Improving Perturbation-based Explanations by Understanding the Role of Uncertainty Calibration
Authors: Thomas Decker
Volker Tresp
Florian Buettner
Venue: NeurIPS 2025 spotlight ()
Keywords: Explainable AI
Uncertainty Calibration
Perturbation-based Explanations
Primary area: social_and_economic_aspects_of_machine_learning

Abstract: Perturbation-based explanations are widely utilized to enhance the transparency of machine-learning models in practice. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This paper investigates the relationship between uncertainty calibration - the alignment of model confidence with actual accuracy - and perturbation-based explanations. We show that models systematically produce unreliable probability estimates when subjected to explainability-specific perturbations and theoretically prove that this directly undermines global and local explanation quality. To address this, we introduce ReCalX, a novel approach to recalibrate models for improved explanations while preserving their original predictions. Empirical evaluations across diverse models and datasets demonstrate that ReCalX consistently reduces perturbation-specific miscalibration most effectively while enhancing explanation robustness and the identification of globally important input features.

Improving Perturbation-based Explanations by Understanding the Role of Uncertainty Calibration
Thomas Decker
Volker Tresp2. 2.3
Florian Buettner
Siemens AG
LLM Munich
Munich Center for Machine Learning (MCML)
'Goethe University Frankfurt
German Cancer Research Center (DKFZ)
*German Cancer Consortium (DKTK)
thomas. decker com, volker. www.erttreeemmm.mmmmmmmmmmm de, florian, buettneråkkf..dd
Abstract
Perturbation- based explanations are widely utilized to enhance the transparency pacchiee-learing models in practice. However, their reliability is often compro- mised by the unknown model behavior under the specific perturbations used. This paper investigates the relationship between uncertainty calibration the alignment of model confidence with actual accuracy and perturbation-ben explanations. We show that models systematically produce unreliable probability estimates when subjected to explainability-speciii
perturbations and theoretically prove that this directly undermines global and local explanation quality. To address this, we intro- duce ReCalX, a novel approach to recalibrate models for improved explanations while preserving their original predictions. Empirical evaluations across diverse models and datasets demonstrate that ReCalX consistently reduces perturbation- specific miscalibration most effectively while enhancing explanation robustness and the identification of globally important input features.
Introduction
The ability to explain model decisions and ensure accurate confidence estimates are fundamental requirements for deploying machine learning systems responsibly (34) Perturbation-basee techniques [54] have been established as a popular way to enhance model transparency in practice [6] [4]. Such methods systematically modify input features quantify their importance by evaluating and aggregating subsequent changes in model outputs [IT]. This intuitive principle and the flexibility explain any prediction model-agnostic way has led to widespread adoption across various domains BT.
Nevertheless, the application of perturbation-based techniques faces fundamental challenge: These methods operate by generating inputs that differ substantially from the training distribution [26] 20 and models often produce invalid outputs for such perturbed samples [18] g 32]. Consequently,
forming explanations by aggregating misleading predictions under perturbations can significantly distort the outcome and compromise its fidelity. On top of that, this can also contribute to fre-
quently observed instabilities of perturbation- based explanations I 4 38 13], which reduces their
effectiveness and could even be exploited for malicious manipulations
55
These issues naturally raise the question of how to attain reliable model outputs under the specific perturbations used when deriving explanations. A classical approach for this purpose is uncertainty calibration [46] 45 25 It aims to ensure that a model's confidence aligns with its actual accuracy, which is crucial to obtaining meaningful probabilistic predictions. Consider, for instance, the situation in Figure [ where a classifier detects a bee in the image with 99% confidence. Then this value is only reliably interpretable if for all predictions with corresponding confidence, precisely 99% are indeed correct. While calibration has been extensively studied in the machine learning literature [63], its
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Uncalibrated:
Uncalibrated:
P(Bee)=0,99
P(Bee)=0099
ReCalX:
ReCalX:
P(Bee)=0.99
P(Bee)=0.92
Perturbation Strength
ML
Uncalibrated:
Uncalibrated:
P(Bee)=0.77
P(Bee)m0034
ReCalX:
ReCalX:
P(Bee)=0.42
P(Bee)=0.02
Perturbation-based Explanation
Calibration Error
trated RaCMi
Uncalibrated Explanation
Explanation with ReCaiX
0.0
Perturbation Strength
Figure 1: Perturbation-basee explanation methods typically query the model on modified inputs and aggregate the resulting prediction changes to identify relevant features. However, we show that models typically produce significantly miscalibrated output probabilities under commonly used perturbations. This means that the underlying predictions used derive explanations do reflect actual changes in class likelihoods, obscuring true feature importance. To mitigate this, we propose ReCalX simple recalibration technique that enables reliable outputs under perturbations, leading to more informative explanation results.
role explanation methods remains largely unexplored. First empirical evidence suggests that basic calibration might indeed benefit explainability (55] 39 40), but rigorous theoretical understanding still missing. In this work, we provide the first comprehensive analysis of the relationship between uncertainty calibration and perturbation-based explanations. Our findings establish calibration as a fundamental prerequisite for reliable model explanations and propose practical solution for enhancing the quality of perturbation-batt explanation methods (see Figure
More precisely, we make the following contributions:
We provide rigorous theoretical analysis revealing how poor calibration can bias the results common perturbation based explainability techniques.
We show that common neural classifiers for tabular and image data exhibit high levels of miscalibration under explainability-relate perturbations.
We propose ReCalX, novel approach that increases the reliability of model outputs under the particular perturbations used to derive explanations and validate its effectiveness.
We demonstrate that after applying ReCalX, explanation results are significantly more robust and better identify input features that are relevant for high performance.
2 Background and Related Work
Basic Notation Consider a probability space (2, (,P), where is the sample space, F a a- algebra of events, and P is probability measure. Let X Ω X' be random variable representing the feature space X. and let Y : - + joint data distribution of (X,Y) Y) is denoted by Рx,,, the conditional distribution of Y given X by Pyix, and the marginal distributions by Px, Py. During our theoretical analysis, we will also make of the following quantities. The mutual information between two random variables X and Y. measures the reduction in uncertainty of one variable given the other and is defined as:
random variable representing the target space y. The
T(X,Y) (X,Y)= = -{(M)) log Px,r(X,Y)
Px(X)Py

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A related measure is the Kullback-Leibler (KL) divergence, which expresses the difference between two probability distributions P and Q over the same sample space:
(P(()) = Ex log P(X) Q(X)
Perturbation-baser Explanations Perturbation-base explanations quantify the importance of individual input features by evaluating how model output changes under specific input corruptions. Let f X - [0, l| be classification model over K classes, where X' S IR is the d-dimensional input space. Given a sample x E X, a perturbation- based explanation produces an importance vector <(x) E Rd, where (z) quantifies the importance of feature To derive 6(x), we first introduce perturbation function ı X' x 2(I.....) + X' that, given an instance and subset of feature indices S S d), returns a perturbed instance т (ar, S) where features in remain unchanged while modified. Various perturbation strategies have been investigated 160 9 [1]. with common approaches being the replacement of features with fixed baseline values
the complementary features
32 or blurring [99 33 for images. The model prediction under such perturbation is given by:
fz == f((x)==(T(r;55)) (TT(x
To compute the final explanation o, the outcomes of fs for different subsets S are systematically examined and aggregated. While numerous strategies exist for this purpose [9 17 47 66 [53] 42). we focus on methods that employ a linear summary strategy (38]. In this case, there exists a summary matrix A E Iddx such that ((x) A0(x). where & E R contains the predictions fs)) for all possible subset perturbations S. Two prominent methods in this category are Shapley Values 42
and LIME (53)
Uncertainty Calibration In general, model is said to be calibrated if its predicted confidence levels correspond to empirical accuracies for all confidence levels. Formally, this calibration property requires that Sy)((X) f(X) [7 59 24). In classification, this intuitively implies, that for any
confidence level p E [0. 1] it holds:
P(Y f(X)x =)
Vk (1..... K},
where f(X)x denotes the predicted probability for class and Y is the true label. This means that among all instances for which the model predicts a class with probability approximately a p fraction should be correctly classified. In practice, modern neural classifiers often exhibit miscalibration
25 44, in particular when facing out-of-distribution samples [88 61 65 This can be formalized
using a calibration error ( (CE), which quantifies the mismatch between ((X) and Pyis())- this work, will consider the KL- EL--ivergence-base
calibration error [51]. this is the proper calibration
error directly induced by the cross- coss-entropy loss which is typically optimized for in classification:
CE E DKz. (Prirc))l(((x)]
Our work investigates how violations of this calibration property affect the quality of the derived explanations ((x) and develops methods to improve calibration specifically for perturbation based techniques, which has not been analyzed before.
