Pith. sign in

REVIEW 5 major objections 5 minor 41 references

Parametric $\rho$-Norm Scaling Calibration

T0 review · 5 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read A post-hoc calibrator that divides logits by a learnable ρ-norm reduces expected calibration error to 0.007–0.019 on standard image benchmarks while preserving classifier accuracy.

desk verdict A plausible new parametric calibrator, but the norm in Eq. (2) is undefined for negative logits with non-integer ρ, the proofs are shaky, and the closest baselines are missing; fixable but needs real work. read the letter →

arxiv 2412.15301 v1 pith:OUGIFROQ submitted 2024-12-19 cs.LG cs.CV

Siyuan Zhang , Linbo Xie This is my paper · ORCID
classification cs.LGcs.CV
keywords confidencecalibrationexpectederrortemperaturescalingpost-hocρ-normKLdivergenceregularizationorder-preservingmappingoutputamplitude
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

This paper claims that the overconfidence of modern classifiers can be corrected after training by a simple parametric remapping: divide each logit by a learnable ρ-norm of the logit vector (plus constants) before applying softmax. The authors argue that this 'ρ-Norm Scaling' expands the expressiveness of temperature scaling and directly counteracts the growing output amplitude that pushes softmax probabilities toward one-hot saturation. They further claim that adding an instance-level KL-divergence penalty between pre- and post-calibration probability distributions to the bin-level squared calibration error prevents the calibrator from losing per-sample information. If correct, the method yields substantially lower ECE and AdaECE than temperature scaling on CIFAR-10/100, Tiny-ImageNet, SVHN, and 102 Flower, with accuracy unchanged because the mapping is order-preserving.

What carries the argument

The central object is the ρ-norm-scaling softmax: $g_c(z) = e^{r_c}/\sum_j e^{r_j}$ with $r_j(z) = z_j/(\gamma\|z\|_\rho + \beta)$, where $\|z\|_\rho = (\sum_j z_j^\rho)^{1/\rho}$. The ρ-norm term normalizes the logit amplitude before the exponential, so high-magnitude logits no longer saturate the softmax. The second mechanism is the multi-level objective $l = (\mathrm{acc}(D)-\mathrm{conf}(D))^2 + \alpha \sum_i \mathrm{KL}(g(z_i) \| s(z_i))$, where the KL term anchors the calibrated distribution to the original softmax distribution at the instance level.

What would settle it

Take a classifier output vector with a negative entry, set $\rho=1.5$, and evaluate $r_j = z_j/(\gamma\|z\|_\rho + \beta)$ as written: the norm term $(\sum_j z_j^\rho)^{1/\rho}$ is not a real number. If the implementation still runs, it must be using $|z_j|^\rho$, in which case Proposition 1's bounds need to be re-derived; inspecting the released code or running this calculation settles which mapping is actually being evaluated.

Watch

Extended reading notes

Core claim

The central claim is that the calibration mapping $r_j(z) = z_j/(\gamma\|z\|_\rho + \beta)$, with $\rho$ selected by grid search and $\gamma, \beta$ learned, produces well-calibrated confidence while preserving classification decisions. Proposition 1 gives upper and lower bounds showing that for finite $\gamma$ the confidence is pulled away from 1, mitigating overconfidence; Proposition 2 shows the mapping is strictly order-preserving for any $\gamma, \beta > 0$, so accuracy is unchanged; Proposition 3 generalizes this to any positive sample-dependent temperature $\sigma(z)$. The authors also claim that optimizing this calibrator with $l = \mathrm{SCE} + \alpha \mathrm{KL}$, where SCE is a batch-level squared calibration error and KL is the KL divergence from the calibrated distribution to the original softmax distribution, retains instance-level information and yields the reported state-of-the-art calibration.

Load-bearing premise

The formula $(z_1^\rho + \cdots + z_m^\rho)^{1/\rho}$ is used even when some classifier output values $z_j$ are negative and $\rho$ is not a whole number, which is only well-defined if absolute values are taken; the paper never states that, so the exact mapping being evaluated is ambiguous.

