Pith. sign in

REVIEW 3 major objections 6 minor 58 references

TULiP: Test-time Uncertainty Estimation via Linearization and Weight Perturbation

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read TULiP claims entropy of predictions averaged over small Gaussian weight perturbations is a better near-OOD detector than raw softmax entropy.

desk verdict A promising weight-perturbation OOD heuristic whose stated theoretical grounding breaks at the step where Eq. 6 becomes Algorithm 1; still worth a referee. read the letter →

arxiv 2505.16923 v2 pith:3YQC7YFF submitted 2025-05-22 stat.ML cs.LG

Yuhui Zhang , Dongshen Wu , Yuichiro Wada , Takafumi Kanamori This is my paper · ORCID
classification stat.MLcs.LG MSC 68T07
keywords uncertaintyestimationout-of-distributiondetectionneuraltangentkernelweightperturbationlazytrainingpost-hocmethodepistemicnear-distributionshift
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

TULiP is a post-hoc way to estimate how uncertain a trained image classifier should be about a new input, without retraining or access to the original training data. The paper's central claim is that if you slightly perturb the network's weights at test time and average the resulting predictions, the entropy of that average is a better out-of-distribution (OOD) detector than the standard softmax entropy, especially when the new input is only subtly different from the training distribution. The method is justified by a bound on how much a hypothetical pre-convergence perturbation would change the final network, derived under linearized training dynamics. The paper reports top or near-top results on standard image benchmarks, with the clearest gains on near-OOD samples.

What carries the argument

The central object is a hypothetical perturbation applied to the network at a time before training converges, followed by the same gradient-flow training. In the linearized (lazy) regime, the effect of that perturbation on the final predictions is bounded by the distance from the test point to the training set in the space of network gradients, which is in turn estimated by the trace of the neural tangent kernel and the norm of the Jacobian times parameter displacement. Algorithm 1 implements this by sampling Gaussian weight perturbations and averaging the resulting softmax outputs, using the calibrated bound as a variance-matching envelope for the surrogate posterior samples.

What would settle it

Train two identical architectures, one in the lazy regime (wide network, small learning rate) and one in the feature-learning regime (narrow network, large learning rate), and compare TULiP's near-OOD AUROC against plain softmax entropy; the paper's bound predicts a larger advantage in the lazy case, so observing the opposite would undermine the theoretical story.

Watch

Extended reading notes

Core claim

The central claim is that epistemic uncertainty at a test point $z$ can be quantified by the variance of predictions produced by perturbed versions of the final network, and that this variance is upper-bounded by an expression involving the neural tangent kernel and the product of the network Jacobian with the parameter displacement during training. Concretely, Theorem 1 bounds $\|f_T(z)-\hat{f}_T(z)\|$ by a term proportional to the gradient distance from $z$ to the training set plus the perturbation size and convergence error. The bound is then converted into an implementable score: sample Gaussian perturbations of the weights, estimate the trace of the neural tangent kernel via a randomized estimator, estimate the Jacobian-displacement term via a finite difference, scale the sample spread by a calibrated constant, and take the entropy of the averaged softmax outputs. The paper claims this score outperforms raw softmax entropy and several other post-hoc detectors on near-OOD inputs across CIFAR-10, CIFAR-100, ImageNet-200, and ImageNet-1K settings.

Load-bearing premise

The load-bearing premise is that real neural network training is well approximated by linearized (lazy) training dynamics, so the bound from Theorem 1 and the variance-matching step in the algorithm both depend on a kernel that changes little during training.

Editorial extensions

If this is right

  • On near-OOD inputs, TULiP's entropy score is reported as the top or second-best AUROC across CIFAR-10, CIFAR-100, ImageNet-200, and ImageNet-1K.
  • The method requires only the trained model and a small validation set, not the original training data, so it can be added to already-deployed classifiers.
  • Averaged TULiP predictions can be fed into other scoring rules; the paper shows this pushes MSP scores further apart between in-distribution and OOD data.
  • TULiP's advantage is consistent across several convolutional and transformer architectures on ImageNet-1K, while some baselines degrade when the training protocol changes.