3 Understanding the Effect of Uncertainty Calibration on Explanations
In this section, we provide a thorough mathematical analysis of how poor calibration under explainability perturbation can degrade global and local explanation results. All under- lying proofs and further mathematical details are provided in Appendix A.
Effect on Global Explanations Calibration is inherently global property of a model related to the
entire data distribution and in general, is impossible to evaluate for individual samples (69
Hence, we first analyze its effect on global explanations about the model behavior [41 such as the
importance of individual features for overall model performance [12 Following 12 we define the global predictive power of feature subset S for model f. as follows:

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Definition 3.1. Let S C fl.....d] d be feature subset and let fī be the model that only observes features in S while the other are perturbed using a predefined strategy म, then the predictive power vz (S) for model f and a loss function L y x 3 - IR+ is defined as:
2y (S) = E -
Note, that the predictive power captures the performance increase resulting from observing features in S compared to a baseline prediction where all features are perturbed using In classification, models are typically optimized for the cross-entropy loss (CE(s(a),,) y) = log (o We show that in this case the predictive power can be decomposed follows:
Theorem 3.2. Let LCE be the cross-entropy loss, -xi(-.-) be the KL-Divergence between two distributions, and let I(:,)) denote the mutual information between random variables. Then we have:
(S) (xI (1
(X3(X);Y)
Perturbation Baveline Bias
Information f3 about
Calibration Error f3
This theorem is in line with existing decomposition results 7 36 24 that hold for a general class of performance measures related to proper scoring rules (2I), including LCE. It further allows for an intuitive interpretation of what drives the predictive power when evaluated with specific perturbation and reveals a fundamental relationship with calibration. The first term can be interpreted as bias due to the perturbation strategy, implying that an optimal uninformative baseline prediction should yield Py. The second term is the mutual information between the target Y and the model that only observes features in S. This corresponds to the reduction in uncertainty about the target Y that knowledge about fī provides. The third term is the -i-Divergence-baeee calibration error of the restricted model 1 when facing the perturbation и. The theorem implies that if the model to be explained produces unreliable predictions under the perturbation used, then the resulting calibration error directly undermines the predictive power. Moreover, Theorem 3.2 has the following immediate consequence:
Corollary 3.3. If a model f is perfectly calibrated under all subset perturbations faced during the explanation process, then we have:
(18)=1([](X))))
This implies that / (X), can be considered an idcalized predictive power that can only be attained when the model always gives perfectly calibrated prediction under every perturbation faced. Note this also directly extends a corresponding result in [12 showing that this relationship holds for the naive Bayes classifier Pr|x- It rather holds for any model that is perfectly calibrated under the perturbations faced, which is also the case for Pylx. Moreover, explaining by directly approximating similar mutual information objectives has also been proposed as distinct way to enhance model transparency 10 56
Effect on Local Explanations Local explanations enable the understanding of which features are important for an individual prediction. As emphasized above, calibration group-level property so evaluating it for a single sample is impossible. Nevertheless, we can still estimate how an overall calibration error under the perturbations might propagate to an individual explanation result:
Theorem 3.4. Let Φ(x) be a local explanation for input x with respect to model prediction fax and perturbation w. Let o² (I)) denote the explanation that would be obtained if the model f were perfectly calibrated under all subset perturbations. Define the maximum calibration error across all perturbation subsets as: C. == maxscld ( Then, with probability at least (1 8). the mean squared difference belween the actual and ideal explanations is bounded by:
1 2 (l(((=) - -00 < = 2C + / (8/8))
The theorem above shows that poor calibration under perturbations can at worst also directly distort the outcomes of a local explanation result ((z) Importantly, it demonstrates that order to improve
Note that the particular bound presented in Theorem 3.4 holds specifically for perturbation based methods with a bounded linear summary strategy which is satisties by many popular choices such as Shapley Values and LIME. In Appendix A we provide a more general version of this theorem that equivalently holds for non nonelr aggregation approaches.

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explanation quality through uncertainty calibration, it is insufficient to only reduce the calibration error on unperturbed samples. as proposed by [55]. Instead, reliable explanations explicitly require models to be well-calibrated under all subset perturbations л (T., S) used during the explanation process. In the next section, we propose an actionable technique, called ReCalX, to achieve this goal.
Improving Explanations with Perturbation-speccfic Recalibration
Recalibration techniques aim to improve the reliability of the probability estimates for already trained model in a post-hoc manner. While a variety of different algorithmic approaches exist for this purpose [57]. none of them is explicitly designed enhance explanations. In this section, introduce ReCalX as a novel and practical approach to recalibrate models to achieve both more reliable confidences and better perturbation- -based explanations simultaneously.
Cnoommation-prseevinng Calibration Recalibration methods typically transform the model's origi- nal outputs to better align predicted probabilities with empirical frequencies (57]. However, arbitrarily postprocessing predictions might distort the underlying model behavior, which we originally sought to explain. Hence, we first introduce the concept of information- prrironiipeeeiiigggggg recalibration:
Definition 4.1. Let f X + [o, 1]K be classifier and T : [0, 1] x 2(!....d) + [0, 1]K be recalibration function that post-procees proccssecssss raw probabilities depending on the unperturbed feature subset S. Then T is information- -ereerrvinnneeiiinggggo if for all feature subsets S S f1.....d}
(TT
can be considered as idealized predictive power of subset under perfect calibration. Thus, we want any calibration method preserve this quantity in order to attain explanations that are consistent with the original model we intended to explain. This can, for instance, be achieved using calibration maps' T of the following kind:
Remember Corollary 3.3. implies that
Proposition 4.2. Let T [0, 1jK 2(1....d) + [0. 1jK be a deterministic and componentwise strictly monotonic function for every fixed S. Then T is informatiion-preseviigg
The proof of this proposition is provided in Appendix along with further mathematical details. Note that [68] has shown that such calibrators also ceturaacy-preervvnng meaning that they will not affect the original model predictions as the ranking of outcomes remains unchanged. Moreover, many
existing techniques for post-hoc calibration satisfy this property 25 37 also suitable to enhance perturbation- based explanation.
68
52]
and are therefore
Recalibration for Explanations (ReCalX) Based on theoretical analysis, ideal recalibration method for explanations should satisfy two key requirements: (1) should be information information-preservingg as defined in Definition 4.1, and (2) it should effectively reduce calibration error under all perturbations faced during the explanation process. For the first requirement, we focus on calibration methods that are componentwise strictly monotonie, and among these, temperature scaling has emerged as the most widely adopted method due to its simplicity and empirical effectiveness (25] 44). Given a
model X + jo, 11dd that outputs logits z(x) RK before the final softmax layer, temperature scaling introduces a single scalar parameter T > 0 that additionally rescales the logits:
(x)(2x(x)/T))
f(; = Σ/= exp(2;(x)/T)
The temperature parameter T is optimized on a held-out validation set, typically by minimizing the cross-entropy loss Lee in the case of classification. To address the second requirement, propose to go beyond classical temperature scaling and introduce ReCalX as a generalized version. aims to reduce the calibration error under all perturbations faced during the explanation process by scaling logits using an adaptive temperature that depends on the perturbation level implied by S. Formally, for subset S C [1, [1..... ......dd., d). define the perturbation level X(S) as the fraction of perturbed features: X(5) = (d / /d E 1). To account for different perturbation intensities, we partition [0, into B eiuh bins and leam specific temperature for each bin. Given validation set Deai = (2i, / we optimize a temperature T₁ for each bin by minimizing the cross-entropy loss Lce on perturbed samples with corresponding perturbation levels. Note that in this way, we directly
5

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optimize the SL-Divergenceebasee calibration error, while the discriminative power and ranking of predictions remain unaffected. This results in set of temperature parameters that adapt to different perturbation intensities, enabling better calibration across all explanation-relevant perturbations. A more detailed description of the algorithm presented in Appendix B. During the explanation process, ReCalX infers the perturbation-level and applies the corresponding temperature (S) when making predictions:
exp(2)(T(x, S))T(()
Reeaxx (z. S; (Tolma))
Ak = K
==1
where T(S) selects the temperature from {To] based on the bin index b containing the pertur- bation level of S. This adaptive temperature scaling ensures appropriate confidence calibration for different perturbation intensities, ultimately aiming towards more reliable explanations by reducing the maximum calibration error across all perturbation subsets CLR..