Editorial extensions

If this is right

  • Corollary of the experiments: post-hoc calibration can be improved without retraining the classifier, so accuracy is preserved while ECE drops sharply.
  • Proposition 1 implies ρ-Norm Scaling is guaranteed not to produce one-hot-like confidence for finite $\gamma$, which can be used as a design check for calibrators.
  • Proposition 3 gives a general criterion—any positive logit scaling $\sigma(z)$ preserves accuracy—so other amplitude-controlling mappings beyond ρ-norms could be explored.
  • The KL regularization offers a way to inject instance-level information into any bin-level calibration objective, not just SCE.
  • The method is cheap: only three parameters ($\gamma$, $\beta$, $\rho$) with grid search over $\rho \in \{1, 1.25, \ldots, 3\}$.

Reading between the lines

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

  • The paper never says what happens when logits are negative and $\rho$ is non-integer; if the implementation uses $(|z_j|^\rho)^{1/\rho}$, the bounds in Proposition 1 need to be re-derived for that absolute-value norm, and the reported results describe that mapping, not the one written.
  • Because the order-preserving property holds for any positive $\sigma(z)$, the same idea could be extended to per-class or input-dependent temperature functions without losing accuracy—a natural next step the paper leaves implicit.
  • The KL regularizer could be replaced by other distributional divergences (e.g., Jensen-Shannon) or applied in logit space; the paper only tests KL, so the choice's specificity is untested.
  • As a practical extension, one could test whether the same gains appear on language models or long-tail datasets, where output amplitude and logit distributions differ from image classifiers.
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

5 major / 5 minor

Summary. The paper proposes a post-hoc calibration method, ρ-Norm Scaling, which replaces the temperature in temperature scaling with a denominator γ||z||_ρ + β, where the norm is parameterized by a learnable ρ selected by grid search. The calibrator is optimized with a two-level loss that combines a bin-level square calibration error with an instance-level KL regularization between the pre- and post-calibration probability distributions. Experiments on CIFAR-10/100, SVHN, 102 Flower, and Tiny-ImageNet report substantially lower ECE and AdaECE than temperature scaling and other baselines, together with ablation studies that isolate the effect of the structure and the objective. The paper also states three propositions, the first bounding the calibrated confidence, the second and third giving order-preserving sufficient conditions for accuracy preservation.

Significance. If the empirical results hold, the proposed method would be a valuable addition to the post-hoc calibration toolbox: it is simple, accuracy-preserving, and appears to give large ECE reductions. The paper has several strengths: the problem framing is clear, the ablations in Tables 2 and 3 isolate the contributions of the structure and the objective, and the authors include multiple datasets and architectures, with five runs and standard deviations. The theoretical claims are meant to support the design, but as written the central construction is not well defined and one proposition is numerically false, which prevents the current version from being assessed reliably. The lack of source code and of any reporting of the fitted γ, β, and ρ values further undermines the testability of the empirical claims.

