Title: Minimizing False-Positive Attributions in Explanations of Non-Linear Models
Venue: NeurIPS 2025
Accepted: yes
Keywords: Explainable AI

Interpretability

Suppressor Variables

Non-Linear Problems

Machine Learning

EEG
Abstract: Suppressor variables can influence model predictions without being dependent on the target outcome, and they pose a significant challenge for Explainable AI (XAI) methods. These variables may cause false-positive feature attributions, undermining the utility of explanations. Although effective remedies exist for linear models, their extension to non-linear models and instance-based explanations has remained limited. We introduce PatternLocal, a novel XAI technique that addresses this gap. PatternLocal begins with a locally linear surrogate, e.g., LIME, KernelSHAP, or gradient-based methods, and transforms the resulting discriminative model weights into a generative representation, thereby suppressing the influence of suppressor variables while preserving local fidelity. In extensive hyperparameter optimization on the XAI-TRIS benchmark, PatternLocal consistently outperformed other XAI methods and reduced false-positive attributions when explaining non-linear tasks, thereby enabling more reliable and actionable insights. We further evaluate PatternLocal on an EEG motor imagery dataset, demonstrating physiologically plausible explanations.

Minimizing False-Positive Attributions in Explanations of Non-Linear Models

Abstract

Suppressor variables can influence model predictions without being dependent on the target outcome, and they pose a significant challenge for Explainable AI (XAI) methods. These variables may cause false-positive feature attributions, undermining the utility of explanations. Although effective remedies exist for linear models, their extension to non-linear models and instance-based explanations has remained limited. We introduce PatternLocal, a novel XAI technique that addresses this gap. PatternLocal begins with a locally linear surrogate, e.g., LIME, KernelSHAP, or gradient-based methods, and transforms the resulting discriminative model weights into a generative representation, thereby suppressing the influence of suppressor variables while preserving local fidelity. In extensive hyperparameter optimization on the XAI-TRIS benchmark, PatternLocal consistently outperformed other XAI methods and reduced false-positive attributions when explaining non-linear tasks, thereby enabling more reliable and actionable insights. We further evaluate PatternLocal on an EEG motor imagery dataset, demonstrating physiologically plausible explanations.

1 Introduction

In recent years, the growing demand for transparent, accountable, and ethical AI systems across various industries and research communities has driven substantial advancements in explainable artificial intelligence (XAI). The need to understand machine learning models' decision-making processes is well-established, particularly in high-stakes domains such as healthcare, finance, and criminal justice. While researchers have made promising progress with so-called self-explainable models such as prototypical networks, these approaches often fail to achieve the same downstream performance as conventional models and typically require complete retraining [22]. Consequently, researchers focus significant attention on post-hoc XAI methods that apply to existing models without retraining. Post-hoc XAI methods encompass a diverse array of approaches, including architecturespecific techniques such as Layer-wise Relevance Propagation (LRP) [1], concept-based explanations like TCAV [14], and model-agnostic frameworks such as SHAP [17] and LIME [21]. These methods promise to support model validation, data quality checks, and actionable intervention suggestions [23]. To provide evidence, researchers evaluate XAI methods against criteria such as faithfulness to the model, robustness to perturbations, and human interpretability [32]. However, none of these criteria guarantee that the features highlighted as important are discriminative for the target variable, an assumption behind many uses of XAI [13].

Several studies [34, 35] have shown that widely used XAI methods often assign importance to suppressor variables [9, 33], features that affect model predictions without having a direct statistical dependency with the target. Suppressors may capture correlations in noise or other auxiliary signals that models exploit to improve predictions without offering causal or correlational insights. For instance, a model might predict epilepsy from seizure activity in a specific brain region, but to

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optimally do so, it also relies on a noise probe from an unaffected region; common XAI methods may then highlight both regions, mistakenly assigning significance to the irrelevant area.

To support interpretations that rely on statistical relevance, a feature should depend on the target variable [34, 13]. The Pattern method [12] formalizes this idea by separating prediction from explanation: a discriminative model makes predictions, and a corresponding generative model provides explanations. Extensions such as PatternNet and PatternAttribution generalize this idea to deep neural networks [15] but have shown weaknesses on non-linear suppressor benchmarks like XAI-TRIS [8]. Unlike human-centered evaluations, benchmarks like XAI-TRIS provide controlled environments with objective ground-truth explanations to evaluate the robustness of XAI methods against suppressors and other uninformative variables. Also, model-agnostic methods such as SHAP, LIME, and LRP largely ignore training data structure, making them prone to suppressor bias [34, 35, 8].

In this work, we introduce PatternLocal , a data-driven, model-agnostic XAI method that extends the Pattern approach to non-linear cases. PatternLocal converts locally discriminative explanations, produced by methods such as LIME or KernelSHAP, into generative representations that more accurately reflect statistical relevance; see Figure 1. This transformation helps reduce the impact of suppressor and other non-informative variables while maintaining local fidelity to the model's decision behavior. PatternLocal assumes access to representative training data and a meaningful input simplification (e.g., superpixels or feature masks) shared across samples. We evaluate PatternLocal on the XAI-TRIS benchmark, artificial lesion MRI benchmark, and an EEG Motor imagery dataset, and compare it with a range of established XAI methods. The results show that PatternLocal consistently provides more reliable and interpretable explanations without changing the underlying model.

2 Preliminary

2.1 Notation

Let X ⊂ R D and Y ⊂ R denote the input and output spaces, respectively. Consider a model f : X → Y . For an instance x ⋆ ∈ X we wish to explain the prediction f ( x ⋆ ) . Because highly complex models such as deep networks are notoriously hard to interpret, they are approximated locally by a simpler, intrinsically interpretable model g . We therefore restrict attention to local explanations for the specific instance x ⋆ rather than to the behavior of f on X as a whole.

Many XAI methods first replace x ⋆ with a lower-dimensional or more semantically meaningful representation x ′ ⋆ = h x ⋆ ( x ⋆ ) ∈ R D ′ . In image analysis, for example, x ′ ⋆ may encode superpixels; in other settings, it may correspond to a low-rank projection or simply a subset of raw features.

Such simplification often makes for easier interpretation and, when D ′ ≪ D , also reduces the computational cost. See Appendix A for a summary of the notation.

Remark. In general, models that predict y from x are termed backward or discriminative , whereas models that reconstruct x (or its sources) from latent factors are called forward or generative . We adopt this convention to avoid terminological clashes.

2.2 Suppressor Variables

Various studies [e.g., 9, 12] demonstrated that linear models may need to assign significant non-zero weight to correlated noise variables (suppressors). Given x ∈ R D , assume each instance is generated from a linear model of the form

where K is the number of latent factors, A = [ a 1 , . . . , a K ] ∈ R D × K contains the activation patterns a k , and ε denotes additive noise. A linear backward model attempts to recover the latent vector m via

Consider D = 2 and K = 1 with x 1 = m + d and x 2 = d , where the scalar m is the signal of interest and d is a suppressor . The signal is exactly recovered by ˆ m = x 1 -x 2 = w ⊤ x with w = [1 , -1] ⊤ . Interpreting w directly as feature importance, however, suggests x 1 and x 2 contribute equally, even though the second channel carries only the suppressor, which is removed entirely in ˆ m by subtraction. This issue with suppressor variables extends to common explainable AI methods used to interpret machine learning models [35, 8].

Remark. While suppressor variables can improve prediction accuracy, they do not reflect genuine statistical dependence on the target. Such variables should be excluded from explanations, as they have no direct or indirect (causal, anti-causal, or confounded) link to the target. This differs from phenomena like the Clever Hans effect or shortcut learning, where models rely on spurious yet predictive features.

2.3 Forward vs. backward models

Instead of using the weights of the linear backward model, Haufe et al. [12] propose to use the corresponding forward model. They show that the weight matrix W has a unique forward model counterpart

where Σ X = Cov[ x ] and Σ M = Cov[ ˆ m ] which recovers the activation pattern in Eq. (1). If the estimated factors are uncorrelated, Σ M is diagonal and Eq. (3) reduces to A ∝ Σ X W = Cov [ x , ˆ m ] . The resulting global feature importance map for the entire data set D ⊂ X is which mitigates suppressor variables for the linear model. For example, in unregularized linear discriminant analysis, where W = Σ -1 X ( µ + -µ -) with µ + / -denoting the class means, this approach completely removes the influence of suppressor variables in the activation pattern.