Applying ReCaIX beyond Classification The algorithmic implementation of ReCalX presented above relies on temperature scaling, which specific to classification problems. However, both our theoretical framework and the underlying principle of perturbation-specifi recalibration extend naturally to other predictive modeling tasks as well. For a regression setup, consider model : + P(Y) that outputs probability distribution over a continuous target space ) C R. Note that all theoretical results developed in Section 3 hold equivalently when explaining probabílistic regression outputs with perturbation-basel methods. Also the notion of information- prteriovnn-reeriinnggg calibration (Definition 4.1) and the requirement for strictly monotonic transformations to preserve the model's 'ss learned information content extend directly to this setting. While temperature scaling can be used for classification, alternative techniques such as affine transformations [50] or injective variants of isotonic regression [68] satisfy the monotonicity property more generally. Therefore such techniques are also applicable to perform appropriate calibration for regression models. In Appendix C, we conducted corresponding experiments that ReCalX effectively reduces the quantile- baasd calibration error 351 under explainability-spee perturbations for regression tasks well.
two tabular regression datasets, which demonstrate
Experiments
We conducted comprehensive empirical evaluation of ReCalX considering neural classifiers on different tabular datasets [23] [2 and various computer vision models on the ImageNet ILSVRC2012 dataset. Detailed descriptions of all experiments and further computational details are provided in Appendix B. while additional results supporting each finding are presented in Appendix C. Accompanying source code is available at https:/ / http///gtttttbtt www. thondeck/eeaaax.
Analyzing Calibration under explainability-speiffi Perturbations We first investigate how the calibration properties of neural classifiers are affected by common perturbations used in explanation methods. To implement ReCalX, we selected 200 random validation samples from each considered dataset and used 10 perturbed instances per considered perturbation level. This results in a calibration set of 2000 samples per bin. We explicitly evaluated the l--Divergence-based calibration error using the consistent and asymptotically unbiased estimator proposed by [5]] to be fully aligned with our theoretical analysis above. Each error is derived based on at least 5000 unseen samples from each dataset. Tables [ and present corresponding calibration errors for tabular and image models under different perturbation strategies. For tabular data (Table Tp. we evaluate a standard Multi-
(MLP) as well as a tabular ResNet model [22] across four datasets using mean value replacement as perturbation. For image data (Table 2 we assess diverse architectures represented by a ResNet50 (27). a DenseNet121 [30]. a VIT [16] and SigLIP (67) zero-shot model using both zero baseline and blur as perturbations. The results reveal substantial miscalibration across all models when subjected to explanation-specii perturbations. For tabular data, uncalibrated models exhibit maximum KL-divergence calibration errors (C (CEMAXs) ranging from 0.012 to 0.863, while image models show errors between 0.037 and 0.418. Standard temperature scaling, which only calibrates using a static temperature unperturbed samples, often fails to address this issue and can even worsen calibration under perturbations (e.g., increasing the maximum error from 0.262 to 0.306 for ViT). On the other hand our adaptive ReCalX approach consistently improves calibration with

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substantial reductions in the average and maximum encountered error. In Appendix C, we present complementary results on other datasets confirming the efficacy of ReCalX.
Uncalibrated
Temperature Scaling
ReCalX
Dataset
CE
CE
EMXA C
AAVVs KL
CEMAX
+MAX (%
MLP Model
Electricity
0.0423
0.1534
0.0452
0.1664
0.0097
0.0163
89.4%
Covertype
0.0412
0.0797
0.0564
0.1115
0.0047
0.0061
92.3%
Credit
0.2127
0.4763
0.2638
0.5961
0.0355
0.0533
88.8%
Pol
0.1740
0.6735
0.1689
0.6521
0.0570
0.1679
75.1%
ResNet Model
Electricity
0.0032
0.0118
0.0090
0,0355
0.0017
0.0049
58.5%
Covertype
0.0439
0.0963
0.0614
0.1413
0.0058
0.0080
91.7%
Credit
0.0721
0.0830
0.0778
0.0847
0.0366
0.0773
6.9%
Pol
0.2853
0.8633
0.3187
1.0173
0.0727
0.0910
89.5%
Table 1: Calibration error comparison actoss datasets for MLP and ResNet models using mean value replacement perturbation. C' C'E and C.MAAs represent average and maximum KL divergence- based calibration errors, across perturbation levels. Lower values indicate better calibration. The improvement column (IMAx) shows the relative reduction in maximum calibration error achieved by ReCalX compared to uncalibrated models. ReCalX consistently outperforms both uncalibrated models and Temperature Scaling across all settings, with improvements ranging from 6.9% to 92.3%.
Uncalibrated
Temperature Scaling
ReCalX
Model
CEN
CEMAX
CEAVAa
C CEMAXs
CEAAVGs
C MAXs KL
+MAX (%)
Zero Baseline Perturbation
ResNet50
0.2240
0.4177
0.0595
0.1810
0.0092
0.0128
96.9%
DenseNet121
0.1626
0.3769
0.0965
0.2640
0.0060
0.0098
97.4%
ViT
0.0936
0.2618
0.1172
0.3057
0.0045
0.0078
97.0%
SigLIP
0.0721
0.2013
0.0449
0.1476
0.0130
0.0300
85.1%
Blur Perturbation
ResNet50
0.2467
0.4158
0.0618
0.1659
0.0127
0.0139
96.7%
DenseNet121
0.0351
0.0714
0.0113
0.0259
0.0057
0.0092
87.1%
ViT
0.0137
0.0365
0.0224
0.0559
0.0041
0.0072
80.3%
SigLIP
0.0256
0.0547
0.0104
0.0246
0.0055
0.0098
82.1 12.1%
Table Calibration error comparison across models and perturbation types. CEAVS and C.-MMAN represent average and maximum KL divergence- calibration errors, across perturbation levels. Lower values indicate better calibration. The improvement column (4Max) shows the relative reduction in maximum calibration error achieved by ReCalX compared to uncalibrated models. ReCalX consistently outperforms both uncalibrated scores and basic Temperature Scaling across all settings, yielding substantial improvements with relative maximum calibration error reductions of 80%.
To further validate the robustness and generality of ReCalX, we conducted several additional sensitiv- ity and ablation experiments detailed in Appendix C. summary, the results confirm that ReCalX remains highly effective even for advanced domain-specific perturbation methods and show that miscalibration patterns can exhibit strong correlations across different perturbation types. Further- more, ReCalX achieves most of the potential calibration improvements with only few hundred validation samples, and using a higher number of perturbation level bins B typically yields monotonic improvements with diminishing returns beyond 10 bins.
To better understand the relationship between miscalibration and the number of perturbed features during the explanation process, present calibration errors as function of the perturbation level.

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Figure 2 visualizes the normalized calibration error across 10 different tabular datasets. For both models, miscalibration tends increase uniformly with higher perturbation levels. Fogure the high variability of calibration properties across perturbation strengths, while also indicating that errors do not always grow. The ResNet50, for instance, exhibits worse miscalibration at lower perturbation levels, and we provide additional examples in Appendix C. These diverse miscalibration patterns across models and perturbation strengths highlight the need for adaptive recalibration strategies like ReCalX, which consistently reduces maximum calibration errors across all settings, significantly outperforming standard temperature scaling. Next, we want to validate whether these improvements also translate better perturbation- based explanation results.
MLP
ResNet
Calibration Error (CFx)
1.0
Uncelibreted ReCalX
0.8
0.8
Normalized
0.4
0.2
0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
0.8
Perturbation Strength
Perturbation Strength
Figure 2: Normalized calibration emrors aggregated across 10 tabular datasets for an MLP (left) and ResNet model (right), including 95% confidence intervals. For both models, the miscalibration under the mean replacement perturbation tends to increase uniformly with higher perturbation levels.
ResNet50
DenseNet
SigLIP
Calloration Error (CE..)
0.4
Uncalibrated ReCaix
0.35
ReCalX
Uncalibreted
0.25
Uncalibrated
ReCaiX
0:200
Uncalibrated
RaCal
0.3
0.125
0.-
0.200
0.10
0.060
0.005
0.00
0.0
0.2
0.4
0.5
0.3
0.0
022
0.4
06
0.0
0.2
0.4
0.6
0.8
0.5
0.2
0.4
0.5
0.3
Perturbation Strength
Perturbation Strength
Perturbation Strength
Perturbation Strength
Figure 3: Calibration eгror results for popular image classifiers on ImageNet under fixed baseline perturbation with zeros. Across all methods, miscalibration varies significantly across the perturbation severity. While also for most image models the еттог tends to grow with perturbation level, for ResNet50, miscalibration is worst for lower levels. This flexible behavior highlights the importance of calibration strategies that are adaptive to the perturbation strength.
