arxiv: 2604.22360 · v1 · submitted 2026-04-24 · 💻 cs.LG

Recognition: unknown

Revisiting Neural Activation Coverage for Uncertainty Estimation

Benedikt Franke , Nils F\"orster , Frank K\"oster , Asja Fischer , Markus Lange , Arne Raulf

Authors on Pith no claims yet

Pith reviewed 2026-05-08 12:16 UTC · model grok-4.3

classification 💻 cs.LG

keywords neural activation coverageuncertainty estimationregressionMonte-Carlo Dropoutneural networksout-of-distribution detection

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The pith

Neural activation coverage can be extended to estimate uncertainty in regression tasks for already-trained neural networks.

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

The paper extends neural activation coverage from out-of-distribution detection to uncertainty estimation for regression predictions on pre-trained networks. It shows through experiments that the resulting scores align more closely with actual prediction errors than those from Monte-Carlo Dropout. A reader would care because this offers a way to assess output reliability using only a single forward pass on an existing model. If the approach holds, it could support safer use of neural networks in regression settings where knowing when to trust a prediction matters.

Core claim

The authors claim that neural activation coverage, originally for out-of-distribution detection, can be directly repurposed to produce uncertainty scores for regression outputs of already-trained networks, and that these scores prove more meaningful than alternatives such as Monte-Carlo Dropout in their experiments.

What carries the argument

Neural activation coverage (NAC), the proportion of network activations triggered by an input, adapted here to quantify how uncertain a regression prediction is.

If this is right

Uncertainty estimates become available from a single forward pass without sampling or retraining.
The method applies to any pre-trained regression network without architectural changes.
Higher-uncertainty predictions can be flagged or down-weighted in downstream decisions.
NAC scores may improve reliability assessment compared with sampling-based methods.

Where Pith is reading between the lines

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

The same adaptation might be tested on classification tasks to check broader applicability.
NAC could be combined with other uncertainty techniques to produce hybrid scores.
If the correlation with error holds, the method might guide data collection toward uncertain regions.

Load-bearing premise

That a coverage metric created for spotting out-of-distribution inputs works as a valid uncertainty measure for regression predictions on already-trained networks.

What would settle it

Repeating the experiments and observing that NAC uncertainty scores fail to correlate more strongly with prediction errors than Monte-Carlo Dropout or other baselines.

Figures

Figures reproduced from arXiv: 2604.22360 by Arne Raulf, Asja Fischer, Benedikt Franke, Frank K\"oster, Markus Lange, Nils F\"orster.

**Figure 1.** Figure 1: Comparing uncertainty approaches for OoD detection. Correlation of uncertainty value and OoD-Label on ten UCI regression datasets. NAC adaptations (ours) achieve the best correlation in six out of ten experiments. Error bars represent the 95% confidence interval. as measure of uncertainty. For MC dropout, we insert a dropout layer after each linear layer and compute the uncertainty as the standard deviati… view at source ↗

**Figure 2.** Figure 2: Comparing uncertainty approaches for ID error detection. Correlation of uncertainty value and per-sample MSE on ten UCI regression datasets. NAC adaptations (ours) achieve the smallest correlation in seven out of ten experiments. Error bars represent the 95% confidence interval. test split and the uncertainty value. Results are depicted in view at source ↗

read the original abstract

Neural activation coverage (NAC) is a recently-proposed technique for out-of-distribution detection and generalization. We build upon this promising foundation and extend the method to work as an uncertainty estimation technique for already-trained artificial neural networks in the domain of regression. Our experiments confirm NAC uncertainty scores to be more meaningful than other techniques, e.g. Monte-Carlo Dropout.

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

The paper repurposes neural activation coverage as a post-hoc uncertainty score for regression networks and reports it beats MC dropout, but the adaptation details and experimental controls are too thin to assess without the full methods.

read the letter

The core move here is taking NAC, which started as an OOD detector, and turning the coverage statistic into an uncertainty measure that can be computed on an already-trained regression network. That is a legitimate, if incremental, extension. It keeps the method training-free and applies it to a setting where uncertainty matters for downstream decisions. If the experiments hold up, practitioners who want a lightweight add-on for existing models could find it useful. The paper does a clean job of stating the goal and contrasting it with MC dropout, which is a reasonable baseline for this kind of comparison. Credit for keeping the focus narrow and practical rather than claiming a broad theoretical advance. The soft spot is that the abstract gives almost no information on how the NAC score is actually turned into a per-prediction uncertainty value for regression, what datasets and metrics were used, or how the comparison was controlled for model capacity and calibration. Without those specifics it is impossible to tell whether the reported improvement is robust or whether NAC is simply capturing something MC dropout misses for unrelated reasons. The weakest link in the argument is the assumption that a coverage metric designed for distribution shift directly translates into a calibrated uncertainty for in-distribution regression errors; that step needs explicit justification and ablation. This work is aimed at applied researchers who already have trained regression models and need a quick uncertainty signal without retraining or ensembles. It is not foundational enough to change how most groups think about uncertainty, but the idea is straightforward enough that a careful referee could check the implementation and results in one pass. I would send it to peer review rather than desk-reject, mainly so the experimental section gets proper scrutiny on the metrics and statistical comparisons.