2.4 Local explainability methods

LIME. LIME works by constructing a local surrogate model g of f around x ′ ⋆ ; the surrogate's coefficients form the feature-importance explanation for x [21]. Its original formulation is ξ = argmin g ∈ G L ( f, g, Π x ′ ⋆ ) + Ω( g ) , where G is a class of interpretable functions, L is a loss evaluated on samples in the simplified space, Π x ′ ⋆ is a local kernel, and Ω penalizes model complexity. In the common usage where L is squared loss and g is linear, can be written as

where R is a regularization weighted by λ , Z is the simplified input space, and h -1 x ⋆ : Z→X maps a simplified sample back to the original space. This notation is similar to the one by Tan et al. [31]. For

image explanations, the default choices are Π x ′ ⋆ ( z ′ ) = exp( -∥ 1 -z ′ ∥ 2 0 /σ 2 ) , R ( v ) = ∥ v ∥ 2 2 , and h -1 x ′ ⋆ ( z ′ ) = z = x ⋆ ⊙ B ( z ′ ) + r ⊙ ( 1 -B ( z ′ )) , with z ′ ∼ Uni ( { 0 , 1 } D ′ ) , ⊙ denoting element-wise product, r being a reference value, and where B : { 0 , 1 } d → { 0 , 1 } D copies each bit z ′ j to every pixel in superpixel. As mentioned, LIME can assign non-zero importance to suppressor variables [35].

KernelSHAP & Gradient methods. As shown by Lundberg and Lee [17], Tan et al. [31], KernelSHAP can be written in the form of Eq. (5) by setting R ( v ) = 0 and Π x ′ ( z ′ ) = ( D ′ -1) / [( D ′ choose ∥ z ′ ∥ 0 ) · ∥ z ′ ∥ 0 · ( D ′ -∥ z ′ ∥ 0 )] . Tan et al. [31] further demonstrate that Eq. (5) unifies SmoothGrad [28] and the plain Gradient method [37].

3 PatternLocal

We now unify the Pattern insight that forward model parameters reveal statistically relevant features with the ability to probe highly non-linear models locally with methods like LIME. We call this PatternLocal . PatternLocal converts any linear surrogate explanation w produced around an instance x ⋆ into a data-driven pattern a that (1) suppresses false positives caused by suppressor variables, (2) remains faithful to the model because it builds on the very surrogate that approximates the decision boundary, (3) preserves local fidelity by weighting the surrounding data with a local kernel, and (4) remains practical in high-dimensional settings by operating in a simplified, low-dimensional space with regularized estimation.

(1) Suppressor-variable mitigation. PatternLocal mitigates suppressor effects by regressing the neighborhood of x ⋆ onto the local surrogate output ˜ y = w ⊤ x under a Gaussian noise model. This reconstruction of x from ˜ y effectively down-weights suppressor contributions.

(2) Model faithfulness. PatternLocal inherits w from Eq. (5), which approximates the model f locally around x ⋆ . By regressing the simplified input x on the surrogate response ˜ y rather than the true label y , PatternLocal ensures that explanations describe the model's behavior, not the underlying task.

(3) Local fidelity. In non-linear models, the important features can vary across different regions of the input space. PatternLocal enforces locality by weighting all terms in its regression objective using the local kernel Π x ′ ⋆ . This ensures that the explanation focuses on the neighborhood around x ⋆ and does not reflect global structure.

(4) Feasibility and dimensionality. PatternLocal assumes sufficient local samples near x ⋆ and operates in the simplified space defined by h x ⋆ , which aligns with Eq. (5) and reduces the dimensionality. To maintain stability in sparse or high-dimensional settings, the regression includes a regularization term Q .

3.1 Formal objective

Let h x ⋆ : X → R D ′ be the simplified input representation used in Eq. (5) and w be its solution. Also let ˜ y = w ⊤ h x ⋆ ( x ) denote the local surrogate prediction. PatternLocal estimates a pattern a by regressing the local prediction onto the simplified input of the original data within the local neighborhood of x ⋆

When Q ( u ) = ∥ u ∥ 1 , the objective can be solved with a kernel-weighted Lasso regression. For Q ( u ) = ∥ u ∥ 2 2 the problem reduces to a kernel-weighted ridge regression with a closed-form solution given by

where expectations, covariances, and variances are taken with respect to the normalized kernel Π x ′ ⋆ ( h x ⋆ ( x )) over X . See Appendix B.1 for derivations. Eq. (7) therefore expresses a ℓ 2 as the kernel-weighted covariance between the simplified features and the surrogate response, scaled by its regularized variance. Also see Appendix B.3 for more on sample complexity.

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We present a small-scale toy example to better illustrate the intuition behind the PatternLocal method. Let m 1 , m 2 ∼ N (0 , 1) and d ∼ N (0 , σ 2 d ) be independent latent variables. We observe

which induces a classical XOR-like dependency between ( x 1 , x 2 ) and the label y . The variable x 3 acts as a suppressor. The optimal classifier for this non-linear problem is given by ˜ y = sign( ˜ f ( x )) , ˜ f ( x ) = ( x 1 -x 3 )( x 2 + x 3 ) . Asmooth approximation to this classifier is f τ ( x ) = tanh((1 /τ ) ˜ f ( x )) , 0 < τ ≪ 1 . Fixing an input x ⋆ , the first-order (linear) approximation of the decision function at this point is f τ ( x ) ≈ f τ ( x ⋆ ) + w ⊤ ( x -x ⋆ ) with

̸

noting that w 1 -w 2 + w 3 = 0 . Therefore, we generally have w 3 = 0 , implying that local linear XAI methods (e.g., gradients, LIME, KernelSHAP) will incorrectly assign nonzero importance to the suppressor variable x 3 .

Let Π x ⋆ ( x ) = φ ( ∥ x -x ⋆ ∥ ) be any isotropic local kernel. For λ = 0 and identity mapping h x ⋆ ( x ) = x , the PatternLocal explanation vector is defined as a = Cov Π x ⋆ [ x , ˜ y ] / Var Π x ⋆ [˜ y ] and ˜ y = w ⊤ x .

Consider the third component a 3 = Cov Π x ⋆ [ x 3 , ˜ y ] / Var Π x ⋆ [˜ y ] , we compute

Thus,

and hence a 3 = 0 . Similar calculation can be done for a 1 and a 2 which yields a ∝ [ w 1 , w 2 , 0] ⊤ . See Appendix B.2 for derivations. We conclude that PatternLocal correctly assigns zero feature importance to the suppressor variable x 3 , in contrast to standard local linear methods. This is also confirmed with simulation as seen in Figure 2.

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4 Experiments

The experimental workflow begins with the construction of synthetic image datasets whose pixel-level ground-truth attribution maps are known by design, giving us complete control over class-conditional distributions. 1 We train each candidate classifier on a standard train/validation split and assess its performance on an unseen test set. For every test image, the selected XAI method produces a normalized importance map in the range [ -1 , 1] . These maps are then quantitatively compared with the ground-truth attributions using the evaluation metrics introduced below. All XAI hyperparameters are tuned on the validation split before the final assessment to ensure a fair comparison.

4.1 Datasets

We focus on the XAI-TRIS benchmark dataset [8] and the artificial lesion MRI dataset [19]. Both datasets specifically enable the assessment of XAI methods in the context of suppressor variables.

XAI-TRIS Benchmark. We follow the methodology outlined in Clark et al. [8] and provide complete details in Appendix C.1. The XAI-TRIS benchmark dataset consists of 64 × 64 images (with N = 40 , 000 samples) generated by combining a class-dependent foreground tetromino shape with background noise. The relative weighting between signal and noise is set by α . We consider two noise scenarios:

WHITE : uncorrelated Gaussian noise,

CORR : spatially smoothed Gaussian noise (leading to suppressor variables ).

We evaluate three scenarios:

LIN : A 'T'-shaped tetromino near the top-left indicates y = 0 ; an 'L'-shaped tetromino near the bottom-right indicates y = 1 .