Reading between the lines

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

  • If the bound's linearization assumption is doing the work, architectures closer to the lazy regime should show a larger gain from TULiP; this is a testable prediction the paper does not make.
  • The calibration step uses a validation set to set one constant; one could attempt to derive that constant from layer-wise weight norms, removing the need for any extra data.
  • Because TULiP only transforms predictions, it could be stacked with input-level OOD methods such as temperature scaling or input preprocessing, which the paper does not explore.
  • For non-classification tasks, the entropy step would naturally be replaced by predictive variance or dispersion of the averaged samples; the paper states the construction generalizes but does not demonstrate it.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes TULiP, a post-hoc OOD detection score for pre-trained classifiers. It models epistemic uncertainty as the effect of a hypothetical functional perturbation applied before convergence under linearized (lazy) training dynamics, derives a bound (Theorem 1, Eqs. 5-6) on the resulting logit difference, and then implements the bound using Gaussian and deterministic weight perturbations. A surrogate-posterior envelope is constructed by matching the variance of perturbed predictions to the estimated bound, and the entropy of the averaged softmax output is used as the OOD score. The method is evaluated on OpenOOD v1.5 for CIFAR-10/100, ImageNet-200, and ImageNet-1K, and it reports consistent near-OOD improvements over post-hoc baselines, with additional experiments on several architectures.

Significance. The paper has a clear strength: it provides a self-contained theoretical framework with a proof of Eq. 5-6 in the appendix, validates Eq. 5 on a synthetic infinite-width regression problem using the neural-tangents library, and evaluates on a large, standardized benchmark across multiple architectures and ID/OOD splits, including a consistency check on ViT, VGG, and RegNet. The near-OOD empirical gains, especially on CIFAR-10 and ImageNet-1K, are promising and would be a useful contribution if the connection between theory and algorithm were made rigorous. As it stands, the significance is conditional: the implemented score is not derived from the bound by a chain of equalities, and the main experimental gains are not shown to be consequences of Theorem 1.

major comments (3)
  1. [§4.1, Algorithm 1 lines 6-8; Proposition 1; Eq. (6)] Proposition 1 states that lim_{ε→0} ε^{-2} E_v ||f(z;θ_T+v)-f(z;θ_T)||² = Tr Θ(z,z), yet line 6 of Algorithm 1 computes eΘTr(z,z) = (1/M)Σ_i ||f(z;θ_T+v_i)-f(z;θ_T)||² without the ε^{-2} factor, so for ε=0.005 it estimates 0.005² TrΘ(z,z), not TrΘ(z,z). Line 7 estimates D ≈ εδ√o ||∇θf_T(z)(θ_T−θ_ts)||. Consequently line 8 estimates J²[ε²(TrΘ(z,z)+ΘXX) − λ εδ√o ||...||], whereas Eq. (6) has trace terms and a gradient term with coefficients independent of ε and o. The ratio of the gradient coefficient to the trace coefficient in the implementation is λδ√o/ε ≈ 6×10^4 with the reported hyperparameters (λ=1.25, δ=8, o=1000), so the D-term completely dominates the z-dependent trace term; tuning the single scalar J cannot repair this relative weighting. The claim in §4.1 that line 8 is an "Estimation of Eq. 6 up to square root" is therefore not supported. Please either rescale eΘTr by ε^{-2} and D so that the implemented expression matches Eq. (6) up to the stated constants, or explicitly reframe S as a heuristic score and provide evidence that it tracks the predicted bound.
  2. [§4.3, Algorithm 1 lines 9-13; Eq. (7)] The final score U = H_y(1/M Σ softmax(f̃_i(z))) is not obtained from the bound by any stated inequality. Equation (7) only bounds the trace of the variance of the logits, and the surrogate samples are constructed to match that variance via γ. Entropy of the averaged softmax is a nonlinear function of those samples, and no monotonicity or Lipschitz argument is given to show that low or high entropy corresponds to small or large values of Eq. (6). Thus the near-OOD AUC results in Table 1 are empirical properties of the heuristic surrogate construction, not consequences of Theorem 1. A formal link, or an explicit disclaimer that the entropy step is an empirical design choice, is needed.
  3. [§3.1 and §5] Theorem 1 is derived for the linearized dynamics of Eqs. (2)-(3) and assumes a constant NTK over training, i.e., the lazy regime. The main experiments use ResNet-18/50 trained with SGD, and Sec. 5 acknowledges that empirical deep networks are typically trained non-linearly. No quantitative evidence is provided that the trained checkpoints remain in the lazy regime, such as the relative change of the empirical NTK during training or the distance between f_emp and the linearized trajectory Eq. (2). Without such a check, the theoretical result does not cover the setting in which the method is evaluated. The paper should add such a measurement, restrict the theoretical claims accordingly, or present the theory as motivation only.
minor comments (6)
  1. [Table 1] The table reports averages over three runs but no standard deviations or confidence intervals; many near-OOD differences are small (e.g., CIFAR-100 near AUROC 80.81 vs. 80.27 for ENT), so error bars are needed to support the ranking claims.
  2. [Figure 2(c)] The panel labeled "Verification of A5" appears to contain no visible curve or axes in the manuscript; please add axis labels, a legend, and a description of the plotted quantity.
  3. [Equation (6)] The notation "≲" already means "up to a constant independent of z," so saying "up to constants J and K" in the same sentence is redundant and ambiguous; please clarify whether J and K are absorbed into ≲ or are explicit.
  4. [§4.2] The sentence "we find the optimal non-negative J* by maximizing the likelihood of 1/M Σ_i softmax(f̃_i(z))" is incomplete: the probabilistic model, the validation labels, and the loss used for maximum likelihood are not specified.
  5. [§5.1] "Improved AUROC over 15%" should be reported as percentage points with the exact numerical improvements, since an AUROC increase from 0.76 to 0.89 is 13 points, not 15 percent in relative terms.
  6. [Table 2] The footnote contains placeholder "?" markers for the pretrained model references; these should be completed before publication.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: TULiP's score is a heuristic built on an independent perturbation bound; the epsilon-squared scaling gap is a derivation flaw, not a circular reduction.

