration intrinsically, while maintaining substantially lower confidence on incorrect predictions

Since TS optimizes NLL rather than ECE, applying TS may slightly improve or slightly worsen ECE depending on the model (Table 11). Overall, these diagnostics support that GEM achieves strong ID cali- bration intrinsically, while maintaining substantially lower confidence on incorrect predictions. F.8. Uncertainty Distributions (ID vs OOD) Figure 11 visual...

2017