major comments (5)
  1. [Methodology, Eq. (2) and Algorithm 1] The ρ-norm in Eq. (2) is defined as ||z||_ρ = (z_1^ρ + ... + z_m^ρ)^{1/ρ} with no absolute values. Algorithm 1 grid-searches non-integer ρ ∈ {1, 1.25, ..., 3}, and classifiers routinely produce negative logits. For non-integer ρ, z_j^ρ is not real, so the expression is undefined on standard logits and the method as stated is not computable. If the implementation instead uses (Σ |z_j|^ρ)^{1/ρ}, that is a different mapping, and the proofs of Proposition 1 and the order-preserving argument must be restated for that norm. Since no source code is provided, the numerical results in Table 1 cannot be traced to any precisely specified function. This is the load-bearing issue for the paper's central claim.
  2. [Appendix, proof of Proposition 1 and Eq. (3)] The proof of Proposition 1 is not valid as written. The constraint in Eq. (7) is Σ r_j^ρ = 1/γ^ρ without absolute values, but the extremal solutions in Eqs. (15)-(16) set r_j negative for j ≠ c, which is undefined for non-integer ρ. Moreover, the claimed bound is numerically false: take m = 2, ρ = 2, γ = 1. The true maximum of g_c under the constraint is 1/(1 + e^{-√2}) ≈ 0.805, while the upper bound from Eq. (3) evaluates to 1/(1 + e^{-(1/2)^{3/2}}) ≈ 0.587, which is below the true maximum. Proposition 1 therefore cannot be used to justify the confidence-restricting behavior of the method.
  3. [Appendix, proof of Proposition 2] The proof of Proposition 2 is garbled. It contains the line "γ√(Σ z_j^2)+β" (Euclidean norm) instead of the ρ-norm used in Eq. (2), and the fragment "p(zj)=e^{zj/a}/b" is not a coherent derivation. The claim itself is true in the simple case where γ||z||_ρ + β > 0 (which holds for γ, β > 0 and a well-defined norm), because the denominator is positive and z_j → z_j/(positive constant) is strictly order-preserving. The proof needs to be rewritten cleanly for the actual ρ-norm in Eq. (2) (with absolute values if that is the intended definition).
  4. [Experiments and Reproducibility Checklist] The paper never reports the fitted values of γ, β, or the selected ρ for each dataset and model. Table 4 shows only a subset of candidate ρ values for ResNet35 and does not state which ρ was selected by Algorithm 1. The reproducibility checklist states "This paper lists all final (hyper-)parameters used for each model/algorithm in the paper's experiments (yes)", but this is not the case. In addition, no statistical significance tests are reported (the checklist answers "no" on that item), so the claimed improvements over the second-best baseline are not assessed for significance. These omissions make the strong empirical claims difficult to verify.
  5. [Experiments, Table 1 and Related Work] The paper claims state-of-the-art calibration performance but omits the closest parametric baselines. Parameterized Temperature Scaling (Tomani, Cremers, and Buettner 2022) is cited in the related work but never evaluated, and Dirichlet calibration (Kull et al. 2019) is also absent from Table 1. The comparison in Table 1 is limited to Histogram Binning, temperature scaling, vector scaling, and TS-AvUC. Adding these closely related methods is necessary to support the "state-of-the-art" claim, especially because the proposed structure is a generalization of parameterized scaling.
minor comments (5)
  1. [Methodology, Eq. (5)] The KL term in Eq. (5) is written as Σ_j g_j (log g_j - log s_j), which is KL(g || s). The text says it is the "KL divergence of the original output distribution s(z) concerning the calibrated probability distribution g(z)", which would suggest KL(s || g). The direction should be clarified.
  2. [Algorithm 1, line 3] The loop condition reads "while ρ ∈ {1, . . . ,3}" but the paper's grid search is {1, 1.25, ..., 3}. This is a typo that affects the reproducibility of Algorithm 1.
  3. [Table 1] The notation "(↓ 0.016)" after some entries is not defined in the caption. The caption mentions bold for best results and relative improvements, but the parenthetical arrow and number are unexplained.
  4. [Figure 4 caption] The caption says "Using sample-level SCE alone in post-calibration results in a significant deviation from the original distribution." SCE is a bin-level (set-level) objective, so "sample-level" is misleading; the sentence should say "set-level" or "bin-level".
  5. [Appendix, proof of Proposition 1, Eqs. (10)-(11)] Equations (10) and (11) contain unresolved "±" and "∓" signs. The signs must be fixed and the derivation must be completed before the proof can be checked.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the calibrator is fitted and evaluated empirically; the theoretical claims are independent derivations, not restatements of the inputs.

full rationale

No circularity found. The calibrator g(z) in Eq. (2) is a new parametric family; its parameters γ, β, and ρ are fitted on a validation set and evaluated on test data, which is standard empirical evaluation rather than a prediction forced by construction. The KL regularizer intentionally enforces similarity between pre- and post-calibration distributions, but this is a stated design objective, not a claimed independent result, and the paper does not present the resulting similarity as a prediction derived from first principles. Proposition 2's accuracy preservation follows from the strictly order-preserving form of the mapping (zj > zq implies pj > pq when the denominator is positive), and Proposition 1's bounds are obtained from a constrained optimization, not from the experimental outcomes. There are no load-bearing self-citations, and no uniqueness theorem is imported from prior work by the same authors. Selection of ρ via validation ECE is ordinary hyperparameter tuning and does not make the test ECE a fitted quantity. The main caveats are correctness and reproducibility concerns outside the circularity definition: Eq. (2)'s ρ-norm is not real-valued for negative logits and non-integer ρ as written, and the reproducibility checklist states that source code is not included; these undermine verifiability but do not constitute circular reasoning.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The method's central mapping depends on fitted scale and offset parameters, a grid-searched norm order, a hand-set regularizer weight, and a smoothing constant. The most fragile assumption is that the rho-norm is well-defined for negative logits; the paper does not state whether absolute values are used. No new entities are postulated.

