Interpreting Kolmogorov-Arnold Networks in Neuroimaging: A Path-Based Attribution Framework
Authors: Suhrud Murthy
Venkatesh Babu Radhakrishnan
Neelam Sinha
Venue: Accepted by TMLR ()

Abstract: Explainability aspects of most classification models are learnt through instance-specific analysis. However, in understanding diseases, it is important to consider population-wide analysis in order to identify affected regions that are consistently seen across cohorts of diseased population. In this study, we report utility of Kolmogorov-Arnold Networks (KANs) in understanding population-wide characteristics seen in subjects affected by Alzheimer's disease (AD). KANs offer enhanced interpretability through learnable activation functions on network edges. Thus, the learned functions reflect the characteristics of the entire span of training data. In a KAN network trained for classification, attributions through the network can be traced to understand how specific inputs influence the output label. In this study, we propose a path-based attribution framework that generates global importance maps by tracing exhaustive information flow through all potential paths. Our method initially scores the functions on the edges of a trained KAN using an appropriate scoring function. Subsequently, these scores are propagated through the network to compute path-attributions. This approach scales linearly with network depth, and is only dependent on model training and does not need further analysis on training data post-hoc. Evaluation on three public AD neuroimaging datasets (OASIS, ADNI, Mendeley, totally comprising 7428 acquisitions), were carried out on 2D brain slices as well as 3D brain volumes. The corresponding KAN test accuracies are $93.24\%$, $81.85\%$, and $91.25\%$ on OASIS, ADNI, and Mendeley datasets, respectively. Alongside, competitive or improved performance via metrics such as Insertion AUC, Deletion AUC and Sufficiency, is also demonstrated. The generated attribution maps identify clinically meaningful regions including the body and genu of corpus callossum, corona radiata, bilateral caudate nuclei, medial prefrontal cortex and temporal lobe structures, aligned with established AD pathology literature. By providing voxel-level global attributions as network-intrinsic properties, our framework addresses a critical gap in AI interpretability and supports exploratory clinical analysis and model auditing of AI-assisted AD diagnosis systems.

Published in Transactions on Machine Learning Research (03/2026)
Interpreting Kolmogorov-Arnold Networks in Neuroimaging: A Path-Based Attribution Framework
Suhrud Murthy!
R. Venkatesh Babu² Neelam Sinha
Centre for Brain Research, IISc Bangalore
Vision and Al Lab, Deportment of Computational and Data Sciences, 11Sc Bangalore
Reviewed on OpenReview: https: // openreview. net/ forun? id= cPtRpNdYc2
Abstract
Explainability aspects of most classification models are learnt through instance-specific analysis. However, in understanding discases, it is important to consider population wide analysis in order to identify affected regions that are consistently seen across cohorts of the diseased population. In this study, we report the utility of Kolmogorov-Aroold Net- works (KANs) in understanding population-wide characteristics seen in subjects affected by Alzheimer's disease (AD). KANs offer enhanced interpretability through learnable activa- tion functions on network edges. Thus, the learned functions reflect the characteristies of the entire span of training data. In a KAN network trained for classification, attributions through the network can be traced to understand how specific inputs influence the output label. In this study, we propose path-based attribution framework that generates global importance maps by tracing exhaustive information flow through all potential paths. Our method initially scores the functions on the edges of trained KAN using an appropriate scoring function. Subsequently, these scores are propagated through the network to compute path-attributions. This approach scales linearly with network depth, and is only dependent on model training and does not need further analysis on training data post-hoc. Evaluation on Uhree public AD neuroimaging datasets (OASTS, ADNI, Mendeley, totally comprising 7428 acquisitions), were carried out on 2D brain slices as well as 3D brain volumes. The corresponding KAN test accuracics are 93.24%, 81.85%, and 91.25% on OASIS, ADNI, and Mendeley datasets, respectively. Alongside, competitive or improved performance via metrics such Insertion AUC, Deletion AUC and Sufficiency, is also demonstrated. The generated attribution maps identify clinically meaningful regions including the body and genu of corpus callosum, corona radiata, bilateral caudate muclei, medial prefrontal cortex and temporal lobe structures, aligned with established AD pathology literature. By provid- ing voxel-level global attributions as network-intrinss properties, our framework addresses a critical gap in AI interpretability and supports exploratory clinical analysis and model auditing of Al-assisted AD diagnosis systems.