Global Remove and Retrain Fidelity As a first experiment, evaluated whether ReCalX improves the ability to identify truly important features that model relies on. This global fidelity can be assessed through semove-and-retraie experiments [2 [2]. where features are sequentially removed according to their importance ranking, and the model is retrained to measure the actual performance degradation caused. Higher performance drops indicate more accurate identification of genuinely important features. Figure 4 shows corresponding results across several tabular datasets for a Multi- Layer Perceptron (MLP) and tabular ResNet architecture 22 For both models, we used Shapley Values 42] with feature mean replacement as perturbation and derived global importances as an average over 1000 samples. As suggested by 229] we performed retraining over 3 different random seeds and report the average loss increases across all runs per dataset. ReCalX consistently leads to importance rankings that, when used to drop features, cause steeper loss surge compared the original model's explanations. This aligns with our theoretical analysis in Section 3, which established
8

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electricity
covertype mlp
credit mlp
pol
ReCalK Uncailbrated
0.66
Cross Entropy
0.60
0.54
0.55
0.53
0.30
0.53
0.60
0.25
0.50
0.38
0.15
0.40
0.40
0.54
0.10
Unca lbbrtted
Uncallbrated
Uncalibrated
0.35
2
Top Features Removed
Top Features Removed
Top Features Removed
Top Features Removed
electricity resnet
covertype | resnet
credit | resnet
pol resnet
0.62
0.05
0.74
0.72
0.40
Uncal librleredd
ReCalX
Clocs Entropy
0.58
0.35
0.53
0.68
0.30
0.54
0.65
Uncalibrated
0.25
0.54
0.50
0.48
ReCalK
0.40
Uncalibrated
ReCalX
0.60
Top Features Removed
Top Features Removedd
Top Features Removed
Top Features Removed
Figure 4: Retraining results on four tabular datasets for an MLP (top row) and a ResNet (bottom row) when the features removed based their global importance estimated via Shapley Values. Whenever calibrated explanations imply a different importance ranking (green area), the resulting performance loss is consistently higher compared the uncalibrated importance indications. Hence, ReCalX enables better identification of truly relevant features that are crucial for good performance.
that calibration errors directly undermine the predictive power assessment of feature subsets. By reducing certurbation-speciiee calibration errors, ReCalX enables more accurate estimation of mutual information between feature subsets and the target variable, resulting importance rankings that better reflect the true contribution of features model performance. For instance, the electricity dataset, removing the top three features ranked by ReCalX-enhancen explanations increased the original loss by 33%, compared to only 24% when using the original model's explanations. In Appendix C, we provide similar results on six additional datasets as well as for global importances obtained via LIME (53, all confirming the effectiveness of ReCalX in this regard.
Explanation Robustness
Perturbation suarbattion-bssed techniques can lack stability when subjected to minor input variations, resulting unreasonably different explanation results for seemingly equivalent Sensitivity metrics [64] 5 28 are a popular way to quantify explanation Table 3 we present Average and Max Sensitivity results across multiple image classifiers and explanation methods, each evaluated using 200 random samples from the ImageNet validation set. ReCalX substantially improves both metrics for all analyzed models, explanation methods, and both considered perturbation types. This indicates that proper recalibration also promotes explanation robustness, tracing one potential source of instabilities back to miscalibration effects.
predictions [ 38 3]
robustness by measuring how explanations change under tiny input modifications.
Visualizing the Effeet of ReCalX on Explanations Finally, we show how ReCalX can impact explantion results a qualitative level. In Figure we display four representative examples where the calibrated explanation deviated substantially from the original one for image classifier. All explanations have been computed based on Shapley Values with zero replacement on a DenseNet121 model (top row) and SigLIP zero-shot model (bottom row) respectively. The examples demonstrate that after calibration with RecalX, the indicated feature importances are more concentrated around the actual object of interest, which typically contains the discriminative information with respect to its target label. Moreover, the calibrated ones also appear less noisy in general, which may contribute to higher explanation robustness in line with the experimental results reported above.

---

Zero Baseline Perturbation
Perturbation
LIME
Kemel SHAP
Feature Ablation
LIME
Kernel SHAP
Feature Ablation
Model
Uncal.
ReCaIX
Uscal.
ReCaiX
Uncal.
ReCalX
Uncal.
ReCaiX
Uncal.
ReCalX
Uncal
ReCalX
Average Sensitivity (Swa J)
ResNet50
1.349
1.364
0.965
0.825
1.321
1.202
1.403
1.335
0.965
0.845
DenseNet111
1.174
0.952
1.465
1.125
0.716
0.602
1.224
1.118
1.500
1.425
0.602
0.556
1.224
1.571
SigLIP
1.215
0.963
1.434
1.222
1.140
0.922
1.518
1.349
1.714
1.659
1.140
1.015
Maximum Sensitivity (SMAX !)
ResNe150
1,658
DenseNet211
1.649
1.101
2.649
1,535
0.777
0.776
1.760
1.525
2.779
2.404
0.777
0.701
1.746
2,998
SigLIP
1.737
1.093
2.729
1.787
1.606
1,033
2.327
1.921
3.493
2.897
1,606
1,379
Table 3: Average (Swa) and Maximum (SMAx) sensitivity results for different perturbation based explanation methods across diverse image classifiers on ImageNet. Results are shown for both zero baseline and blur perturbation techniques. Lower values indicate better robustness. ReCalX consistently improves robustness compared uncalibrated (Uncal.) explanations in all cases.
Image: mink
Uncalibrated
ReCaiX
Image hummingbird
Uncalibrated
ReCalX
Image: snorkel
Uncalibrated
ReCelX
Image: football hhelme
Uncalibrated
ReCelX
Figure 5: Qualitative comparison of Shapley Value explanations before and after ReCalX calibration for DenseNet121 (top row) and SigLIP zero-shot model (bottom row). The calibrated explanations exhibit stronger focus discriminative object regions and reduced noise, demonstrating how miscalibration correction leads to more informative and robust feature attributions.
Discussion and Conclusion
In this work, we established a fundamental connection between uncertainty calibration and the relia- bility of perturbation-basee explanations. Our theoretical analysis reveals that poor calibration under feature perturbations directly impacts explanation quality, leading to potentially misleading interpreta- tions. To address this, we introduced ReCalX, novel recalibration approach that specifically targets explanation-rellvant miscalibration. Our empirical results demonstrate that ReCalX substantially reduces calibration error across differrntt perturbation levels and consistently improves explanation quality, as measured by robustness and retraining fidelity. Although our approach is tailored particu- larly for perturbation-bant explanation families, such as gradient-basse based [2) or counterfactual [62] methods, pointing towards potential directions for future work. While ReCalX requires additional computational efforts to be
methods, the underlying principles may also have implications for other
properly set up, including access to validation samples. it only introduces minor extra load during inference arising from adaptive temperature selection when deriving explanations. However, this overhead is typically in the order of milliseconds (see Appendix D for corresponding experiments), and we believe that this is well justified to not only obtain more reliable predictions but also better explanations via uncertainty calibration.