free parameters (5)
  • gamma = not reported (optimized on validation)
    Scale parameter in denominator of ρ-Norm Scaling; fitted by gradient descent on loss (6).
  • beta = not reported (optimized on validation)
    Offset parameter in denominator; fitted together with gamma.
  • rho = not reported per dataset (grid search over 1 to 3 in steps of 0.25)
    Norm order; selected by validation ECE.
  • alpha = 1 (main experiments); varied in ablations
    Weight of the KL regularizer; hand-chosen, with sensitivity shown in Table 5.
  • kappa = 1e-4
    Smoothing constant for the sum-exp-up approximation of max confidence.
assumptions (4)
  • domain assumption The validation set used to fit calibrator parameters is representative, and ECE on validation is a reliable selection criterion for rho.
    Parameters gamma, beta, and rho are fit or selected on a validation set (Algorithm 1), then ECE is reported on test; this assumes no significant distribution shift and no overfitting to validation ECE.
  • ad hoc to paper Classifier logits can be treated as nonnegative, or the rho-norm is computed with absolute values.
    Equation (2) defines z_j^rho without absolute values and grid-searches non-integer rho; for negative logits this is not real-valued. The paper never states this assumption.
  • domain assumption The bin-level SCE with batch-as-bin approximates population calibration error.
    Equation (4) treats each mini-batch as a bin, with a small kappa smoothed max; this is an approximation to ECE used for optimization.
  • ad hoc to paper The KL divergence g log(g/s) preserves useful instance-level information, and alpha=1 is a reasonable balance.
    The regularizer and weight alpha are introduced ad hoc; Table 5 shows sensitivity to alpha.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Parametric $\rho$-Norm Scaling Calibration." pith.science (2026). https://pith.science/paper/OUGIFROQ

@misc{pith2026241215301,
  author       = {Pith},
  title        = {Pith review of: Parametric $\rho$-Norm Scaling Calibration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OUGIFROQ}},
  note         = {Machine review of arXiv:2412.15301}
}
abstract

Output uncertainty indicates whether the probabilistic properties reflect objective characteristics of the model output. Unlike most loss functions and metrics in machine learning, uncertainty pertains to individual samples, but validating it on individual samples is unfeasible. When validated collectively, it cannot fully represent individual sample properties, posing a challenge in calibrating model confidence in a limited data set. Hence, it is crucial to consider confidence calibration characteristics. To counter the adverse effects of the gradual amplification of the classifier output amplitude in supervised learning, we introduce a post-processing parametric calibration method, $\rho$-Norm Scaling, which expands the calibrator expression and mitigates overconfidence due to excessive amplitude while preserving accuracy. Moreover, bin-level objective-based calibrator optimization often results in the loss of significant instance-level information. Therefore, we include probability distribution regularization, which incorporates specific priori information that the instance-level uncertainty distribution after calibration should resemble the distribution before calibration. Experimental results demonstrate the substantial enhancement in the post-processing calibrator for uncertainty calibration with our proposed method.

Figures

Figures reproduced from arXiv: 2412.15301 by the authors.

Figure 1
Figure 1. Overview of our proposed post-hoc calibrator structure and optimization objective after pipeline of classifier optimization: (1) Addressing the issue of output magnitude amplification during supervised learning, we introduce a ρ-Norm Scaling calibration within the post-calibration framework. (2) Uncertainty represents the entire dataset statistically, making its optimization prone to losing sample-level information.… view at source ↗
Figure 2
Figure 2. Amplitude changes in classifier optimization. In these figures, the overall output magnitude of all samples is defined as 1 Nm PN i=1 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Confidence histograms and reliability diagrams for different post-hoc calibration methods with ResNet35 on CIFAR-100. Confidence histograms display the sample count within each bin, whereas reliability diagrams illustrate the difference between the average confidence (marked in red) and the accuracy (indicated in blue) in each bin. e P rj m j=1 e rj and rj (z) = zj γ2∥z∥ρ+β2 . The function for max confidence in each… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Coincidence distribution of different optimiza￾tion objective in Vector Scaling. In (a), samples are catego￾rized into bins based on confidence levels through Softmax. Each sample in (b) and (c) belongs to the same bin as in (a). Using sample-level SCE alone in post-ca…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 36 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.a...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    E.; and Deisenroth, M

    Calandra, R.; Peters, J.; Rasmussen, C. E.; and Deisenroth, M. P. 2016. Manifold Gaussian processes for regression. In International joint conference on neural networks (IJCNN), 3338--3345. IEEE

    work page 2016

  4. [4]

    Gal, Y.; and Ghahramani, Z. 2016. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International Conference on Machine Learning, 1050--1059. PMLR

    work page 2016

  5. [5]