1 Introduction
The intersection of medical imaging and computational neuroscience has been driven forward by the advent of artificial intelligence and deep learning. Imaging modalities such as magnetic resonance imaging (MRT), such as structural MRIs (sMRI) and functional MRIs (IMRI), among several others, provide spatial and temporal data at a very high resolution. This allows researchers to investigate the anatomy of the brain at fine granularity, assisting early diagnosis and understanding of disorders Lundervold & Lundervold (2019). Deep learning models achieve high accuracies on brain imaging tasks, yet their opacity limits clinical adoption and regulatory approval in neuroscience Kelly el al. 2019 with model decisions often being inscrutable.
* *Corresponding Authors: Neelam Sinha <neclambcrr-isec. in>, R. Venkatesh Babu <venkydiisc.ac..n3

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Interpretability of network is crucial in medical analysis. Unlike consumer domains, medical decisions require transparent reasoning, and clinicians must. be able to trace model decisions to anatomically fune- tionally meaningful biomarkers, which can also aid in distinguishing between medically backed model deci- sions and erroncous correlations that can occur due to noisy or unclcan data Wang et al. (2024) Salahuddin et al. 2022). Several altribution methods have been put forth to understand model decisions and generate input attributions. Localized attribution methods such as gradient saliency maps, Layer-wise Relevance Propagation, Integrated Gradients, and occlusion-based methods, among others, have contributed insights to brain imaging by highlighting which voxels or regions contribute to model predictions. However, these approaches often produce localized, sample-specific explanations, making it difficult to identify which fea- tures or regions are consistently important across training data. While such local attributions can indicate potential importance for individual cases such as tumour detection, where tumours are unique to the subject and it is difficult to generalize the location a tumour across subjects, they may provide limited clarity into patterns seen across brain populations for nourodegenerative discases such as Alzheimer's discase (AD) and dementia, among others, which involve diffuse, population-level structural changes that are better captured through global attribution methods.
Additionally, arriving at potentially thousands of local attributions for individual data items can be difficult to interpret. Global feature attributions, which show how features influence the decision of a model across the entire training distribution, instead provide a consolidated view of feature importance that highlights sys- tematic patterns learned by the model during training rather than instance-specific effects. This distinction is particularly important in medical imaging, for problems such as Alzheimer's detection, where clinicians and researchers need to understand which anatomical regions the model has learned to consistently rely upon across patient populations Munroe et al. (2024..
Global attributions can provide several advantages over localized attribution in medical imaging contexts. It enables the identification of biomarkers that are present across the patient distribution in training data, It also aids model debugging by revealing biascs or spurious correlations by highlighting the point of focus of the model, enabling users to identify, with known ground-Iruth markers, the model is identifying appropriate features. By accurately highlighting clinically meaningful features learnt by the model and demonstrating that models rely these features alone for their decision, regulatory approval and clinical trust can be potentially gained. It provides complementary insights to physician diagnosis Hill (2024). It also bridges the communication gap between the AT and medical world by providing population-level insights that align with medical knowledge. By attributing global features not as an aggregated property of the inputs, but as an intrinsic property of the trained network itsclf, we can generate attribution maps that highlight medically relevant regions of the brain.