XOR : Both tetrominoes appear with differing signs depending on y .

RIGID : Each tetromino is randomly translated and rotated by 90 ◦ increments.

The tetromino shape determines the set of important (ground-truth) pixels. For training and evaluation, each dataset is split into D train , D val , and D test in a 90/5/5 ratio. Figure 3 shows examples of all scenarios. Spatially correlated noise in the CORR setting introduces suppressor pixels , background locations correlated with the foreground through the smoothing operator G . Although these pixels carry no direct class information, the model can exploit them to denoise the true signal [12, 34].

Artificial lesion MRI dataset. Following Oliveira et al. [19], the Artificial Lesion MRI dataset contains grayscale medical downscaled images, with D = 128 × 128 = 16384 . It includes N = 7500 samples, evenly split into D train , D val , and D test . Each sample simulates a brain MRI slice with artificial lesions of predefined shapes and intensities, loosely resembling real-world white matter hyperintensities (WMH). Unlike XAI-TRIS, this dataset introduces challenges with more complex, organic lesion structures and anatomical background variations, making it a valuable benchmark for neuroimaging explainability. See Appendix C.2 for more details.

EEG Motor Imagery dataset. We use the PhysioNet EEG Motor Movement/Imagery dataset [24], containing recordings from 109 subjects performing motor tasks. EEG was acquired from 64 scalp electrodes at 160 Hz following the 10-10 system. We focus on runs R03 , R07 , and R11 , where subjects repeatedly opened and closed their left or right fist. Labels T1 and T2 mark left- and right-fist movements, defining a binary classification problem ( y = 1 for left, y = 0 for right). We use 19 standard 10-20 electrodes, resample to 100 Hz, apply a 0.5 Hz high-pass filter, and re-reference to the common average. A 3s window (1s before to 2s after onset) is extracted for each event, yielding 19 channels and 300 time points per trial. After removing invalid segments, the final dataset comprises N = 4 , 927 balanced trials (2,456 right, 2,471 left), split into D train , D val , and D test in a 90/5/5 ratio.

4.2 Models

We use two types of classifiers for the synthetic datasets: a multi-layer perceptron (MLP) and a convolutional neural network (CNN). For the EEG Motor Imagery dataset, we use the ShallowFBCSPNet from Schirrmeister et al. [25]. Each classifier f : X → Y is trained on the training dataset D train . We train the models with early stopping based on validation performance on D val , and then evaluate them on the test set D test . We consider a classifier to have generalized to the classification problem if its test accuracy exceeds 90%. See Appendix D.1 for details on model architecture, training, and performance.

4.3 XAI methods

We evaluate nine methods on the models, including the PatternLocal approach and baselines. The XAI methods applied are: LIME [21], Integrated Gradients [30], Saliency [27], DeepLift [26], GradientShap [10], and GuidedBackProp [29]. Additionally, we incorporate two edge detection filters, Sobel and Laplace, which prior work shows outperform more advanced XAI techniques in suppressor variable scenarios [8]. Note that KernelSHAP is a special case of LIME. Since we perform extensive hyperparameter optimization, we may also select KernelSHAP during this process.

For the XAI-TRIS dataset, we benchmark LIME and PatternLocal with three input-simplification schemes for h x ⋆ ( · ) : the identity mapping, a superpixel representation, and a low-rank approximation. We evaluate the same three variants on the artificial-lesion MRI dataset. Superpixels are generated on a uniform grid for XAI-TRIS, whereas we use the slic algorithm for the MRI dataset.

4.4 Metrics

We evaluate explanation quality using two complementary metrics: the Earth Mover's Distance (EMD) and the Importance Mass Error (IME). See Appendix F.1 for a discussion of additional metrics such as faithfulness.

Earth Mover's Distance (EMD). The Earth Mover's Distance (EMD) measures the optimal cost to transform one distribution into another. For a continuous-valued importance map s and ground truth F + , both normalized to have the same mass, we compute the EMD using the Euclidean distance as the ground metric. The optimal transport cost, OT ( | s | , F + ) , is calculated following the algorithm proposed by Bonneel et al. [7] and implemented in the Python Optimal Transport library [11]. We define a normalized EMD performance score as

where δ max is the maximum Euclidean distance between any two pixels.

Importance Mass Error (IME). As argued in Clark et al. [8] and Arras et al. [2], it is plausible that the given model only uses a subset of the important pixels for its prediction. Thus, false positives should be preferentially penalized while false negatives should be largely ignored. To this end, we provide an additional metric, Importance Mass Error (IME),

4.5 Hyperparameter optimization

For both the synthetic XAI-TRIS Benchmark and the semi-synthetic Artificial Lesion MRI dataset, we conduct extensive hyperparameter optimization across all datasets, scenarios, SNR levels, and corresponding models to ensure a fair evaluation of all XAI methods. We employ Bayesian optimization using the Tree-structured Parzen Estimator (TPE) algorithm [4], implemented via the hyperopt package [5], which efficiently manages mixed continuous and categorical search spaces. The optimization objective minimizes the Earth Mover's Distance (EMD) between the absolute normalized explanation and the ground truth on the validation set. Additional implementation details are provided in Appendix D.2.

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5 Results

XAI-TRIS Benchmark. We evaluate the performance of the XAI methods on the XAI-TRIS benchmark both qualitatively and quantitatively. We conduct qualitative evaluation through visual inspection, which is standard in XAI research [e.g., 3, 17, 8], and illustrate it in Appendix E.1. The quantitative evaluation uses ground truth along with the EMD and IME metrics, as shown in Figure 4. The results presented here are for the MLP model, h x ⋆ ( · ) as the identity function and R ( · ) = Q ( · ) = ∥ · ∥ 2 2 . Results for the CNN model, h x ⋆ ( · ) as superpixels or low-rank approximation, and for R ( · ) = Q ( · ) = ∥ · ∥ 1 , are provided in Appendix E.1.

In Figure 4, we present the aggregated results of the methods across the test set for the EMD and IME metrics. Overall, the PatternLocal method substantially outperforms all other methods in the XOR and RIGID scenarios. However, we observe mixed results in the RIGID CORR scenario: PatternLocal performs substantially better than other XAI methods but is comparable to or worse than the filter methods Sobel and Laplace. These filter methods also performed well in Clark et al. [8] due to XAI-TRIS images having rigid bodies with sharp lines, making them especially easy for filter-based methods to detect. This advantage does not apply to images with more complex backgrounds, such as those in the artificial lesion MRI dataset.

Additional ablation studies on hyperparameters' impact and the suppressor variable's role are in Appendix G.

Artificial lesion MRI dataset. We evaluate the XAI methods using the same procedure on the artificial lesion MRI dataset. The results reported here correspond to the CNN model, with h x ⋆ ( · ) defined over superpixels and R ( · ) = Q ( · ) = ∥ · ∥ 2 2 . Figure 5 illustrates the performance of PatternLocal compared to LIME and the filter-based methods Sobel and Laplace. We provide additional qualitative and quantitative benchmark results in Appendix E.2.

EEG Motor Imagery dataset. Since the EEG motor imagery dataset does not have a ground-truth, we assess the explanations' physiological plausibility. This didactic example demonstrates how explanations can be meaningfully analyzed when they align with the underlying neurophysiology.

We used PatternLocal with the bandwidth set to the median pairwise distance, h x ⋆ ( · ) as the identity function and no regularization. Applying PatternLocal to the motor-imagery EEG data produced explanations with clear temporal and spatial structure. The explanations concentrate on task onset and retain distinct oscillatory patterns in the alpha and gamma bands. When we apply spatiospectral decomposition (SSD) [18] to single-trial explanations, the resulting components remain

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physiologically interpretable and localize with eLORETA[20] to the expected motor regions. For the right-hand example shown in Figure 6, the source reconstruction reveals increased left-hemisphere activity, reflecting contralateral motor engagement. Across the test set, dipole fits of SSD patterns indicate higher physiological plausibility for PatternLocal ( 0 . 756 ± 0 . 090 ), with the raw instances showing similar results ( 0 . 738 ± 0 . 013 ) and LIME performing worse ( 0 . 604 ± 0 . 013 ). These findings demonstrate that PatternLocal yields explanations consistent with the physical forward model, enabling valid time-frequency and source analyses, unlike methods such as LIME, which do not permit meaningful decomposition of their outputs in this way.