full rationale

The claimed derivation chain is not circular. Theorem 1 (Eqs. 5 and 6) is proved from the linearized dynamics (Eqs. 2-4) under assumptions A1-A4 using Grönwall and Hölder arguments (Sec. A.3-A.4); none of these steps take the final OOD score as an input, and the synthetic check in Fig. 2(a) is an independent comparison against the exact Gaussian ensemble obtained with the neural-tangents library. The bridge to Algorithm 1 is explicitly advertised as heuristic (Sec. 3.3: 'we will present a heuristic method to estimate f_T(z) by matching variances'), and the final score is the entropy of averaged softmax predictions over surrogate samples whose variance is matched to S (Eq. 11), not S itself; the OOD ranking of this entropy is then measured on held-out OpenOOD test sets. The calibration of J and Jscaling on a validation set is standard hyperparameter tuning and is applied to all competing methods in the benchmark, so it does not make the test-set predictions statistically forced. The paper contains no load-bearing self-citation: the NTK/lazy-training premises are imported from external references [28,36], and no uniqueness claim is borrowed from the authors' own prior work. I also weighed the admitted limitations: Sec. 5 concedes real networks are trained non-linearly, Sec. B.3 concedes O(M) inference cost, and Sec. 6 notes only functional perturbations are treated; these weaken the theoretical claim but are not circularity. The one concrete implementation gap is that eThetaTr in Algorithm 1 line 6 estimates epsilon-squared times TrTheta(z,z) rather than TrTheta(z,z) under Proposition 1 (Appendix A.6 even writes 'eThetaTr(z,z) be an approximation of epsilon-squared TrTheta(z,z)'), so line 8 is not literally Eq. 6 up to square root; but this is a non-equivalence, a correctness and derivation gap, not an equivalence by construction, and therefore it does not raise the circularity score.