10

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Reviews:
[{"review_id": "zPMIL6QS4P", "reviewer": "Reviewer_CfX7", "summary": "This paper proposes a connection between uncertainty calibration and explanation performance for perturbation based explainability in linear subset aggregation methods. The authors show that calibration error can be directly connected to the predictive power for perturbation-based predictions, and can thus derail explainability approaches within this framework when not considered. A calibration framework based on temperature scaling is proposed to mitigate this.", "questions": "1. Is there anything about the theoretical results which requires linearity of the subset-based perturbation aggregations?\n2. How sensitive is your recalX approach to the number of bins selected? Are there any tradeoffs to be aware of?\n3. It seems that, given that the temperature scaling is tuned at validation time and that this tuning becomes more complex as the number of perturbations and binning levels increases, this approach may suffer from overfitting issues. Have you noticed or investigated robustness to overfitting of the tuned temperature scaling with respect to calibration error when the perturbations may change at test time?", "limitations": "yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 2, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n1. The connection between calibration error and perturbation-based predictive power is interesting, and clearly has implications for how to design further explainability approaches.\n2. I found the paper to be very clearly written with a good flow, particularly for the theoretical contents of the paper.\n3. The authors discuss the implications of the work for both global and local explanations. Unfortunately the local explanation results may not have a very tight bound, however this is presumably to be expected and it is good for it to be discussed, as often in practice one will be interested in local explanations.\n\n## Weaknessess\n1. The proposed solution to the calibration problem, namely a binned temperature scaling, feels somewhat simplistic and is specific to classification tasks. It would have been nice to see more discussion about alternative ideas to address the calibration issues, for example exploring training-time approaches, particularly given that the temperature based recalibration approach will always be restricted to the classification setting.\n2. Given that notions of calibration can be extended to regression, it would have been interesting to see a more complete discussion about the implications of the work in this setting also. Indeed, many relevant prediction tasks may also be for regression.\n3. The paper focuses the experiments exclusively on linear subset aggregation explanation methods (LIME and Shapley). Is this required for the theory to hold? If not, it is odd to focus only on linear explanation methods when the context of the experiments focuses squarely on non-linear networks where complex inter-dependencies between features are likely to exist.", "was_revised": true, "final_justification": "The paper introduces a novel connection between uncertainty calibration and performance for perturbation based explainability approaches. While I initially recommended borderline acceptance, with some concerns remaining for the full generality of the results to non-linear aggregation methods and regression tasks, the authors have adequately addressed these concerns in their response. In particular, the authors have clarified that their theoretical contributions can be generalized to non-linear aggregation methods, in additional to general target distributions. \n\nAssuming the author's clarifications and extended results are incorporated into the final manuscript, I am thus comfortable in more strongly recommending acceptance.", "rebuttal": "We want to thank the reviewer for their thoughtful questions and helpful suggestions.\n\nBased on your feedback, we have now performed **additional ablation studies on the number of bins** for ReCalX and analyzed the **generalization capabilities across different perturbation types**. The results show **monotonic but saturating improvements in calibration with higher bin count** and demonstrates **strong correlation between calibration patterns across perturbation strategies**. We have also clarified that our **theoretical results extend to non-linear aggregation strategies**, and we address your concerns about the simplicity of our approach and its **applicability beyond classification settings**. These findings and clarifications will be included in the revised version of the paper.\n\nDetailed answers to all your questions and concerns are provided below.\n\nQ1: Is there anything about the theoretical results which requires linearity of the subset-based perturbation aggregations?\n\nA: Thank you for this important question, as it helps clarify a central aspect of our work.\nIn fact, all the theoretical results and conclusions in our paper can be extended to also hold for perturbation-based methods with non-linear aggregation strategies.\nFor our first theoretical result (Theorem 3.2 and Corollary 3.3), which decomposes predictive power into information-theoretic components, the analysis is completely independent of the aggregation strategy. This theorem applies universally to any perturbation-based approach since it focuses on the fundamental relationship between calibration error and predictive power.\nRegarding Theorem 3.4 (local explanation bounds), while we initially presented it for linear aggregation strategies due to their popularity, the result can be naturally extended to non-linear aggregation methods. For any general non-linear aggregation function $G$ that maps model predictions under perturbations to feature importance vectors, we can reformulate the bound using a more general Lipschitz property. \nLet $G$ be a non-linear aggregation strategy, and let $\\nu(x)$ and $\\nu^*(x)$ represent the vectors of model predictions under subset perturbations for the uncalibrated and perfectly calibrated models, respectively. All we additionally need for the non-linear case is the existence of a constant L such that:\n\n$$\n\\lVert G(\\nu(x)) - G(\\nu^*(x)) \\rVert_2 \\le L \\lVert \\nu(x) - \\nu^{\\ast}(x) \\rVert_{\\infty}\n$$\n\nThis leads to the following more general version of Theorem 3.4:\n\n$$\n\\frac{1}{d}\\lVert \\phi(x) - \\phi^*(x) \\rVert_2^2 \\le \\frac{L^2}{d} CE_{\\textit{KL}}^{\\max_S} + \\sqrt{\\frac{L^4}{2d}\\log(1/\\delta)}\n$$ \n\nFor linear aggregation strategies used by methods like SHAP and LIME, one can show that $L = 2\\sqrt{d}$ [1], which yields the specific bound presented in Theorem 3.4 of the paper.\nThis demonstrates that our theoretical framework can be generalized to non-linear aggregation strategies as well. We will add a corresponding discussion to the revised version of the paper.\n\n[1] Lin, Chris, Ian Covert, and Su-In Lee. \"On the robustness of removal-based feature attributions.\" Advances in Neural Information Processing Systems 36 (2023): 79613-79666.\n\nQ2: How sensitive is your recalX approach to the number of bins selected? Are there any tradeoffs to be aware of?\n\nA: Thank you for this insightful question regarding the sensitivity of ReCalX to the number of bins.\nWe have conducted a dedicated ablation study to investigate this. Using a Vision Transformer (ViT) model on ImageNet with the same experimental setup described in our main paper, we systematically varied the number of bins from 1 up to 25. \n\n| Number of Bins | ReCalX $CE_{KL}^{avg}$ | ReCalX $CE_{KL}^{max}$ |\n|----------------|------------------------|------------------------|\n| 1          \t| 0.0506             \t| 0.0915             \t|\n| 3          \t| 0.0137             \t| 0.0440             \t|\n| 5          \t| 0.0092             \t| 0.0215             \t|\n| 10         \t| 0.0075             \t| 0.0138             \t|\n| 15         \t| 0.0070             \t| 0.0128             \t|\n| 20         \t| 0.0070             \t| 0.0116             \t|\n| 25         \t| 0.0067             \t| 0.0116             \t|\n\nThe results reveal that increasing the number of bins generally improves calibration performance. This is expected because a finer-grained binning strategy allows ReCalX to learn a more nuanced set of temperatures that better match the model's varying calibration properties across different perturbation levels.\nHowever, we observe diminishing returns, with the most significant improvements occurring up to about 10 bins. Beyond this point, the reduction in calibration error saturates.\n\nThis presents a minor tradeoff between calibration granularity and computational cost during initial setup.\nA higher number of bins allows ReCalX to learn a more fine-grained set of temperatures, better adapting to the model's specific miscalibration at different perturbation levels. As shown in our ablation study, this generally leads to a lower maximum calibration error.\nHowever, each bin requires a separate temperature parameter to be optimized on the validation set. Therefore, increasing the number of bins linearly increases the computational efforts associated with the one-time calibration procedure.\nOur empirical results indicate that the performance gains from adding more bins diminish and eventually saturate. To manage this trade-off one can choose a number of bins (e.g., 10) that captures most of the potential calibration improvement without incurring unnecessary high computational cost during setup. \n\nQ3: Have you noticed or investigated robustness to overfitting of the tuned temperature scaling with respect to calibration error when the perturbations may change at test time?\n\nA: Thank you also for this insightful question.\n\nThe risk of overfitting with ReCalX is inherently low due to the simplicity of our approach. We are only optimizing a very small number of parameters (e.g., 10 temperatures for 10 bins), which is a model of extremely low complexity. This makes it highly unlikely for the learned temperatures to overfit to statistical noise in the calibration data.\nMoreover, applying a perturbation-based explanation method typically assumes a predefined single, fixed perturbation strategy making changing perturbations at test time unusual. However, we also investigated the interesting question of whether the calibration learned for one perturbation type could generalize to another.\n\nDuring the experiments in the paper, we already optimized two separate sets of ReCalX temperatures for different classifiers on ImageNet: one using blur perturbations and another using zero-baseline replacement perturbations. This allows us to compute the correlation between the resulting sets of temperatures across the perturbation levels to assess their correspondance.