6 Conclusion

This paper presents PatternLocal , a data-driven, model-agnostic XAI method that improves local explanations by reducing false-positive attributions caused by suppressor variables. By transforming standard local surrogate outputs into more reliable feature attributions, PatternLocal enhances interpretability without retraining the underlying model. Across three datasets, including XAI-TRIS, artificial lesion MRI, and EEG motor imagery, PatternLocal consistently outperforms existing methods, providing more precise and trustworthy explanations, particularly in challenging scenarios with misleading noise.

Limitations

The primary limitation of PatternLocal is its reliance on access to representative training data in the neighborhood of each explanation. While this is feasible, it may be challenging in privacy-sensitive or data-scarce environments. Additionally, because PatternLocal fits a local generative model, it assumes a degree of consistency or alignment across samples in the input space. This assumption holds well in structured domains like medical imaging, where standardized views are common. However, it may break down in less constrained settings, such as natural images or user-generated content, where spatial alignment across instances cannot be guaranteed. PatternLocal reduces false-positive feature attribution; however, like other XAI methods, it can still misattribute importance, so saliency maps should be seen as suggestive rather than definitive.

Acknowledgments

We thank Sebastian Weichwald, William Lehn-Schiøler, Teresa Dorszewski, and Lina Skerath for their contributions during the early stages of this work. We are also grateful to the anonymous reviewers for their valuable feedback. This work was supported by the Danish Data Science Academy, funded by the Novo Nordisk Foundation (NNF21SA0069429) and VILLUM FONDEN (40516), as well as the Pioneer Centre for AI (DNRF P1) and the Novo Nordisk Foundation ("Cognitive spaces Next generation explainability", NNF22OC0076907).

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A Notation

B Mathematical details

B.1 Derivation of equation (7): Kernel-weighted ridge solution

We start with the PatternLocal definition from Eq. (6)

where the surrogate response is ˜ y = w ⊤ h x ⋆ ( x ) and the kernel Π x ′ ⋆ : R D ′ → R ≥ 0 is normalized. For any function f define

which coincides with the usual expectation because of the kernel's normalization. Using this notation, we set

We can expand the squares like

and taking the kernel-weighted expectation gives

Then setting ∇ u J ( u ) = 0 yields

hence

Because E Π x ′ ⋆ [˜ y 2 ] + λ > 0 , the inverse exists and the ridge solution is

Assuming that h x ⋆ ( x ) and ˜ y is centered, the first-order moments vanish and we obtain the compact form

B.2 Derivation for toy example

Optimal classifier. The optimal classifier for the non-linear problem in Eq. (8) is given by as we can write

and we have y = sign( m 1 m 2 ) . However, the gradient of sign( ˜ f ( x )) is not well-defined when

These conditions define a union of two hyperplanes in R 3 across which the sign function is discontinuous, and hence not differentiable. To address this, we instead use a smooth approximation to the sign function

which is infinitely differentiable for all x ∈ R 3 . As τ → 0 , f τ ( x ) converges pointwise to sign( ˜ f ( x )) , while maintaining a smooth and well-defined gradient everywhere.

Gradient. To derive the local linear approximation of the smooth decision function, we apply the chain rule

Expanding ˜ f ( x ) = x 1 x 2 + x 1 x 3 -x 2 x 3 -x 2 3 , we compute its gradient

Evaluating at a point x ⋆ = ( x 1 ⋆ , x 2 ⋆ , x 3 ⋆ ) , we define

and obtain the local weight vector

Thus, the first-order approximation becomes

Finally, note that the identity w 1 -w 2 + w 3 = 0 holds.

PatternLocal. Let Π x ⋆ ( z ) = φ ( ∥ z -x ⋆ ∥ ) be an isotropic kernel and write E Π x ∗ [ · ] for expectations taken with respect to the normalized kernel weights. The non-zero variances Var( m 1 ) = Var( m 2 ) = 1 and Var( d ) = σ 2 d yield the full feature-covariance matrix

With identity mapping h x ⋆ ( x ) = x and λ = 0 , the PatternLocal explanation is

Using the gradient weights w = ( w 1 , w 2 , w 3 ) ⊤ of Eq. (9) in the main text, obeying w 1 -w 2 + w 3 = 0 ,

The third component simplifies immediately,

so a 3 = 0 . For the remaining two components, use the same identity once to obtain

which removes the suppressor variable x 3 even though w 3 = 0 .

Consequently

̸

B.3 Sample complexity of kernel-weighted moment estimation

It is important to note that an explicit matrix covariance estimate (and its multiplication) is not always required, especially when the surrogate already contains an inverse-covariance form. The key computation in PatternLocal is the kernel-weighted moment

which for binary classification requires only (1) the scalar local variance of ˜ y and (2) the vector crosscovariance with the simplified features h x ⋆ ( x ) . Both moments are estimated with a Nadaraya-Watson kernel smoother. For any function g ( x ) we write

where K σ is an isotropic kernel with bandwidth σ in the D ′ -dimensional interpretable space, and n loc is the number of local samples.

Classical Nadaraya-Watson analysis [36] gives for each entry of the conditional covariance

Balancing these two terms yields the optimal bandwidth σ ⋆ ∝ n -1 / (4+ D ′ ) loc and the corresponding mean-squared error

Equivalently, to achieve an ε -accurate estimate of the required local moments, understood as RMSE ≤ ε , one needs

which scales only with the simplified input dimension D ′ ≪ D .

When D ′ is not small compared to n loc , we apply Ledoit-Wolf shrinkage to the local covariance. Ledoit and Wolf [16] analyze a linear shrinkage estimator that remains invertible even when D ′ > n loc , is well-conditioned in probability, and is asymptotically optimal when D ′ /n loc stays bounded. Importantly, PatternLocal does not require a matrix inverse, since Eq. (7) divides only by the scalar variance of ˜ y .

Finally, recent locality-aware sampling results for GLIME [31] provide sample-complexity bounds that show exponentially faster convergence and substantially fewer samples than LIME under subGaussian local sampling and regularization. PatternLocal can adopt the same sampling strategy, which further reduces the number of data points per explanation without altering its closed-form update.

C Dataset generation

C.1 XAI-TRIS Benchmark

Following the methodology outlined in Clark et al. [8], the XAI-TRIS benchmark dataset consists of images of size 64 × 64 , represented as D = { ( x ( n ) , y ( n ) ) } N n =1 . The feature dimensionality is D = 64 2 = 4096 , and the dataset contains N = 40000 samples. These samples are independent and identically distributed (i.i.d.) realizations of random variables X and Y , governed by the joint probability density function P X ,Y ( x , y ) .

Each instance x ( n ) comprises a foreground signal a ( n ) ∈ R D , which is class-dependent and defines the ground truth, combined with background noise η ( n ) ∈ R D . The additive generation process is defined as

where α determines the relative contribution of signal and noise. The signal a ( n ) is based on tetromino shapes that depend on the binary class label y ( n ) ∼ Bernoulli ( 1 2 ) . To smooth the signal, a Gaussian spatial filter H : R D → R D with a standard deviation σ smooth = 1 . 5 is applied, using a maximum support threshold of 5% .

The background noise η ( n ) is sampled as η ( n ) ∼ N (0 , I D ) . Two noise scenarios are considered:

WHITE : The operator G is the identity function, resulting in uncorrelated noise.

CORR : The operator G : R D → R D is a Gaussian spatial filter with σ smooth = 10 , introducing spatially correlated noise.

We analyze three distinct binary classification scenarios:

LIN : The operator R ( n ) is the identity operator. The signal a ( n ) is defined as a 'T'-shaped tetromino a T located near the top-left if y = 0 , and as an 'L'-shaped tetromino a L located near the bottom-right if y = 1 .

XOR : The operator R ( n ) is the identity operator, and each instance contains both a T and a L . For y = 0 , the signals are a XOR++ = a T + a L and a XOR-= -a T -a L . For y = 1 , the signals are a XOR+-= a T -a L and a XOR-+ = -a T + a L .