Assumptions & free parameters 6 free parameters · 9 assumptions · 0 invented entities

The central claim rests on five explicit assumptions (A1-A5) plus the lazy-training and constant-NTK assumption, which the experiment section admits is violated in practice. The method also depends on five calibrated or selected hyperparameters (J, lambda, delta, epsilon, M) and an estimated Theta_XX; the final score is built by an ad hoc variance-matching construction. No new physical entities are introduced.

free parameters (6)
  • J (overall scaling, J* x Jscaling) = Jscaling grid searched in {1.0, 1.25, 1.5, 1.75, 2.0}; J* chosen by likelihood on ID validation
    Controls strength of the TULiP correction; fitted to validation ID data in Sec. 4.2.
  • lambda = 1.25
    Proxy for constant K in Eq. 6; fixed by the authors, ablation in Fig. 4 shows sensitivity.
  • delta = 8
    Step size for the directional perturbation D; fixed in Sec. 5 setup, should be lowered when lambda is raised.
  • epsilon = 0.005
    Standard deviation of Gaussian weight perturbation for the trace estimate; fixed in Sec. 5 setup.
  • Theta_XX = estimated from ID validation expectation
    Needed in S; estimated empirically on the validation set, not derived.
  • M = 10
    Number of posterior samples and forward passes; chosen by hand as a computational budget.
assumptions (9)
  • domain assumption A1: For t in [0,T], f(x), grad f(x), loss and gradient stay bounded uniformly on x.
    Used in the proof of Theorem 1 to control norms and justify interchanging expectations; not guaranteed for deep networks.
  • domain assumption A2: Gradient of the loss function is Lipschitz continuous with constant L.
    Essential for the Gronwall inequality step in Eq. 16.
  • domain assumption A3: The perturbation Delta f is uniformly bounded by alpha for all x.
    Defines the hypothetical perturbation; alpha is inaccessible in the post-hoc setting.
  • domain assumption A4: Near-perfect convergence of both original and perturbed networks on the training set at time T, with ||f_T(x) - f_hat_T(x)|| <= beta on X.
    Justified by citing overparameterized NN convergence results; beta is not known.
  • domain assumption A5: Closeness of test point z to the training set in the NTK embedding, as stated in Sec. 3.3.
    Appears weak but is exactly what is needed to replace the inf in Eq. 5 with the trace expression to obtain Eq. 6; verified only empirically in Fig. 2(c).
  • domain assumption Network training follows linearized gradient flow Eq. 3 with a constant NTK Theta.
    The core lazy-training idealization; Sec. 5 says real training is non-linear, so this is violated in the experiments.
  • domain assumption Unique solution to Eq. 3 exists.
    Assumed for the gradient-flow formulation.
  • ad hoc to paper The distribution of the hypothetical retrained network can be represented by linear interpolation between the original output and random perturbed outputs, with scaling chosen so variance matches S.
    Introduced in Sec. 4.3 without proof; this is the bridge that turns the bound into a sampling scheme.
  • ad hoc to paper Entropy of the average softmax of surrogate posterior samples is a valid OOD score.
    Stated in Sec. 4.3 line 13; not derived from the bound; relies on the generic fact that OOD inputs produce flatter distributions.

how reviews work

0 comments
Cite this review

Pith. "Pith review of TULiP: Test-time Uncertainty Estimation via Linearization and Weight Perturbation." pith.science (2026). https://pith.science/paper/3YQC7YFF

@misc{pith2026250516923,
  author       = {Pith},
  title        = {Pith review of: TULiP: Test-time Uncertainty Estimation via Linearization and Weight Perturbation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3YQC7YFF}},
  note         = {Machine review of arXiv:2505.16923}
}
read the original abstract

A reliable uncertainty estimation method is the foundation of many modern out-of-distribution (OOD) detectors, which are critical for safe deployments of deep learning models in the open world. In this work, we propose TULiP, a theoretically-driven post-hoc uncertainty estimator for OOD detection. Our approach considers a hypothetical perturbation applied to the network before convergence. Based on linearized training dynamics, we bound the effect of such perturbation, resulting in an uncertainty score computable by perturbing model parameters. Ultimately, our approach computes uncertainty from a set of sampled predictions. We visualize our bound on synthetic regression and classification datasets. Furthermore, we demonstrate the effectiveness of TULiP using large-scale OOD detection benchmarks for image classification. Our method exhibits state-of-the-art performance, particularly for near-distribution samples.

Figures

Figures reproduced from arXiv: 2505.16923 by the authors.