\n\n| Model   \t| Pearson Correlation \t|\n|-------------|-----------|\n| ResNet50\t| 0.984  |\n| DenseNet\t| 0.975  |\n| ViT\t| 0.914  |\n| SigLip  | 0.956    |\n\nThe results show a strong positive correlation, suggesting that a model's underlying miscalibration patterns can be similar across different perturbation types. While this indicates that ReCalX may offer some generalization, we recommend explicitly calibrating for the specific perturbation strategy being used. This ensures that the theoretical benefits of our method are fully realized for the explanation method at hand.\n\nNext,  we also provide individual responses to all additional weaknesses (W) mentioned in the review.\n\nW1.1: The proposed solution to the calibration problem, namely a binned temperature scaling, feels somewhat simplistic and is specific to classification tasks.\n\nA: Thank you for raising this point. We view the simplicity of our approach as a key strength, as it leads to a practical and efficient method that is easy to apply and due to its small number of parameters not prone to overfitting. Our experiments consistently show that ReCalX based on temperature scaling is highly effective, delivering substantial improvements in calibration and explanation quality with minimal overhead. \n\nW1.2: It would have been nice to see more discussion about alternative ideas to address the calibration issues, for example exploring training-time approaches, particularly given that the temperature based recalibration approach will always be restricted to the classification setting.\n\nA: Thank you for this suggestion. When applying perturbation-based explanations the goal typically is to explain an existing, already-trained model. Therefore, any calibration method we use should be information-preserving (Definition 4.1) to avoid altering the model's core logic. Training-time approaches would create a new, different model, which is not what we aim to explain. Importantly, ReCalX and its core idea to apply an adaptive, information-preserving calibration map during the explanation process generalizes beyond classification. We detail in our response to reviewer idkw below how for instance, affine transformations can be used for learning suitable calibration maps in the regression setting and provide experiments on 2 tabular regression datasets.\n\nW2: Given that notions of calibration can be extended to regression, it would have been interesting to see a more complete discussion about the implications of the work in this setting also.\n\nA: Thank you for mentioning this, we agree that discussing how ReCalX can be applied to regression problems would be helpful. In fact, all theoretical results and conclusions can be extended to arbitrary target distributions. We will include a comprehensive discussion on this in the revised version of the manuscript. For more details on this, we would like to refer to the answer to W 2 provided for reviewer idkw below, where we also provide additional experiments on tabular regression datasets that show ReCalX efficacy in regression tasks as well."}, {"review_id": "upQrKmk8pI", "reviewer": "Reviewer_idkw", "summary": "This paper makes a key contribution by establishing the first comprehensive relationship between uncertainty calibration and the reliability of perturbation-based explanations. The authors introduce ReCalX, a novel and practical solution designed to enhance the quality of these explanations. Grounded in the theoretical principle of preserving information while reducing calibration error under perturbation, ReCalX employs a unique temperature scaling method sensitive to both perturbation level and intensity. Extensive experiments are conducted to validate the proposed approach.", "questions": "The theory presented is confined to linear summary strategies and classification problems. It remains an open question how these findings generalize to non-linear aggregation methods (e.g. use decision trees as surrogates or others, whether the boundedness property and Operatornorm are still valid) and how ReCalX would perform in that context. I am willing to reconsider my score if the authors provide more intuition or justification for the extensions.", "limitations": "(minor) can discuss the potential extension to regression problems and explanations with non-linear summaries.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is well-written and the study is well-executed. The motivation, theory, and method are all stated clearly, and the experimental results align well with the theoretical claims. The work is also novel, as it is the first to provide a theoretical basis for the relationship between uncertainty calibration and perturbation-based explanations. Following this, the proposed ReCalX method is a novel and promising approach that incorporates perturbation level and intensity for calibration and reliable explanations.", "was_revised": true, "final_justification": "The rebuttal effectively addresses my questions. It strengthens the paper's generalizability by extending the theory to include non-linear aggregation strategies and general prediction tasks. Therefore, I've decided to raise my score.", "rebuttal": "We want to thank the reviewer for their thoughtful comments and suggestions.\n\nWe have addressed both key concerns raised in your review. Regarding non-linear aggregation methods, we demonstrate that our **theoretical framework fully extends beyond linear aggregation strategies** by reformulating our bounds using a general Lipschitz property. We also **explain how our theory naturally applies to general prediction tasks** beyond classification. For regression problems, we've conducted **additional experiments on tabular regression datasets** that show ReCalX **effectively reduces miscalibration under explanation-specific perturbations in regression tasks** as well. These extensions and experimental results will be incorporated into the revised manuscript to provide a more comprehensive treatment of our approach.\n\nDetailed responses to each point are provided below.\n\nW1: It remains an open question how these findings generalize to non-linear aggregation methods \n\nA: Thank you for this important remark, as it helps clarify a central aspect of our work.\nIn fact, all the theoretical results and conclusions in our paper can be extended to also hold for perturbation-based methods with non-linear aggregation strategies.\n\nFor our first theoretical result (Theorem 3.2 and Corollary 3.3), which decomposes predictive power into information-theoretic components, the analysis is completely independent of the aggregation strategy. This theorem applies universally to any perturbation-based approach since it focuses on the fundamental relationship between calibration error and predictive power.\n\nRegarding Theorem 3.4 (local explanation bounds), while we initially presented it for linear aggregation strategies due to their popularity, the result can be naturally extended to non-linear aggregation methods. For any general non-linear aggregation function $G$ that maps model predictions under perturbations to feature importance vectors, we can reformulate the bound using a more general Lipschitz property. \n\nLet $G$ be a non-linear aggregation strategy, and let $\\nu(x)$ and $\\nu^*(x)$ represent the vectors of model predictions under subset perturbations for the uncalibrated and perfectly calibrated models, respectively. All we additionally need for the non-linear case is the existence of a constant L such that:\n\n$$\n\\lVert G(\\nu(x)) - G(\\nu^*(x)) \\rVert_2 \\le L \\lVert \\nu(x) - \\nu^{\\ast}(x) \\rVert_{\\infty}\n$$\n\nThis leads to the following more general version of Theorem 3.4:\n\n$$\n\\frac{1}{d}\\lVert \\phi(x) - \\phi^*(x) \\rVert_2^2 \\le \\dfrac{L^2}{d} CE_{\\textit{KL}}^{\\max_S} + \\sqrt{\\frac{L^4}{2d}\\log(1/\\delta)}\n$$ \n\nFor linear aggregation strategies used by methods like SHAP and LIME, one can show that $L = 2\\sqrt{d}$ [1], which yields the specific bound presented in Theorem 3.4 of the paper.\n\nThis demonstrates that our theoretical framework generalizes to non-linear aggregation strategies as well. We will add a corresponding discussion to the revised version of the paper.\n\n[1] Lin, Chris, Ian Covert, and Su-In Lee. \"On the robustness of removal-based feature attributions.\" Advances in Neural Information Processing Systems 36 (2023): 79613-79666.\n\nW2: can discuss the potential extension to regression problems\n\nA: Thank you for this thoughtful suggestion. We primarily focus on classification problems in the main paper due to their popularity in the explainability and calibration literature. However, our theoretical framework and the ReCalX approach of performing perturbation-specific recalibration can be extended to regression problems as well.\n\nFirst notice, that the core principles of our paper are information-theoretic and generalize to any predictive modeling task. For regression, we consider a model $f: \\mathcal{X} \\to \\mathcal{P}(\\mathcal{Y})$ that maps to a continuous target space $\\mathcal{Y} \\subseteq \\mathbb{R}$ with continuous distribution $P_Y$. In this setup, all theoretical statements developed in section 3 of the paper hold equivalently when explaining the propability of an output with perturbation-based methods. \n\nMoreover, also the notion of information preserving calibration and the concept of strictly monotonic transformations to preserve the model’s learned information content extend naturally.  While temperature scaling is indeed tailored to classification settings, techniques like affine transformations [3] or injective versions of Isotonic Regression [4] satisfy this property more generally and are also applicable to regression problems.\n\nTo demonstrate this compatibility, we conducted experiments on two tabular regression datasets to evaluate miscalibration under fixed baseline replacement with the feature mean. Following a setup equivalent to our main experiments, we trained a simple MLP regression model with gaussian output distribution [5] and applied ReCalX by learning a simple Platt-scaling like affine transformation (a scaling and a shift parameter) for each perturbation level.\nThe table below show average and maximum quantile-based calibration errors [2] across perturbation strengths.  \n \n| Dataset  | Uncalibrated $CE^{AVG_S}$  | ReCalX $CE^{AVG_S}$ | Uncalibrated $CE^{MAX_S}$  | ReCalX  $CE^{MAX_S}$  |\n|--------------|----------------------------|---------------------------|----------------------------|--------------------------|\n| wine_quality   | 0.06495                       \t| **0.01182**                       \t| 0.1053                          \t|**0.0183**                 |\n| houses         \t| 0.18078                       \t|**0.00741**                       \t| 0.2512                          \t|**0.0178**                 |\n\nThe results indicate that ReCalX is also capable of reducing miscalibration under explainably-specific perturbations for regression tasks. We will provide a comprehensive discussion in the revised version of the manuscript.