RIGID : The operator R ( n ) applies a rigid-body transformation. In this case, the tetromino shapes a T and a L are randomly translated and rotated in increments of 90 ◦ .

Lastly, the transformed signal and noise components are horizontally concatenated into matrices and normalized by the Frobenius norm and a weighted sum is calculated with the scalar α ∈ [0 , 1] which determines the signal-to-noise ratio (SNR).

This results in six scenarios across 64 × 64 image sizes. The ground truth set, representing the important pixels based on the positions of the tetromino shapes, is

̸

For the LIN scenario, the presence of a T is as informative as the absence of a L , and vice versa. Therefore, the set of important pixels for this setting is

̸

̸

The ground truth F + ( x ( n ) ) defines important pixels based on the data generation process. However, a model may rely on only a subset of these for its prediction, which is equally valid. As in Clark et al. [8], we employ metrics to de-emphasize the impact of false-negative omissions.

For model training and later analysis, each dataset is split into three subsets D train , D val , and D test with a 90/5/5 ratio.

XAI-TRIS Benchmark for Ablation Study Additionally, we generate another XAI-TRIS benchmark dataset following the same procedure but for D = 8 2 = 64 and N = 10000 . This is only used for the ablation study in Appendix G.

C.2 Artificial Lesion MRI Benchmark

The methodology of constructing the Artificial Lesion MRI Benchmark dataset is described in Oliveira et al. [19] and we provide a brief overview here. See Figure 7 for examples of instances.

Source images. They selected 1 007 T1-weighted axial volumes of healthy adults (22-37 y) from the Human Connectome Project (HCP). After the standard FSL/FREESURFER 'minimal' preprocessing and defacing pipelines, each slice with background occupancy < 55% was retained. Raw matrices ( 260 × 311 ) were zero-padded vertically, centre-cropped horizontally to 270 × 270 , clipped to the intensity range [0 , 0 . 7] , and bicubic down-sampled to 128 × 128 so as to match the resolution used in the main paper.

Lesion synthesis. (i) Prototype masks. White Gaussian noise ( 256 × 256 ) was smoothed with a σ = 2 kernel, Otsu-thresholded, and morphologically processed (erosion-opening-erosion) to yield irregular blobs. (ii) Shape selection. From every connected component they computed the compactness

where A is area and p its perimeter. Components with c ≥ 0 . 8 were labelled regular , those with c ≤ 0 . 4 irregular . (iii) Boundary refinement. Candidate shapes were zero-padded by two pixels and softened with a σ = 0 . 75 Gaussian blur, yielding final binary masks L ∈{ 0 , 1 } 256 × 256 .

Image composition. For every background slice B : (i) Draw k ∼ U{ 3 , 4 , 5 } lesions L 1: k of the same shape class. (ii) Uniformly translate each L j inside the brain bounding box, rejecting placements with overlap (IOU > 0 ). (iii) Aggregate the lesion mask L ( x, y ) = max j L j ( x, y ) and mix intensities

fixing the signal-to-noise weighting α = 0 . 5 for all experiments. Pixels with L ( x, y ) = 1 constitute the exact attribution ground truth supplied to evaluation metrics.

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D.1 Model architectures and training

All classifiers are implemented in PyTorch 2.6 and PyTorch-Lightning 2.5 . Training, early stopping, and checkpointing are handled entirely by the Lightning trainer; the relevant source code is in the GitHub repository for full transparency. Unless stated otherwise, all models are trained with the same optimization hyperparameters listed in Table 2.

Multi-layer perceptron (MLP). The network is a 4-layer perceptron that receives a flattened input vector. Hidden dimensions are { 128 , 64 , 32 , 16 } with ReLU activations, batch-normalization after every linear layer, and 25% drop-out regularization. The output layer is fully connected with |Y| logits.

Convolutional neural network (CNN). The canonical CNN processes single-channel square images of side 64 × 64 or 128 × 128 pixels, selected by the input_size argument ( 4096 , 16384 vector elements, respectively). It stacks four convolution blocks

each followed by ReLU and a 2 × 2 max-pool, after which the feature map is flattened and passed to a single fully connected output layer. When the input is 8 × 8 , we employ a compact architecture with two 3 × 3 convolutions (channels 1 → 8 → 16 ), each followed by batch-norm, ReLU, max-pool, and 25% drop-out. The resulting 4 × 4 feature map feeds a single fully connected classifier.

Optimisation and early stopping. Parameters are updated with Adam ( η 0 = 1 × 10 -4 ). A ReduceLROnPlateau scheduler monitors validation accuracy and scales the learning rate by 0 . 1 after 100 epochs. Training terminates via early stopping under the same patience condition, and the model state with the highest validation accuracy is restored before final testing. Mini-batches contain 128 samples, and the hard cap on epochs is 500 , although the best model is usually after around ∼ 60 -120 epochs.

All random seeds are fixed through pl.seed_everything to ensure that the reported numbers are exactly reproducible. For every model used, the test accuracy exceeds 90 %.

D.2 Hyperparameter optimization

Optimization procedure. We perform Bayesian optimization with the Tree-of-Parzen Estimators (TPE) algorithm [4] as implemented in the hyperopt package [5]. Each run consists of 200 trials; during every trial, the candidate configuration is evaluated on the validation set, and the mean Earth Mover's Distance (EMD) between the normalized explanation and the ground-truth mask is minimized.

Locally linear methods. LIME and PatternLocal are tuned independently. PatternLocal optimizes the three parameters listed in Table 3 and the LIME parameters, yielding four variables in total.

Baseline methods. We run with their default implementations for filter-based methods (Laplace, Sobel) and several XAI methods (Saliency, DeepLift, GuidedBackprop). Integrated Gradients and GradientShap have modest search spaces that cover the step count, integration scheme, and, for GradientShap, the noise characteristics.

D.3 Computational details

Hardware. All experiments were executed on a local high-performance computing (HPC) cluster equipped with Intel ® Xeon E5-2650 v4 CPUs (12 cores, 24 threads, 2.20 GHz) and 256 GB RAM per node. No dedicated GPUs were required. Jobs were managed with SLURM 22.05 and ran under AlmaLinux 9.5 .

Software. The codebase is primarily written in Python 3.13.0 . Key libraries are:

NumPy 2.1.3 ,

PyTorch 2.6 for model definition,

PyTorch-Lightning 2.5 for model training and evaluation,

scikit-learn 1.6.1 for classical baselines and metrics,

hyperopt 0.2.7 for Bayesian optimization,

POT 0.9.5 for Earth-Mover-Distance evaluation,

Hydra 1.3.2 for experiment handling.

The requirements.txt file includes exact versions and is included in the project repository.

Runtime for classifiers. Training a single classifier on XAI-TRIS or the Artificial-Lesion MRI data required ∼ 10 -15 min on one CPU core. By far the dominant cost stemmed from hyperparameter optimization of the XAI methods. For each combination of scenario ( LIN , XOR , RIGID ) and signalto-noise ratio ( α ∈ { 0 . 1 , . . . , 0 . 90 } ) we ran 200 TPE iterations, evaluating on the full validation split ( 500 -2000 instances, depending on the dataset). After ∼ 100 -150 iterations, we confirmed the convergence plateaus. Each optimization run was parallelized across 12 CPU cores via multiprocessing , resulting in a wall-clock time of 12-24 hours.

Runtime for XAI methods. We report runtime measurements for the XAI methods in Table 4. PatternLocal adds a single weighted regression per explanation on top of the cost of the local surrogate. Since fitting the surrogate (e.g., with LIME) is the most expensive step, the additional regression keeps the runtime in the same order of magnitude. Moreover, PatternLocal only regresses on samples in the local neighborhood, and in practice, we further reduce cost by discarding samples with very low weight. Like LIME, we use superpixels to reduce computational cost and include a low-rank approximation. See more details in Appendix E.1.

Although runtimes are difficult to compare across different hardware and implementations, we control for this by keeping all settings fixed and averaging over 1000 instances of the XAI-TRIS dataset on an AMD EPYC 9124 16c/32t 3.0 GHz machine (also for LIME inference). Given that PatternLocal is only slightly slower than other model-agnostic methods such as LIME or KernelSHAP, while consistently achieving better explanations, we believe the overhead is justified.