    Ghosh, A.; Schaaf, T.; and Gormley, M. 2022. AdaFocal: Calibration-aware adaptive focal loss. In Advances in Neural Information Processing Systems, volume 35, 1583--1595

    work page 2022

  6. [6]

    Guo, C.; Pleiss, G.; Sun, Y.; and Weinberger, K. Q. 2017. On calibration of modern neural networks. In International Conference on Machine Learning, 1321--1330. PMLR

    work page 2017

  7. [7]

    H.; and Friedman, J

    Hastie, T.; Tibshirani, R.; Friedman, J. H.; and Friedman, J. H. 2009. The elements of statistical learning: data mining, inference, and prediction, volume 2. Springer

    2009

  8. [8]

    Hendrycks, D.; Lee, K.; and Mazeika, M. 2019. Using pre-training can improve model robustness and uncertainty. In International Conference on Machine Learning, 2712--2721. PMLR

    work page 2019

Show all 41 references
  1. [9]

    C.; and Roelofs, B

    Karandikar, A.; Cain, N.; Tran, D.; Lakshminarayanan, B.; Shlens, J.; Mozer, M. C.; and Roelofs, B. 2021. Soft calibration objectives for neural networks. In Advances in Neural Information Processing Systems, volume 34, 29768--29779

    2021

  2. [10]

    Krishnan, R.; and Tickoo, O. 2020. Improving model calibration with accuracy versus uncertainty optimization. In Advances in Neural Information Processing Systems, volume 33, 18237--18248

    2020

  3. [11]

    Kull, M.; Perello Nieto, M.; K \"a ngsepp, M.; Silva Filho, T.; Song, H.; and Flach, P. 2019. Beyond temperature scaling: Obtaining well-calibrated multi-class probabilities with dirichlet calibration. In Advances in Neural Information Processing Systems, volume 32

    2019

  4. [12]

    Kull, M.; Silva Filho, T.; and Flach, P. 2017. Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers. In Artificial Intelligence and Statistics, 623--631. PMLR

    2017

  5. [13]

    Kumar, A.; Sarawagi, S.; and Jain, U. 2018. Trainable calibration measures for neural networks from kernel mean embeddings. In International Conference on Machine Learning, 2805--2814. PMLR

    2018

  6. [14]

    Lei, B.; Zhang, R.; Xu, D.; and Mallick, B. 2022. Calibrating the Rigged Lottery: Making All Tickets Reliable. In International Conference on Learning Representations

    2022

  7. [15]

    Lin, T.-Y.; Goyal, P.; Girshick, R.; He, K.; and Doll \'a r, P. 2017. Focal loss for dense object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2980--2988

    2017

  8. [16]

    Liu, B.; Rony, J.; Galdran, A.; Dolz, J.; and Ben Ayed, I. 2023. Class adaptive network calibration. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 16070--16079

    2023

  9. [17]

    K.; Rawat, A

    Menon, A. K.; Rawat, A. S.; Reddi, S. J.; Kim, S.; and Kumar, S. 2020. Why distillation helps: a statistical perspective. arXiv preprint arXiv:2005.10419

    2020 arXiv

  10. [18]

    Milios, D.; Camoriano, R.; Michiardi, P.; Rosasco, L.; and Filippone, M. 2018. Dirichlet-based gaussian processes for large-scale calibrated classification. In Advances in Neural Information Processing Systems, volume 31

    2018

  11. [19]

    Moon, J.; Kim, J.; Shin, Y.; and Hwang, S. 2020. Confidence-aware learning for deep neural networks. In International Conference on Machine Learning, 7034--7044. PMLR

    2020

  12. [20]

    Mukhoti, J.; Kulharia, V.; Sanyal, A.; Golodetz, S.; Torr, P.; and Dokania, P. 2020. Calibrating deep neural networks using focal loss. In Advances in Neural Information Processing Systems, volume 33, 15288--15299

    2020

  13. [21]

    P.; Cooper, G.; and Hauskrecht, M

    Naeini, M. P.; Cooper, G.; and Hauskrecht, M. 2015. Obtaining well calibrated probabilities using bayesian binning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 29

    2015

  14. [22]

    Nguyen, K.; and O’Connor, B. 2015. Posterior calibration and exploratory analysis for natural language processing models. In Proceedings of the Conference on Empirical Methods in Natural Language Processing, 1587--1598

    2015

  15. [23]