Figure 1
Figure 1. Illustration of the hy￾pothetical perturbation process. The shaded area indicates the distribution of ˆfT , and the dashed circle is the Surrogate Posterior Envelope (SPE). See Sec. 4.3 for details. Notations Let z ∈ R d be an arbitrary test point. Let ∥ · ∥ denote the Euclidean norm and induced 2-norm for vectors and matrices. Let ∥ · ∥F denote the matrix Frobenius norm. We also denote ∥·∥X := Ex [PITH_FULL_IMAGE:… view at source ↗
Figure 2
Figure 2. Verification of Thm. 1 (Sec. 5.1). From left to right, (a): Regression on [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. (a) Visualization of S in Alg. 1 (line 13, used to estimate Eq. 6) in various datasets (left to right: ID (ImageNet-1K), NINCO (near), Textures (far)). (b) Visualization of the MSP score before and after applying TULiP on ID (right) and OOD (left). Notice how OOD data is pushed further towards 0 (lower confidence) than ID. We chose MSP due to its simplicity. (c) Effect of TULiP on various OOD scoring criteria for ne… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Results by varying ϵ and λ on ImageNet-1K ID. Solid lines: A validation set is used to find the the optimal J with Jscaling = 2.0. Dashed lines: No validation set calibration for J (results for ϵ = 0.0075 falls out of the range of the plot). 6 Conclusion In this study,…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

58 extracted references · 50 canonical work pages

  1. [1]

    IEEE Access12, 101603–101625 (2024)

    Atakishiyev, S., Salameh, M., Yao, H., Goebel, R.: Explainable artificial intelligence for autonomous driving: A comprehensive overview and field guide for future research directions. IEEE Access12, 101603–101625 (2024)

    work page 2024

  2. [2]

    Journal of the ACM58(2), 1–34 (2011)

    Avron, H., Toledo, S.: Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix. Journal of the ACM58(2), 1–34 (2011)

    work page 2011

  3. [3]

    In: Proceedings of the IEEE/CVF CVPR

    Baek, E., Park, K., Kim, J., Kim, H.S.: Unexplored faces of robustness and out-of- distribution: Covariate shifts in environment and sensor domains. In: Proceedings of the IEEE/CVF CVPR. pp. 22294–22303 (2024)

    work page 2024

  4. [4]

    Bitterwolf, J., Müller, M., Hein, M.: In or out? fixing imagenet out-of-distribution detection evaluation (2023)

    work page 2023

  5. [5]

    In: ICML

    Blundell, C., Cornebise, J., Kavukcuoglu, K., Wierstra, D.: Weight uncertainty in neural network. In: ICML. vol. 37, pp. 1613–1622 (2015) 14 Yuhui Zhang, Dongshen Wu, Yuichiro Wada, and Takafumi Kanamori

    work page 2015

  6. [6]

    In: NeurIPS

    Chen, Z., Rotskoff, G., Bruna, J., Vanden-Eijnden, E.: A dynamical central limit theorem for shallow neural networks. In: NeurIPS. vol. 33, pp. 22217–22230 (2020)

    work page 2020

  7. [7]

    In: 2014 IEEE CVPR

    Cimpoi, M., Maji, S., Kokkinos, I., Mohamed, S., Vedaldi, A.: Describing textures in the wild. In: 2014 IEEE CVPR. pp. 3606–3613 (2014)

    work page 2014

  8. [8]

    In: NeurIPS

    Daxberger, E., Kristiadi, A., Immer, A., Eschenhagen, R., Bauer, M., Hennig, P.: Laplace redux - effortless bayesian deep learning. In: NeurIPS. vol. 34, pp. 20089–20103 (2021)

    work page 2021

Show all 58 references
  1. [9]

    In: 2009 IEEE CVPR

    Deng, J., Dong, W., Socher, R., Li, L.J., Li, K., Fei-Fei, L.: Imagenet: A large-scale hierarchical image database. In: 2009 IEEE CVPR. pp. 248–255 (2009)

    2009

  2. [10]

    arXiv preprint arXiv:1802.04865 (2018)

    DeVries, T., Taylor, G.W.: Learning confidence for out-of-distribution detection in neural networks. arXiv preprint arXiv:1802.04865 (2018)

    2018 arXiv

  3. [11]

    In: ICLR (2023)

    Djurisic, A., Bozanic, N., Ashok, A., Liu, R.: Extremely simple activation shaping for out-of-distribution detection. In: ICLR (2023)

    2023

  4. [12]