E Extended results

E.1 XAI-TRIS Benchmark

Quantitative evaluation. In Figure 8, we investigates how different choices of h x ⋆ ( · ) and Q ( · ) = ∥ · ∥ 1 affect explanation quality. We compare PatternLocal and LIME with a low-rank representation and superpixel representations.

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Qualitative evaluation. In Figure 9, we show qualitative examples of explanations on the XAITRIS Benchmark dataset obtained with the MLP model. For PatternLocal and LIME we set h x ⋆ ( · ) to the identity and use the squared ℓ 2 -penalty, R ( · ) = Q ( · ) = ∥ · ∥ 2 2 . It is evident that PatternLocal produces better explanations, most markedly in the WHITE scenarios and consistently better than LIME in every setting. As expected, the filter-based methods (Sobel, Laplace) perform competitively only in the RIGID CORR case.

Figure 10 shows examples of explanation for different choices of h x ⋆ ( · ) and Q ( · ) = ∥ · ∥ 1 . We compare PatternLocal and LIME with a low-rank representation and superpixel representations. We use the naming PatternLocal ( h x ⋆ ( · ) = id , Q ( · ) = ∥·∥ 2 2 ), PatternLocal LowRank ( h x ⋆ ( · ) = lowrank , Q ( · ) = ∥ · ∥ 2 2 ), and PatternLocal LowRank LASSO ( h x ⋆ ( · ) = superpixel and Q ( · ) = ∥ · ∥ 1 ).

E.2 Artificial Lesion MRI Benchmark

The Artificial Lesion MRI Benchmark dataset [19] was created to provide a semi-realistic, fully controlled setting for evaluating XAI methods on MRI-based lesion detection. Each image is a down-sampled axial slice of size 128 × 128 containing one or more synthetically inserted lesions. The input dimensionality is highly imbalanced ( N = 2500 < D = 16384 ). This pronounced D>N regime makes local surrogate approaches such as LIME, KernelSHAP, and our PatternLocal particularly sensitive to the choice of the input-simplification mapping h x ⋆ ( · ) and to regularization. In all experiments, we therefore segment each slice into superpixels with slic before fitting the surrogates, and set both regularizers to the squared ℓ 2 norm, R ( · ) = Q ( · ) = ∥·∥ 2 2 . The classifier is a CNN model achieving > 90% accuracy on the test set.

Quantitative evaluation. Table 6 reports the mean Earth Mover's Distance (EMD) and Importance Mass Error (IME) over the entire test set. PatternLocal and LIME underperform relative to the other XAI methods. We suspect that this is primarily because the latter suppresses many low-level attributions that inflate the error of the PatternLocal and LIME methods. Crucially, this strategy considers every superpixel, even those that neither method deems highly relevant. It is not uncommon to perform feature selection or only consider the most important superpixels. A more realistic assessment is obtained by considering only superpixels whose importance exceeds a high threshold.

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Restricting the comparison to above 0 . 9 (Table 7) changes the ranking: PatternLocal now attains the lowest EMD and a markedly reduced IME, whereas LIME and the edge filters deteriorate. The gradient-based methods improve their IME scores but exhibit extreme variance, indicating that their few high-magnitude attributions are positioned correctly only about half the time. Additionally, on average, PatternLocal selects 2 . 5 ± 1 . 2 superpixels per slice vs. 4 . 5 ± 2 . 1 for LIME. The contrast between the two evaluation protocols highlights a well-known drawback of superpixel explanations: much of the attribution mass is distributed over moderately important segments that are irrelevant for human interpretation yet heavily penalize set-wise metrics such as EMD and IME. By focusing on high-confidence regions, PatternLocal exposes its intended advantage in reducing false-positive attributions.

±

±

Qualitative evaluation. Explanations are shown in Figure 11. Across all slices, PatternLocal highlights fewer superpixels, and the ones it does highlight align more closely with the ground-truth lesions than those produced by LIME. Both methods are nonetheless limited by the superpixel resolution: lesions that cross superpixel boundaries cannot be perfectly recovered. Filter-based methods (Sobel, Laplace) fail completely because the lesions are diffuse and lack strong boundaries; XAI methods (Integrated Gradients, Saliency, DeepLift, GradientShap, GuidedBackprop) tend to produce noisy attribution maps with only occasional alignment to the lesions.

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E.3 EEG Motor Imagery dataset

Figure 12 illustrates a trial from the EEG motor imagery experiment used for physiological validation. It shows how explanation signals capture task-relevant temporal, spectral, and spatial patterns compared to the raw EEG. The figure summarizes results across methods, highlighting that PatternLocal produces more distinct cue-locked responses and source activations consistent with known motor-imagery physiology.

F Additional Discussion

F.1 Evaluation metrics

Many studies in explainable AI evaluate attribution methods using faithfulness-based metrics such as insertion, deletion, or accuracy drop. These metrics measure how the model's output changes when parts of the input are removed or revealed. They do not use ground-truth information about which features are relevant, but instead reward explanations that match the model's predictive behavior. On suppressor-aware benchmarks, this is problematic. Removing these features still alters the model's output if a model relies on suppressor variables due to statistical dependencies rather than the true signal. As a result, faithfulness metrics can incorrectly reward attributions that highlight suppressors. This behavior follows from how such metrics are defined and is not simply an implementation artifact.

Wilming et al. [35] provide a theoretical analysis of suppressor variables and show that many popular XAI methods assign non-zero importance to suppressor features when the data contain correlated noise. Blücher et al. [6] further show that the PredDiff method, which is based on conditional expectations, is closely connected to Shapley values. Since Shapley values distribute credit according to statistical dependence rather than causal relevance, they can also assign importance to suppressors or other correlated but task-irrelevant features. Therefore, evaluation metrics implicitly following this logic cannot distinguish between true causal relevance and statistical influence. They may judge an explanation as "faithful" even when it highlights misleading parts of the input.

Haufe et al. [13] argue that faithfulness to the model is insufficient for a correct explanation and that relying solely on it can mislead scientific interpretation or model validation. They call for formal criteria of correctness that go beyond reproducing model behavior. It is concerning that many of the most commonly used XAI methods and evaluation metrics share the same weakness: both can appear consistent with the model while failing to reflect the underlying ground truth.

We also include the mean squared error (MSE) in our ablation studies for completeness. MSE does not capture spatial structure and penalizes false positives and negatives equally, yet it produces the same ranking of methods as our primary metrics. This consistency supports the robustness of our findings. Overall, metrics that do not use ground-truth relevance, such as faithfulness-based scores, can reward faithful but misleading explanations. In suppressor-aware settings, this risk is particularly severe. Ground-truth-based metrics are therefore more appropriate for evaluating whether an explanation truly identifies the relevant features.

G Ablation Studies

G.1 Mixing white and correlated noise

Instead of varying the signal-to-noise ratio (SNR), we can fix the SNR and introduce a new parameter β to control the balance between white and correlated noise. Specifically, β = 0 corresponds to the purely white-noise scenario ( WHITE ), while β = 1 corresponds to the purely correlated-noise scenario ( CORR ). Under this setup, the data-generation process can be written as

where α controls the SNR, β governs the relative contributions of white versus correlated noise, G is the same Gaussian spatial filter used in the CORR scenario, and η ( n ) 1 , η ( n ) 2 represent the background noise sources.

Figure 13 shows the XOR scenario under this new scheme, demonstrating that as β increases (i.e., as correlated noise becomes more dominant), the performance gap between LIME and PatternLocal grows accordingly.

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G.2 Model architecture and hyperparameter objective

Figures 14-17 summarise the ablation study carried out in this appendix. For every explanation method under investigation we systematically vary two experimental factors:

Model architecture. We compare a multi-layer perceptron ( MLP ) with a convolutional neural network ( CNN ).

Hyper-parameter objective. Method hyperparameters are tuned either for minimum Earth Mover's Distance ( EMD ) or for minimum mean squared error ( MSE ) on the validation set.

This yields the four result groups

MLP + EMD (Figure 14)

MLP + MSE (Figure 15)

CNN + EMD (Figure 16)

CNN + MSE (Figure 17)

Each figure contains three panels that report, as a function of the signal-to-noise ratio (SNR), the Earth Mover's Distance (top), the Importance Mass Error (middle), and, included here for completeness, the Mean Squared Error (bottom). Shaded bands correspond to one standard deviation across the test images.