\n\n[1] Song, H., Diethe, T., Kull, M., and Flach, P. Distribution calibration for regression. In International Conference on Machine Learning, pp. 5897–5906. PMLR, 2019.\n\n[2]Kuleshov, Volodymyr, Nathan Fenner, and Stefano Ermon. \"Accurate uncertainties for deep learning using calibrated regression.\" International conference on machine learning. PMLR, 2018.\n\n[3] Platt, J. C. Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In Advances in Large-Margin Classifiers, pp. 61–74. MIT Press, 1999.\n\n[4] Zhang, J., Kailkhura, B., and Han, T. Y.-J. Mix-n-match: Ensemble and compositional methods for uncertainty calibration in deep learning. In International Conference on Machine Learning, pp. 11117– 11128. PMLR, 2020.\n\n[5] Bishop, C. M. Mixture density networks. 1994"}, {"review_id": "POxOFBXHeI", "reviewer": "Reviewer_v21P", "summary": "This paper explores how uncertainty miscalibration under input perturbations can degrade the reliability of perturbation-based explanations. The authors introduce **ReCalX**, an adaptive temperature scaling method that recalibrates model confidence specifically for perturbed inputs without altering predictions. Theoretical analysis shows that miscalibration directly impacts explanation quality, and ReCalX is designed to preserve information while reducing perturbation-specific calibration error. Empirical results across tabular and image datasets demonstrate that ReCalX improves explanation fidelity and robustness compared to standard calibration methods.", "questions": "Question: How does ReCalX perform under perturbation strategies that are not based on mean replacement or simple blurring (e.g., adversarial, manifold-preserving, or semantically grounded perturbations)?\nSuggestion: Please discuss or evaluate ReCalX in such settings to assess generality. Including even a small experiment could strengthen the claims of robustness.\n\nQuestion: How sensitive is ReCalX to the size and representativeness of the validation set used for estimating perturbation-level calibration errors?\nSuggestion: Clarify whether performance degrades with smaller or distribution-shifted calibration sets, and if any data-efficient variants could be used.\n\nQuestion: How compatible is ReCalX with other classes of explanation methods (e.g., gradient-based, counterfactual explanations)?\nSuggestion: While the focus is on perturbation-based methods, a brief discussion of limitations or extensions to other explanation families would be helpful.", "limitations": "The authors briefly mention limitations in the conclusion, but a more explicit discussion would be valuable.\n\n- The need for perturbation-specific validation data may limit ReCalX’s applicability in settings where such data is hard to obtain or generate.\n- The computational overhead of applying different temperature scalings at inference time could be a concern for large-scale or real-time deployments.\n- The method is designed specifically for perturbation-based explanations, and it is unclear how it generalizes to other explanation paradigms (e.g., gradient-based, counterfactual).", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1. Strong theoretical foundation and thorough experiments across diverse models and datasets.\n2. Well-written and easy to follow, with helpful figures and explanations.\n3. Addresses an important and underexplored issue—miscalibration in perturbation-based explanations.\n4. First method to explicitly recalibrate for explainability; novel connection between calibration and explanation quality.\n\nWeaknesses:\n\n1. Limited evaluation on complex or domain-specific perturbations.\n2. Assumes access to validation data under perturbations, which may not always be feasible.\n3. Slight increase in computational cost during explanation due to adaptive scaling.", "was_revised": false, "final_justification": "", "rebuttal": "We want to thank the reviewer for their thoughtful questions and constructive comments.\n\nBased on your suggestions, we have conducted **additional experiments** to address your concerns about the **generality and robustness of ReCalX**. For more complex perturbation strategies, we evaluated ReCalX with **advanced inpainting techniques** and found it **remains highly effective in reducing calibration errors**. Regarding validation set sensitivity, our ablation study shows that even **small sets of 50-100 samples achieve most of the potential calibration improvement**, making ReCalX **practical in resource-constrained settings**. We've also **clarified the relationship between ReCalX and other explanation families** like gradient-based and counterfactual methods, identifying potential extensions for future work. Finally, we've quantified the computational overhead of ReCalX, **confirming it adds minimal processing time** during explanation generation. These findings strengthen our claims about ReCalX's effectiveness and practicality across diverse settings and will be included in the revised version of the paper.\n\nDetailed responses to each point follow below.\n\nQ1: How does ReCalX perform under perturbation strategies that are not based on mean replacement or simple blurring (e.g., adversarial, manifold-preserving, or semantically grounded perturbations)? Suggestion: Please discuss or evaluate ReCalX in such settings to assess generality. Including even a small experiment could strengthen the claims of robustness.\n\nA: Thank you for this insightful question and the concrete suggestion to approach it..\nWe followed your advice and conducted an extra experiment evaluating ReCalX with more complex, domain-aware perturbation strategies. We chose two advanced image inpainting techniques available in the official shap library, which leverage the cv2.inpaint_telea and cv2.inpaint_ns algorithms provided by the cv2 package. Unlike simple blurring or zero-filling, these methods are designed to fill corrupted image regions in a semantically plausible way by incorporating information from the surrounding pixels. \n\nWe evaluated the performance of ReCalX on a Vision Transformer (ViT) model when using these inpainting methods. The table below shows the average and  maximum KL-divergence calibration errors before and after applying ReCalX as well as for basic temperature scaling.\n\n| Perturbation   | Initial_Avg | Initial_Max | TS_Avg | TS_Max | ReCalX_Avg | ReCalX_Max |\n|----------------|-------------|-------------|--------|--------|------------|------------|\n| inpaint_ns \t| 0.3796  \t| 1.0337  \t| 0.2327 | 0.6890 | **0.0305**\t| **0.1012** \t|\n| inpaint_telea  | 0.3843  \t| 1.0612  \t| 0.2370 | 0.6993 | **0.0293** \t| **0.0991** \t|\n\nThe results demonstrate that ReCalX remains highly effective and substantially reduces the calibration error even for these sophisticated, domain-specific perturbations.\n\nQ2: How sensitive is ReCalX to the size and representativeness of the validation set used for estimating perturbation-level calibration errors? Suggestion: Clarify whether performance degrades with smaller or distribution-shifted calibration sets, and if any data-efficient variants could be used.\n\nA: Thank you for this important question. We investigated the sensitivity of ReCalX to the size and representativeness of the validation set.\n\nWe performed an ablation study on a ViT model on ImageNet, varying the number of samples in the calibration set. The uncalibrated baseline errors were 0.0936 (Average) and 0.2618 (Max) and below we show the average results across 10 random seeds:\n\n| Cal Size | ReCalX $CE_{KL}^{avg}$ | ReCalX $CE_{KL}^{max}$ |\n|----------|----------------|----------------|\n| 10   \t| 0.0175     \t| 0.0743     \t|\n| 25   \t| 0.0099     \t| 0.0346     \t|\n| 50   \t| 0.0045     \t| 0.0115     \t|\n| 75   \t| 0.0035     \t| 0.0088     \t|\n| 100  \t| 0.0031     \t| 0.0063     \t|\n| 200  \t| 0.0028     \t| 0.0060     \t|\n| 500  \t| 0.0021     \t| 0.0027     \t|\n| 1000 \t| 0.0021     \t| 0.0025     \t|\n\nAs the table shows, even a small, randomly selected validation set of 50-100 samples is sufficient to achieve the vast majority of the potential calibration improvement. Because measurable gains are already achievable with a small random set, we conclude that specialized data-efficient selection techniques are not necessary for the practical application of our method.\n\nRegarding representativeness, ReCalX follows standard machine learning practice: it performs optimally when the validation set is drawn from the same underlying distribution as the data for which explanations will be generated. However, a key advantage of our setting is that we have full control over the perturbation function. This allows us to create a calibration set that is perfectly representative of the perturbed data distribution the model will face during the explanation process, mitigating concerns about unexpected distribution shifts.\n\nQ3: How compatible is ReCalX with other classes of explanation methods (e.g., gradient-based, counterfactual explanations)? Suggestion: While the focus is on perturbation-based methods, a brief discussion of limitations or extensions to other explanation families would be helpful.\n\nA: Thank you for this insightful question, which helps clarify the scope and potential future directions of our work.\nWhile our method is tailored particularly tailored for perturbation-based methods, the underlying principle has indeed connections to other explanation families.\n\nFor instance, it may also be relevant for gradient-based methods like SmoothGrad and Integrated Gradient, which compute explanations by averaging gradients over perturbed inputs. Therefore, ensuring the model is well-calibrated on these very perturbations could also lead to more stable and reliable gradient signals, directly improving the final explanation. Exploring how calibration properties affect such kinds of explanations is an interesting direction for future work.\n\nMoreover, counterfactual explanation methods search for a new data point $x'$ in the proximity of a point $x$ that yields a desired prediction. Evaluating the reliability of the model's output on the generated counterfactual $x'$ could also have an influence on explanation quality. However, ensuring the model is well-calibrated on $x'$ addresses a different problem than ReCalX, which corrects for a given perturbation function used to derive explanation. But analyzing calibration in the context of counterfactuals may also be an interesting direction for future work. \nWe will include a corresponding discussion on the relationship to other explanation families in the revised version of the manuscript. \n\nNext we further provide answers to all additional weakness identified in the review:\n\nW2: Assumes access to validation data under perturbations, which may not always be feasible.