    In: ICML

    Du, S., Lee, J., Li, H., Wang, L., Zhai, X.: Gradient descent finds global minima of deep neural networks. In: ICML. vol. 97, pp. 1675–1685 (2019)

    2019

  5. [13]

    Nature 542(7639), 115–118 (2017)

    Esteva, A., Kuprel, B., Novoa, R.A., Ko, J., Swetter, S.M., Blau, H.M., Thrun, S.: Dermatologist-level classification of skin cancer with deep neural networks. Nature 542(7639), 115–118 (2017)

    2017

  6. [14]

    In: NeurIPS

    Fort, S., Dziugaite, G.K., Paul, M., Kharaghani, S., Roy, D.M., Ganguli, S.: Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the neural tangent kernel. In: NeurIPS. vol. 33, pp. 5850–5861 (2020)

    2020

  7. [15]

    In: ICML

    Gal, Y., Ghahramani, Z.: Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In: ICML. vol. 48, pp. 1050–1059 (2016)

    2016

  8. [16]

    Journal of Statistical Mechanics: Theory and Experiment 2020(11), 113301 (2020)

    Geiger, M., Spigler, S., Jacot, A., Wyart, M.: Disentangling feature and lazy training in deep neural networks. Journal of Statistical Mechanics: Theory and Experiment 2020(11), 113301 (2020)

    2020

  9. [17]

    In: ICML

    Guo, C., Pleiss, G., Sun, Y., Weinberger, K.Q.: On calibration of modern neural networks. In: ICML. vol. 70, pp. 1321–1330 (2017)

    2017

  10. [18]

    In: NeurIPS

    He, B., Lakshminarayanan, B., Teh, Y.W.: Bayesian deep ensembles via the neural tangent kernel. In: NeurIPS. vol. 33, pp. 1010–1022 (2020)

    2020

  11. [19]

    In: 2016 IEEE CVPR

    He, K., Zhang, X., Ren, S., Sun, J.: Deep residual learning for image recognition. In: 2016 IEEE CVPR. pp. 770–778 (2016)

    2016

  12. [20]

    In: ICML

    Hendrycks, D., Basart, S., Mazeika, M., Zou, A., Kwon, J., Mostajabi, M., Stein- hardt, J., Song, D.: Scaling out-of-distribution detection for real-world settings. In: ICML. vol. 162, pp. 8759–8773 (2022)

    2022

  13. [21]

    In: Proceedings of the IEEE/CVF ICCV

    Hendrycks, D., Basart, S., Mu, N., Kadavath, S., Wang, F., Dorundo, E., Desai, R., Zhu, T., Parajuli, S., Guo, M., Song, D., Steinhardt, J., Gilmer, J.: The many faces of robustness: A critical analysis of out-of-distribution generalization. In: Proceedings of the IEEE/CVF ICC...

    2021

  14. [22]

    In: ICLR (2019)

    Hendrycks, D., Dietterich, T.: Benchmarking neural network robustness to common corruptions and perturbations. In: ICLR (2019)

    2019

  15. [23]

    In: ICLR (2017)

    Hendrycks, D., Gimpel, K.: A baseline for detecting misclassified and out-of- distribution examples in neural networks. In: ICLR (2017)

    2017

  16. [24]

    Reliability Engineering & System Safety 54(2), 217–223 (1996)

    Hora, S.C.: Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management. Reliability Engineering & System Safety 54(2), 217–223 (1996)

    1996

  17. [25]

    In: NeurIPS

    Huang, R., Geng, A., Li, Y.: On the importance of gradients for detecting distribu- tional shifts in the wild. In: NeurIPS. vol. 34, pp. 677–689 (2021)

    2021

  18. [26]

    In: Proceedings of the IEEE/CVF CVPR

    Huang, R., Li, Y.: Mos: Towards scaling out-of-distribution detection for large semantic space. In: Proceedings of the IEEE/CVF CVPR. pp. 8710–8719 (2021) TULiP: Test-time Uncertainty Estimation 15

    2021

  19. [27]

    In: ICML

    Ioffe, S., Szegedy, C.: Batch normalization: accelerating deep network training by reducing internal covariate shift. In: ICML. vol. 37, p. 448–456 (2015)

    2015

  20. [28]