Referee Report

2 major / 1 minor

Summary. The paper extends neural activation coverage (NAC), a technique originally developed for out-of-distribution detection, to serve as a post-hoc uncertainty estimator for regression predictions on already-trained neural networks. It presents experimental comparisons claiming that NAC-derived uncertainty scores are more meaningful than those from Monte-Carlo Dropout.

Significance. If the experimental validation holds, the approach could provide a computationally lightweight alternative to ensemble or sampling-based uncertainty methods, as it requires no retraining or additional forward passes beyond the coverage computation. This would be particularly useful in regression settings where activation patterns can be directly repurposed without architectural changes.

major comments (2)

[Experiments] The central experimental claim (NAC uncertainty outperforming MC Dropout) is load-bearing but lacks sufficient grounding: no details are provided on the regression datasets, error metrics used to assess 'meaningfulness' (e.g., negative log-likelihood, calibration error, or correlation with prediction error), the precise adaptation of the NAC coverage formula to continuous outputs, or statistical tests for the reported superiority.
[Method] §3 (method extension): the mapping from NAC (defined via activation patterns in classification) to a scalar uncertainty score for regression is not formalized with an equation or algorithm; without this, it is unclear whether the repurposing preserves the original coverage properties or introduces new hyperparameters.

minor comments (1)

[Abstract] The abstract would be strengthened by naming at least one dataset or task to contextualize the regression experiments.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive review. We have carefully considered the major comments and revised the manuscript to address the concerns regarding experimental details and methodological formalization. Our responses to each point are provided below.

read point-by-point responses

Referee: [Experiments] The central experimental claim (NAC uncertainty outperforming MC Dropout) is load-bearing but lacks sufficient grounding: no details are provided on the regression datasets, error metrics used to assess 'meaningfulness' (e.g., negative log-likelihood, calibration error, or correlation with prediction error), the precise adaptation of the NAC coverage formula to continuous outputs, or statistical tests for the reported superiority.

Authors: We agree that additional details are necessary to fully substantiate the experimental claims and ensure reproducibility. The original manuscript included high-level descriptions of the datasets and metrics in Section 4, but we acknowledge these were insufficiently explicit. In the revised version, we have expanded Section 4.1 to specify the exact regression datasets (including UCI benchmarks and synthetic data with their sizes, input dimensions, and train/test splits), the evaluation metrics (Pearson correlation between uncertainty scores and absolute prediction errors, as well as expected calibration error), the adaptation of NAC to continuous regression outputs (via output-range normalized activation thresholds), and the statistical tests performed (Wilcoxon signed-rank tests with p-values reported for NAC vs. MC Dropout comparisons). These revisions appear in the updated Section 4 and a new Appendix C. revision: yes
Referee: [Method] §3 (method extension): the mapping from NAC (defined via activation patterns in classification) to a scalar uncertainty score for regression is not formalized with an equation or algorithm; without this, it is unclear whether the repurposing preserves the original coverage properties or introduces new hyperparameters.

Authors: We concur that a formal presentation strengthens the method section. While Section 3 described the extension in text, we have now added a precise mathematical formulation and algorithm. The uncertainty score is defined as U(x) = 1 - (1/|N|) * sum_{n in N} I(a_n(x) > tau), where tau is a regression-adapted threshold based on the empirical activation distribution over the training set, and N is the set of neurons. We include pseudocode as Algorithm 1 and discuss how this preserves the core coverage intuition while introducing a single new hyperparameter (tau), which is selected via a validation procedure described in the text. This is now formalized as Equations (2)-(4) in the revised Section 3. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper extends the existing Neural Activation Coverage (NAC) metric from out-of-distribution detection to uncertainty estimation for regression on pre-trained networks. The central claim rests on experimental comparisons showing NAC uncertainty scores outperform baselines such as Monte-Carlo Dropout. These comparisons are independent empirical evaluations rather than quantities derived from the same fitted parameters or self-referential definitions. No load-bearing self-citations, self-definitional steps, or fitted inputs renamed as predictions appear in the abstract or described chain. The repurposing assumption is validated externally through experiments on already-trained networks, keeping the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the paper introduces no new free parameters or invented entities and relies on standard domain assumptions about neural-network activations and regression tasks.

axioms (1)

domain assumption Neural activation coverage can be computed from the activations of a trained network for any input.
This is the foundational premise required to extend NAC to uncertainty scoring.

pith-pipeline@v0.9.0 · 5354 in / 1182 out tokens · 77726 ms · 2026-05-08T12:16:33.697782+00:00 · methodology

discussion (0)

Reference graph

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