\n\nA: Thank you for mentioning this limitation, which we acknowledged in our conclusion. However, relying on at least a limited amount of validation data is a very common assumption that underlies many machine learning approaches. Moreover, we now have also performed an ablation study (see Q3 above)  indicating that even with a small number of validation samples, ReCalX can yield significant gains in calibration under the perturbation used during the explanation process. Hence, we argue that the severity of this limitation is minor.\n\nW3: Slight increase in computational cost during explanation due to adaptive scaling.\n\nA: Thank you also for bringing this up. To quantify this, we measured the per-explanation overhead for various models on ImageNet. The table below shows the additional computation time in seconds induced by ReCalX when computing different explantion metods as average over 100 runs. The results confirm that the extra time is indeed minor. For more details, please also refer to the answer of Q3 provided to reviewer cRdn. \n\n| Method        \t| ResNet18  | DenseNet  | ViT  \t| SigLip |\n|------------------|-----------|-----------|----------|------------|\n| LIME        \t| 0.0193s   | 0.0219s   | 0.0184s  | 0.0210s\t|\n| Shapley Values| 0.2587s   | 0.2517s   | 0.1754s  | 0.3431s    |"}, {"review_id": "al7yEOkyJS", "reviewer": "Reviewer_cRdn", "summary": "The paper analyzes how poor calibration affects the quality of perturbation-based explanations. To address this issue, and improve these explanation, ReCalX is introduced, a novel model calibration method tailored towards improving reliability of perturbation-based XAI, based on temperature scaling. Both the theoretical analysis and the efficacy (improved explanation robustness and fidelity) of ReCalX is validated through extensive experiments on a wide range of models and datasets.", "questions": "- How does the number of bins affect (1) the required number of validation samples and (2) calibration errors and resulting explanation quality. \n- Could you include some qualitative examples of the effects of ReCalX (e.g., in the appendix)?\n- Can the perturbation level $\\lambda(S)$ also be computed for non-binary perturbations? If not, could it be extended to include these as well?\n- Could you elaborate on the additional computational cost induced by ReCalX?", "limitations": "Yes", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths.** The paper is extremely well written (including intuitive descriptions for equation-heavy theoretical results) and structured. The addressed issue is clearly and rigorously analyzed and explained. Experimental validation is extensive, relevant, self-contained, and convincing. The shown effects are (very) significant. Limitations are addressed. Especially the theoretical analysis of the effect of poor model calibration on (perturbation-based) explanations is of significant interest to the community, as it identifies a serious issue, with clear directions how to resolve it. \n\n**Weaknesses.** Tbh, I struggle to find serious weaknesses with this work. The proposed solution, ReCalX is slightly incremental, as it simply optimizes the temperature parameter for bins of perturbation levels. The effect of hyperparameters of this approach is not analyzed further. E.g., how does the number of bins affect (1) the required number of validation samples and (2) calibration errors and resulting explanation quality. \nDespite the quantitative analysis being convincing w.r.t. potential benefits of ReCalX, I would also have liked to have seen some qualitative example of how ReCalX affects the explanations. Beyond binary perturbations (such as setting features to zero or leaving them unperturbed), the exact computation of the perturbation level $\\lambda(S)$ is not clear to me. Is there a way to consider also more continuous perturbations, such as e.g. perturbing features by inducing an alpha value? While the additional computational overhead induced by ReCalX is mentioned as a limitation, it is not quantified, which would aid in estimating the seriousness of this limitation.", "was_revised": true, "final_justification": "I am satisfied with the answers provided to mine and the other reviewers' comments and am therefore raising my score.", "rebuttal": "We highly appreciate the positive feedback and want to thank the reviewer for their insightful questions about ReCalX's implementation details and practical considerations. \n\nWe've conducted additional analyses to address your concerns. Regarding bin count effects, our ablation study **shows increasing calibration improvements with higher bin counts, with diminishing returns**. The **number of bins doesn't directly affect validation sample requirements**, as we can generate sufficient perturbed samples for each bin. We agree that qualitative examples would enhance understanding of ReCalX's impact and **will include additional visualizations** in the revised manuscript. We've also clarified that our perturbation level concept **extends to non-binary perturbations** through a generalized intensity measure. Finally, by precisely quantifying inference times, we confirm that ReCalX adds **negligible computational overhead** during explanation generation in the order of milliseconds. All these findings will be included in the revised version of the manuscript.\n\nBelow, we provide detailed responses to each of your questions.\n\nQ1: How does the number of bins affect (1) the required number of validation samples and (2) calibration errors and resulting explanation quality?\n\nA: Thank you for this relevant question, we will address both parts.\n\nThe number of bins does not directly affect the required number of validation samples. Since one typically has sufficient control over the perturbation function when deriving explanations, we can generate a sufficient number of perturbed samples for any given perturbation level (bin). This ensures each bin has enough data for a stable temperature estimate, making the choice of bin count rather independent of the size of the available validation set.\n\nTo investigate the effect on calibration errors, we conducted a dedicated ablation study. Using a Vision Transformer (ViT) model on ImageNet with the same experimental setup described in our main paper, we systematically varied the number of bins from 1 up to 25.\n\n| Number of Bins | ReCalX $CE_{KL}^{avg}$ | ReCalX $CE_{KL}^{max}$ |\n|----------------|------------------------|------------------------|\n| 1          \t| 0.0506             \t| 0.0915             \t|\n| 3          \t| 0.0137             \t| 0.0440             \t|\n| 5          \t| 0.0092             \t| 0.0215             \t|\n| 10         \t| 0.0075             \t| 0.0138             \t|\n| 15         \t| 0.0070             \t| 0.0128             \t|\n| 20         \t| 0.0070             \t| 0.0116             \t|\n| 25         \t| 0.0067             \t| 0.0116             \t|\n\nThe results reveal that increasing the number of bins generally improves calibration performance, particularly by reducing the maximum calibration error ($CE_{KL}^{max}$). This is expected because a finer-grained binning strategy allows ReCalX to learn a more nuanced set of temperatures that better match the model's varying calibration properties across different perturbation levels.\n\nHowever, we observe diminishing returns, with the most significant improvements occurring up to about 10 bins. Beyond this point, the reduction in calibration error becomes increasingly marginal, and therefore, 10 offers a balanced choice. As established by our theoretical results, this direct reduction in calibration error translates to more robust and faithful explanations.\n\nQ2: Could you include some qualitative examples of the effects of ReCalX (e.g., in the appendix)?\n\nA: Thank you very much for this great suggestion. We completely agree that qualitative examples are helpful for illustrating the practical impact of our method. One qualitative example was already provided as part of Figure 1 but we are happy to include additional ones in the revised version of the manuscript.\n\nQ3: Can the perturbation level also be computed for non-binary perturbations? If not, could it be extended to include these as well?\n\nA: Thank you for this excellent question. Yes, the concept of a perturbation level is highly flexible and can be generalized beyond binary perturbations.\n\nThe fraction of perturbed features we use is a specific instance of a more general principle. For any perturbation strategy, we can define a per-feature perturbation intensity $\\alpha_i \\in [0, 1]$, where $\\alpha_i=0$ means the feature is unchanged and $\\alpha_i=1$ means it is maximally perturbed.\n\nThe overall perturbation level $\\lambda$ can then be universally defined as the average intensity across all $d$ features:\n\n$$\n\\lambda = \\frac{1}{d}\\sum_i \\alpha_i\n$$\n\nThis formulation naturally extends binary perturbations where $\\alpha_i \\in$ {0, 1} to continuous ones (e.g., varying blur strength or noise intensities), ensuring ReCalX is broadly applicable.\n\nQ4: Could you elaborate on the additional computational cost induced by ReCalX?\n\nA: Thank you for this important practical question.\n\nThe additional computational cost of ReCalX at inference time —when an explanation is actually generated— is negligible.\nThis is because the total explanation time is overwhelmingly dominated by the repeated model queries required by the perturbation-based method itself. In contrast, ReCalX only adds two trivial operations: a quick temperature lookup and a single division on the model's logits.\n\nTo quantify this, we measured the per-explanation overhead for various models on ImageNet. The table below shows the additional computation time in seconds induced by ReCalX when computing different explantion metods as average over 100 runs. The results confirm that the extra time is minor.\n\n| Method        \t| ResNet18  | DenseNet  | ViT  \t| SigLip |\n|------------------|-----------|-----------|----------|------------|\n| LIME        \t| 0.0193s   | 0.0219s   | 0.0184s  | 0.0210s\t|\n| Shapley Values| 0.2587s   | 0.2517s   | 0.1754s  | 0.3431s    |"}]

Author rebuttal:

Meta-review: This paper establishes a connection between uncertainty calibration and explanation quality in perturbation-based explainability for linear aggregation methods.
The authors demonstrate that calibration error can undermine explanation reliability and propose a temperature scaling framework to address this.
They introduce ReCalX, a calibration method designed to enhance the robustness and fidelity of perturbation-based explanations.
Theoretical analysis and comprehensive experiments support the effectiveness of ReCalX.
While the theory focuses on linear aggregation methods, the authors clarified that it could be extended beyond the linear case.
Decision: Accept (spotlight)