    In: NeurIPS

    Jacot, A., Gabriel, F., Hongler, C.: Neural tangent kernel: Convergence and gener- alization in neural networks. In: NeurIPS. vol. 31 (2018)

    2018

  21. [29]

    In: NeurIPS

    Kobayashi, S., Vilimelis Aceituno, P., von Oswald, J.: Disentangling the predictive variance of deep ensembles through the neural tangent kernel. In: NeurIPS. vol. 35, pp. 25335–25348 (2022)

    2022

  22. [30]

    Master’s thesis, University of Tront (2009)

    Krizhevsky, A.: Learning multiple layers of features from tiny images. Master’s thesis, University of Tront (2009)

    2009

  23. [31]

    International Journal of Computer Vision128(7), 1956–1981 (2020)

    Kuznetsova, A., Rom, H., Alldrin, N., Uijlings, J., Krasin, I., Pont-Tuset, J., Kamali, S., Popov, S., Malloci, M., Kolesnikov, A., et al.: The open images dataset v4: Unified image classification, object detection, and visual relationship detection at scale. International Jou...

    2020

  24. [32]

    In: NeurIPS

    Lakshminarayanan, B., Pritzel, A., Blundell, C.: Simple and scalable predictive uncertainty estimation using deep ensembles. In: NeurIPS. vol. 30 (2017)

    2017

  25. [33]

    Class CS 231N, Stanford University (2015)

    Le, Y., Yang, X.: Tiny imagenet visual recognition challenge. Class CS 231N, Stanford University (2015)

    2015

  26. [34]

    Proceedings of the IEEE86(11), 2278–2324 (1998)

    Lecun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proceedings of the IEEE86(11), 2278–2324 (1998)

    1998

  27. [35]

    In: ICLR (2018)

    Lee, J., Sohl-dickstein, J., Pennington, J., Novak, R., Schoenholz, S., Bahri, Y.: Deep neural networks as gaussian processes. In: ICLR (2018)

    2018

  28. [36]

    In: NeurIPS

    Lee,J.,Xiao,L.,Schoenholz,S.,Bahri,Y.,Novak,R.,Sohl-Dickstein,J.,Pennington, J.: Wide neural networks of any depth evolve as linear models under gradient descent. In: NeurIPS. vol. 32 (2019)

    2019

  29. [37]

    In: NeurIPS

    Lee, K., Lee, K., Lee, H., Shin, J.: A simple unified framework for detecting out-of-distribution samples and adversarial attacks. In: NeurIPS. vol. 31 (2018)

    2018

  30. [38]

    In: ICLR (2018)

    Liang, S., Li, Y., Srikant, R.: Enhancing the reliability of out-of-distribution image detection in neural networks. In: ICLR (2018)

    2018

  31. [39]

    In: NeurIPS

    Liu, W., Wang, X., Owens, J., Li, Y.: Energy-based out-of-distribution detection. In: NeurIPS. vol. 33, pp. 21464–21475 (2020)

    2020

  32. [40]

    In: 2023 IEEE/CVF CVPR

    Liu, X., Lochman, Y., Zach, C.: Gen: Pushing the limits of softmax-based out-of- distribution detection. In: 2023 IEEE/CVF CVPR. pp. 23946–23955 (2023)

    2023

  33. [41]

    In: NeurIPS Workshop on Deep Learning and Unsupervised Feature Learning (2011)

    Netzer, Y., Wang, T., Coates, A., Bissacco, A., Wu, B., Ng, A.Y.: Reading digits in natural images with unsupervised feature learning. In: NeurIPS Workshop on Deep Learning and Unsupervised Feature Learning (2011)

    2011

  34. [42]

    In: ICLR (2020)

    Novak, R., Xiao, L., Hron, J., Lee, J., Alemi, A.A., Sohl-Dickstein, J., Schoenholz, S.S.: Neural tangents: Fast and easy infinite neural networks in python. In: ICLR (2020)

    2020

  35. [43]

    International Journal of Computer Vision115(3), 211–252 (2015)

    Russakovsky, O., Deng, J., Su, H., Krause, J., Satheesh, S., Ma, S., Huang, Z., Karpathy, A., Khosla, A., Bernstein, M., Berg, A.C., Fei-Fei, L.: Imagenet large scale visual recognition challenge. International Journal of Computer Vision115(3), 211–252 (2015)