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0.4

0.5

0.6

0.7

0.8

0.9

a

(SNR)

0.00

0.11

0.22

0.33

PatternLocal

LIME

Sobel

Laplace

IntegratedGradients

Saliency

DeepLift

GradientShap

GuidedBackprop

(c) Mean squared error (MSE)

0.18

0.14

0.09

0.04

0.17

0.12

0.08

0.04

0.2

0.1

0.2

0.1

0.7

0.7

0.7

0.7

0.8

0.8

0.8

0.8

0.9

0.9

0.2

0.2

0.6

0.3

0.6

0.3

RIGID

0.7

0.4

0.5

0.6

0.8

0.7

a

(SNR)

GuidedBackprop

RIGID

0.7

0.4

0.5

0.6

0.8

0.7

a

(SNR)

GuidedBackprop

0.8

0.8

0.9

0.9

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0.9

NeurIPS Paper Checklist

1. Claims

Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?

Answer: [Yes]

Justification: The abstract and introduction clearly present the core contributions of the paper, including the development of PatternLocal, its theoretical foundation, and its empirical advantages. The key limitation, reliance on training data, is also mentioned early in the introduction.

Guidelines:

The answer NA means that the abstract and introduction do not include the claims made in the paper.

The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.

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It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.

2. Limitations

Question: Does the paper discuss the limitations of the work performed by the authors?

Answer: [Yes]

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The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.

The authors are encouraged to create a separate "Limitations" section in their paper.

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3. Theory assumptions and proofs

Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?

Answer: [Yes]

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Theorems and Lemmas that the proof relies upon should be properly referenced.

4. Experimental result reproducibility

Question: Does the paper fully disclose all the information needed to reproduce the main experimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?

Answer: [Yes]

Justification: The paper provides a detailed description of the methodology and experimental setup in the main text, with additional specifics in the appendices. In the camera-ready version, the GitHub repository includes all necessary datasets, code, scripts, and results to fully reproduce the experimental findings.

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The full details can be provided either with the code, in appendix, or as supplemental material.

7. Experiment statistical significance

Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?

Answer: [Yes]

Justification: The paper includes standard deviation to reflect distribution variance in Section 5. As stated in Figure 4's caption, error bars are omitted because they are too small to be visualized due to the large number of samples used, implying high statistical confidence in the results.

Guidelines:

The answer NA means that the paper does not include experiments.

The authors should answer "Yes" if the results are accompanied by error bars, confidence intervals, or statistical significance tests, at least for the experiments that support the main claims of the paper.

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For asymmetric distributions, the authors should be careful not to show in tables or figures symmetric error bars that would yield results that are out of range (e.g. negative error rates).

If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.

8. Experiments compute resources

Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?

Answer: [Yes]

Justification: The supplementary material provides details on the compute resources and estimated execution times. Due to the high computational demands, the raw experimental results are also shared via GitHub for transparency and reproducibility.

Guidelines:

The answer NA means that the paper does not include experiments.

The paper should indicate the type of compute workers CPU or GPU, internal cluster, or cloud provider, including relevant memory and storage.

The paper should provide the amount of compute required for each of the individual experimental runs as well as estimate the total compute.

The paper should disclose whether the full research project required more compute than the experiments reported in the paper (e.g., preliminary or failed experiments that didn't make it into the paper).

9. Code of ethics

Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines ?

Answer: [Yes]

Justification: The paper uses only synthetic and publicly available benchmark datasets, including de-identified human data, and does not involve any new human-subject experiments, private data, or deprecated resources. The research aims to reduce misleading feature attributions and to enhance transparency and accountability in AI model interpretation.

Guidelines:

The answer NA means that the authors have not reviewed the NeurIPS Code of Ethics.

If the authors answer No, they should explain the special circumstances that require a deviation from the Code of Ethics.

The authors should make sure to preserve anonymity (e.g., if there is a special consideration due to laws or regulations in their jurisdiction).

10. Broader impacts

Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?

Answer: [Yes]

Justification: PatternLocal seeks more trustworthy explanations by mitigating suppressor variables, which can benefit safety-critical auditing; nonetheless, like any XAI tool it can mislead, so over-reliance on its saliency maps is risky. This is briefly mentioned in limitations.

Guidelines:

The answer NA means that there is no societal impact of the work performed.

If the authors answer NA or No, they should explain why their work has no societal impact or why the paper does not address societal impact.

Examples of negative societal impacts include potential malicious or unintended uses (e.g., disinformation, generating fake profiles, surveillance), fairness considerations (e.g., deployment of technologies that could make decisions that unfairly impact specific groups), privacy considerations, and security considerations.

The conference expects that many papers will be foundational research and not tied to particular applications, let alone deployments. However, if there is a direct path to any negative applications, the authors should point it out. For example, it is legitimate to point out that an improvement in the quality of generative models could be used to generate deepfakes for disinformation. On the other hand, it is not needed to point out that a generic algorithm for optimizing neural networks could enable people to train models that generate Deepfakes faster.

The authors should consider possible harms that could arise when the technology is being used as intended and functioning correctly, harms that could arise when the technology is being used as intended but gives incorrect results, and harms following from (intentional or unintentional) misuse of the technology.

If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).

11. Safeguards

Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?

Answer: [NA]

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The answer NA means that the paper poses no such risks.

Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.

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We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.

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Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?

Answer: [Yes]

Justification: All external datasets and methods used, such as XAI-TRIS and artificial lesion MRI, are properly cited in the paper with references to their original publications. These are publicly available benchmarks and tools with known licenses, and no terms of use have been violated.

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If this information is not available online, the authors are encouraged to reach out to the asset's creators.

13. New assets

Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?

Answer: [NA]