    Niculescu-Mizil, A.; and Caruana, R. 2005. Predicting good probabilities with supervised learning. In International Conference on Machine Learning, 625--632

    2005

  16. [24]

    Platt, J.; et al. 1999. Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. Advances in Large Margin Classifiers, 10(3): 61--74

    1999

  17. [25]

    Rahimi, A.; Shaban, A.; Cheng, C.-A.; Hartley, R.; and Boots, B. 2020. Intra order-preserving functions for calibration of multi-class neural networks. In Advances in Neural Information Processing Systems, volume 33, 13456--13467

    2020

  18. [26]

    Si, C.; Zhao, C.; Min, S.; and Boyd-Graber, J. 2022. Re-Examining calibration: The case of question answering. In Findings of the Association for Computational Linguistics: EMNLP 2022, 2814--2829

    2022

  19. [27]

    Tao, L.; Dong, M.; Liu, D.; Sun, C.; and Xu, C. 2023. Calibrating a deep neural network with its predecessors. arXiv preprint arXiv:2302.06245

    2023 arXiv

  20. [28]

    Tao, L.; Dong, M.; and Xu, C. 2023. Dual focal loss for calibration. In International Conference on Machine Learning

    2023

  21. [29]

    A.; Bhattacharya, T.; and Michalak, S

    Thulasidasan, S.; Chennupati, G.; Bilmes, J. A.; Bhattacharya, T.; and Michalak, S. 2019. On mixup training: Improved calibration and predictive uncertainty for deep neural networks. In Advances in Neural Information Processing Systems, volume 32

    2019

  22. [30]

    Tomani, C.; Cremers, D.; and Buettner, F. 2022. Parameterized temperature scaling for boosting the expressive power in post-hoc uncertainty calibration. In European Conference on Computer Vision, 555--569. Springer

    2022

  23. [31]

    V.; Cunningham, J.; Michiardi, P.; and Filippone, M

    Tran, G.-L.; Bonilla, E. V.; Cunningham, J.; Michiardi, P.; and Filippone, M. 2019. Calibrating deep convolutional gaussian processes. In International Conference on Artificial Intelligence and Statistics, 1554--1563. PMLR

    2019

  24. [32]

    Wang, D.-B.; Feng, L.; and Zhang, M.-L. 2021. Rethinking calibration of deep neural networks: Do not be afraid of overconfidence. In Advances in Neural Information Processing Systems, volume 34, 11809--11820

    2021

  25. [33]

    Wang, Y.; Li, L.; and Dang, C. 2019. Calibrating classification probabilities with shape-restricted polynomial regression. IEEE Transactions on Pattern Analysis and Machine Intelligence, 41(8): 1813--1827

    2019

  26. [34]

    Wei, H.; Xie, R.; Cheng, H.; Feng, L.; An, B.; and Li, Y. 2022. Mitigating neural network overconfidence with logit normalization. In International Conference on Machine Learning, 23631--23644. PMLR

    2022

  27. [35]

    Wen, Y.; Tran, D.; and Ba, J. 2019. BatchEnsemble: an alternative approach to efficient ensemble and lifelong learning. In International Conference on Learning Representations

    2019

  28. [36]

    Wenger, J.; Kjellstr \"o m, H.; and Triebel, R. 2020. Non-parametric calibration for classification. In International Conference on Artificial Intelligence and Statistics, 178--190. PMLR

    2020

  29. [37]

    Widmann, D.; Lindsten, F.; and Zachariah, D. 2019. Calibration tests in multi-class classification: A unifying framework. In Advances in Neural Information Processing Systems, volume 32

    2019

  30. [38]

    Yu, Y.; Bates, S.; Ma, Y.; and Jordan, M. 2022. Robust Calibration with Multi-domain Temperature Scaling. In Advances in Neural Information Processing Systems, volume 35, 27510--27523. Curran Associates, Inc

    2022

  31. [39]

    Zadrozny, B.; and Elkan, C. 2001. Obtaining calibrated probability estimates from decision trees and naive bayesian classifiers. In International Conference on Machine Learning, volume 1, 609--616

    2001

  32. [40]

    Zadrozny, B.; and Elkan, C. 2002. Transforming classifier scores into accurate multiclass probability estimates. In Proceedings of the eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 694--699

    2002

  33. [41]

    Zhang, Z.; and Xiang, X. 2023. Decoupling maxlogit for out-of-distribution detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 3388--3397

    2023

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.