    2015

  36. [44]

    In: NeurIPS

    Song, Y., Sebe, N., Wang, W.: Rankfeat: Rank-1 feature removal for out-of- distribution detection. In: NeurIPS. vol. 35, pp. 17885–17898 (2022)

    2022

  37. [45]

    In: NeurIPS

    Sun, Y., Guo, C., Li, Y.: React: Out-of-distribution detection with rectified activa- tions. In: NeurIPS. vol. 34, pp. 144–157 (2021)

    2021

  38. [46]

    CoRR abs/2111.12797 (2021)

    Sun, Y., Guo, C., Li, Y.: React: Out-of-distribution detection with rectified activa- tions. CoRR abs/2111.12797 (2021)

    2021 arXiv

  39. [47]

    Szepesvari, C.: Algorithms for Reinforcement Learning (2010) 16 Yuhui Zhang, Dongshen Wu, Yuichiro Wada, and Takafumi Kanamori

    2010

  40. [48]

    In: 2018 IEEE/CVF CVPR

    Van Horn, G., Mac Aodha, O., Song, Y., Cui, Y., Sun, C., Shepard, A., Adam, H., Perona, P., Belongie, S.: The inaturalist species classification and detection dataset. In: 2018 IEEE/CVF CVPR. pp. 8769–8778 (2018)

    2018

  41. [49]

    In: ICLR (2022)

    Vaze, S., Han, K., Vedaldi, A., Zisserman, A.: Open-set recognition: A good closed- set classifier is all you need. In: ICLR (2022)

    2022

  42. [50]

    ACM Comput

    Wang, H., Yeung, D.Y.: A survey on bayesian deep learning. ACM Comput. Surv. 53(5) (2020)

    2020

  43. [51]

    In: NeurIPS

    Wang, H., Huang, W., Wu, Z., Tong, H., Margenot, A.J., He, J.: Deep active learning by leveraging training dynamics. In: NeurIPS. vol. 35, pp. 25171–25184 (2022)

    2022

  44. [52]

    In: Proceedings of the IEEE/CVF CVPR

    Wang, H., Li, Z., Feng, L., Zhang, W.: Vim: Out-of-distribution with virtual-logit matching. In: Proceedings of the IEEE/CVF CVPR. pp. 4921–4930 (2022)

    2022

  45. [53]

    In: NeurIPS Datasets and Benchmarks Track (2022)

    Yang, J., Wang, P., Zou, D., Zhou, Z., Ding, K., PENG, W., Wang, H., Chen, G., Li, B., Sun, Y., Du, X., Zhou, K., Zhang, W., Hendrycks, D., Li, Y., Liu, Z.: OpenOOD: Benchmarking generalized out-of-distribution detection. In: NeurIPS Datasets and Benchmarks Track (2022)

    2022

  46. [54]

    International Journal of Computer Vision (2024)

    Yang, J., Zhou, K., Li, Y., Liu, Z.: Generalized out-of-distribution detection: A survey. International Journal of Computer Vision (2024)

    2024

  47. [55]

    In: ICLR (2017)

    Zhang, C., Bengio, S., Hardt, M., Recht, B., Vinyals, O.: Understanding deep learning requires rethinking generalization. In: ICLR (2017)

    2017

  48. [56]

    Zhang, J., Yang, J., Wang, P., Wang, H., Lin, Y., Zhang, H., Sun, Y., Du, X., Zhou, K., Zhang, W., Li, Y., Liu, Z., Chen, Y., Li, H.: Openood v1.5: Enhanced benchmark for out-of-distribution detection (2023)

    2023

  49. [57]

    Zhou, B., Lapedriza, A., Khosla, A., Oliva, A., Torralba, A.: Places: A 10 million image database for scene recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 40(6), 1452–1464 (2018) A Proofs A.1 Basic notations For a networkf (x) : Rd → Ro maps inputs...

    2018

  50. [58]

    consider neural networks in an infinite-width limit with specified initialization scheme, which we have referred as the lazy limit in Section 3. Under such limit, the linearized network equation 2 is justified as the empirical NTK (at initialization) converges to a specific de...

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.