Justification: The paper does not introduce or release any new datasets, models, or code assets; it proposes a novel method (PatternLocal) evaluated on existing benchmarks like XAI-TRIS and the artificial lesion MRI dataset.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe manuscript introduces a new XAI method for vision tasks called PatternLocal. Similar to previous methods such as LIME, the proposed PatternLocal method constructs a local linear surrogate, and then constructs a generative model using the resulting weights. It is claimed that the process mitigates the effects of suppressor variables in generating explanations (false-positive attribution).\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n>- The topic is timely and the issue of false-positive attribution (particularly due to suppressor variables) is well known and solutions such as those provided in this work are of interest. \n>- The examples, such as the Toy Example of Section 3.2 and the example in Section 2.2 of the suppressor variable are helpful and well-explained. \n\nWeaknesses: The manuscript is generally not well-written. The notation is not consistent and the explanations are incomplete and vague. More detailed comments are provided below:\n>- On Page 3, Line 67, $h_{x_*}$ is introduced as a mapping that produces a low-dimensional semantically meaningful representation. The definition is vague and needs additional explanation. Furthermore, the output is denoted as $x'_*$, however, in Equation 2, the input to the inverse $h^{-1}$ is shown by z (which seems more suitable). The notational inconsistency is repeated in many other instances and reduces the readability of the manuscript.\n>- It is not clear why on Page 3, Line 94, w is used instead of W, whereas in all previous instances, W was used to represent the transform matrix.\n>- In Page 3, Equation 2, $\\hat{s}$ is recovered with respect to which loss metric? (e.g., is it to minimize the mean squared error?)\n>- The manuscript is not well-organized. For instance, the advantages of PatternLocal are discussed in Page 4 in detail before the method is introduced even at a high level. It seems more appropriate to provide a high level description of the main ideas in PatterLocal first, and then describe its advantages compared to existing methods. \n>- In Figure 4, it is not clear what the x-axis represents. It is stated in the caption that it represents the SNR, however, the value ranges from 0 to 1. It seems from the supplementary material that it represents alpha (as a surrogate for SNR). If so, should we expect that the plots be decreasing in alpha? (as the noise decreases) If so, why are some of the plots increasing in alpha?\n\nQUESTIONS:\n> Please explain the expected behavior of each plot as a function of the x-axis variable (alpha).\n> Please see the weaknesses section for additional comments on the manuscript and organization, and provide clarifications in your rebuttal if needed.\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-10"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis study tackles the problem that existing XAI methods tend to assign high importance to suppressor variables—features that are not directly related to the prediction target but cancel out noise and thereby boost the model’s overall accuracy.\nPrevious work has proposed a method to suppress the influence of suppressor variables in linear models.\nThe proposed method in this study extends those ideas so they can be applied to non-linear predictive models.\nConcretely, around the test instance to be explained, the method trains a local linear surrogate model of the non-linear predictor using LIME.\nIt then estimates parameters that map the surrogate model’s outputs back to simplified inputs of that test instance, and treats those estimated parameters as the feature importances.\nExperiments on datasets constructed to contain suppressor variables demonstrate that the proposed approach produces correct explanations, outperforming existing feature attribution methods.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n- Extending the Pattern proposed by Haufe et al. to work with non-linear models is both novel and practically valuable, and the derivation of the proposed method appears sound.\n- The toy example convincingly shows that—even for a non-linear model—the proposed approach can drive the importance of a suppressor variable to zero, effectively illustrating the method’s validity.\n- On the XAI-TRIS benchmark, the proposed method performs better than many alternative explanation techniques on images corrupted by noise and suppressor variables, demonstrating its usefulness.\n\n# Weaknesses\n- It is unclear why simply adding an L1 regularizer in LIME would not suffice to push suppressor-variable importance toward zero. In the experiments, both LIME and the proposed method seem to use L2 regularization, yet the behavior under L1 regularization is not examined in depth.\n- The evaluation metrics employed are not standard. For image classification, metrics such as Insertion, Deletion, or Infidelity are commonly used to measure explanatory faithfulness, whereas the paper adopts a non-standard metric called EMD; no compelling reason is given for this choice.\n-The validity of that metric is questionable. In (10), defining EMD, |\\mathbf{S}| appears to denote the absolute values of the estimated importance map, but taking absolute values discards whether a feature contributes positively or negatively. In IME (11), the numerator and denominator are summed independently, so it is unclear how false positives and false negatives are captured. Moreover, the meaning of superscripts such as |\\mathcal{F}^+| and |\\mathbf{s}| is ambiguous—do they denote set cardinality, absolute value, or vector norm?\n\nQUESTIONS:\nIf you have rebuttals to the points listed under Weaknesses, please present them.\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the phenomenon of  “suppressor variables”, which are features that influence model predictions but are not statistically dependent on the output variable, potentially leading to false-positive feature attributions.\n\nThe authors propose PatternLocal, a novel  and model agnostic XAI technique that generalizes the Pattern approach into the local, non-linear setting. PatternLocal operates in three steps: it (1) builds a locally linear surrogate model around an instance of interest (via LIME, SHAP, or gradients), (2) transforms the surrogate’s discriminative weights into a generative explanation using local data statistics, and (3) outputs instance-level attributions that suppress the effect of suppressor variables while preserving local model fidelity.\n\nThe authors conduct empirical validation on the XAI-TRIS benchmark and an artificial lesion MRI dataset, which are specialized benchmarks that offer suppressor-variable scenarios. After hyperparemter tuning, PatternLocal tends to outperforms established XAI methods on the Earth Mover’s Distance (EMD) and Importance Mass Error (IME) metric.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n-\tStudying the behavior of explanation methods in the presence of “suppressor variables” is relevant. \n\n-\tThe paper proposes a theoretical sound way to extend Pattern approach to non-linear models by building on top of existing (model agnostic) explanation approaches.\n\n-\tThe paper is well written and easy to follow.\n\nWeaknesses:\n\n- The theoretical contributions are limited as the method is a direct extension of the existing Pattern method. \n\n-\tThe method appears to be computationally way more expensive compared to the baselines and the experimental results only partly justify the effort despite extensive hyperparameter search. \n\n- All experiments are primarily on synthetic, or semi-synthetic image data. The generalization to complex real-world datasets remains unclear.\n\nQUESTIONS:\nWhy focus on Earth Mover’s Distance (EMD) and Importance Mass Error (IME) and not simply using more standard metrics like MSE or PSNR for  visual explanation comparison? How sensitive are your conclusions to metric selection?\n\nThe paper uses exhaustive hyperparameter tuning for all methods. Is this necessary for PatternLocal to perform well, or do optimal hyperparameters at least generalize in some way? How does PatternLocal perform in more typical, default or lightly-tuned scenarios compared to common default settings of existing explanations? \n\nWhat kind of explanations does PatternLocal produce when be applied to datasets like ImageNet or tabular data, where finding sufficient, well-aligned local neighbors is difficult? \n\n Could access to generative models or learned latent spaces provide a substitute for local neighborhood samples where data is limited or not aligned? Would such extensions preserve PatternLocal’s suppressor-mitigation properties?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors investigate the problem of XAI methods mis-attributing *suppressor variables*; that is, variables that affect model prediction but do not have statistical dependency with the target. An existing method, *Pattern*, can remove the effect of suppressor variables for feature attribution, however this method is global and therefore may not work well when applied to complex, nonlinear models. To solve this problem, the authors propose, *PatternLocal*, which extends  Pattern to be able to work on local neighborhoods in conjunction with locally discriminative surrogate models such as KernelSHAP or LIME. The proposed method is evaluated on the XAI-TRIS synthetic dataset and an MRI benchmark dataset.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n* The proposed method is a natural extension of Pattern, and is fairly intuitive.\n* The experimental results on synthetic datasets show that PatternLocal outperforms competing methods in suppressing attributions for suppressor variables.\n\n**Weaknesses:**\n* Writing Quality and Notational Issues. I found the manuscript unnecessarily difficult to understand. In particular, the notation and writing could be more rigorous (see **Minor Issues** and **Questions** below). It would be helpful if there was a written algorithm that summarized PatternLocal. Figure 1 is very confusing -- it is not clear what the different colors, dotted lines, marker shapes, heatmaps, etc. represent, since they are not defined.\n* Motivation. The purpose of most attribution methods (e.g. LIME, KernelSHAP) is to identify the most relevant features for the model prediction. If the model uses a suppressor variable in its prediction, then assigning that variable a nonzero attribution seems like expected behavior. It is not clear to me why a user of LIME or KernelSHAP would want to suppress attributions suppressor variables rather than training a better model. It would be helpful if the authors could add more discussion in the manuscript regarding motivation and use-cases.\n* Missing related works section. It would be helpful to have more discussion around related works.\n* Limited theoretical contribution. The paper could be improved if there was some theoretical results, e.g. sample complexity (especially since one of the stated limitations is having enough training data in the neighborhood of each explanation).\n\n**Miscellaneous Minor Issues / Questions**\n* Line 64: \"Throughout we therefore restrict…\" \n* Line 125 says \"regressing the local surrogate output… onto the neighborhood of x\", but line 128 says \"by regressing the simplified input x on the surrogate model's response…\". These two lines seem to contradict each other.\n* The variable $s$ seems to be overloaded -- it's sometimes used to represent a latent vector (equation 1), and sometimes it's a function (equation 6) which is also equal to a? In Eq. 10, $s$ is also an importance map.\n* In equation 5,  $\\mathcal{Z}$ is treated as a distribution over which you take an expectation, but it's defined as a \"simplified input space\". There is a similar issue in equation 6 for $\\mathcal{X}$.\n* Equation 6 has the term: $(h_{x}(x) - u \\tilde y)^2$. Is u a D'-dimensional vector or a scalar? Should there be a $l_1$ or $l_2$ norm here?\n* $\\mathcal{F}^+$ in equation 10 is not defined. Is this supposed to be the same as $F^+$?\n* In Section 4.4, what does $|s|$ represent? Equation 10 seems to imply that it's an absolute value or normalization, but Equation 11 implies that $|s|$ is an integer.\n\nQUESTIONS:\n* The prediction model is effectively a surrogate of the data generating process. The attribution method is then a surrogate of the prediction model (which is also a surrogate). PatternLocal adds another layer on top of that. Have you evaluated how accurate PatternLocal is with respect to the model prediction or ground truth target? For example, many works on attribution methods use faithfulness or fidelity metrics to evaluate their performance [1].\n\n[1] https://arxiv.org/pdf/2211.05667\n\nLIMITATIONS:\nLimitations are addressed on Page 9.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 1, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-02"}