Our work utilizes the inherent functional transparency of the recently proposed Aalinogorov-Aroooe Networks (KANs). KANs, as originally proposed in Liu et al. (022)), are designed to replace every scalar weight in multi-layer perceptron (MLP) with learnable univariate spline function on each edge, as opposed to a node. They leverage the Kolmogorov-Amold Representation Theorem, which states that "any continuous high-dimensional function can be decomposed into a finite sum of univariate continuous functions", which has made it possible to express the transformation from an input to the output decision as an explicit graph of simple, human interpretable univariate functions on edges that are simply added at each node. Due to the functions on each edge being explicit and univariate, it is possible to analyze the nature of each function and thereby quantify the influence of the function locally. Specifically, a learned function on an edge consists of a base component and spline component, expressed as Φ(x) wyb(xz) + w,,plinn(xz), where b(x) is typically the SILU activation function and spline(x) is a lincar combination of basis splines. This structure makes it possible to identify the individual contributions of these functions, their interactions with the rest of the network, and their association with each individual input.
In neuroimaging, specifically in understanding the contribution of each individual voxel corresponding to a certain part of the brain, input-based attribution can prove to be particularly useful. By tracing the decision of the model back to a particular input/set of inputs, it can be made possible to identify and rank
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the features influencing the model. This makes it possible to construct faithful global attribution maps input-level granularity by analyzing the flow of information through the network, which tell us about the parts of the brain the model has learnt to differentiate between.
In this work, we propose a path- based attribution approach for KANs to generate population importance maps as a property of the trained network, by tracing information flow along explicit computational paths, explicitly represented by a KAN's architecture, thereby scoring input importances based on the information flow. We also evaluate its utility and reliability for neuroimaging and clinical neuroscience applications. We demonstrate that this approach allows for faithful, global attribution maps that can provide clinically and anatomically useful information.
Scope and focus. The proposed framework is designed for analysis of fully trained feedforward networks in which nonlinear transformations are associated with edges, nodes aggregate incoming signals additively or multiplicatively, and directed paths exist from input features to output neurons. KANs constitute a prime example of architectures that satisfy these conditions, and hence we define and evaluate the framework as such. In this work, we focus on fully trained KANs, which we apply to neuroimaging tasks due to their high dimensionality and established interpretability challenges, and additionally evaluate the framework on multiclass classification task using MNIST to assess behaviour in a simpler, well-controlled setting, We list our primary contributions as follows:
i) A path-based attribution framework for KANs aggregating importance across computational paths.
ii) A scalable implementation of path-attribution for data such as neuroimaging.
ii) Voxel-level global-attribution maps applied through KANs for Alzheime'ss detection.
iv) A comprehensive clinical evaluation showing anatomically meaningful regions associated with AD, supported by ROI analyses.
2 Related Literature
Several attribution methods have been proposed to understand the functioning of neural networks as "black boxes". Gradient-based approaches, Simonyan et al. (0033) calculate output gradients with respect to inputs, and Sundararajan et al. (0177) integrate gradients along a baseline path to address gradient saturation. Propagation- based approaches such as Layerwise Relevance Propagation (LRP) Bach et al. (2015) have been applied to Alzheimer's 's detection, Böhle et al. 2019) using LRP on ADNI sMRI, producing maps concentrated in the temporal lobe and hippocampus. However, the authors note a high inter-patient variability in patterns, which is a limitation in generalizing patterns across the data population. Class Activation Mapping (CAM), particularly Eigen-CAM and Grad-CAM have also been adopted for model decision explanations, but fail to provide faithful explanations, often cover unnecessarily large or imprecise regions, exhibit low gramularity in highlighting salient features, and suffer from instability and biases due to architectural factors such as Global Average Pooling and gradient explosion Bac et al.] (2020). Game-theoretic approaches such as LIME, DeepLIFT Shrikumar et al. (2017) are also popular, with SHAP being implemented by Qiu et al. (2022) on the NACC datasot and OASIS cohort and found distinct patterns unavailable through averaging local explanations, which were negative hippocampal values for cognitively normal subjects, positive for AD patients. The problem with trying to arrive at a global explanation from these local attribution methods is it conflates intrinsic feature importance and feature distribution in data Covert et al. (2020). A fcature may accumulate high average SHAP scores simply because it varies widely in training data, not because the model relies on it for decisions. This way, global maps can differ significantly from averaged local attributions Ibrahim et al. (2019), and this theoretical insight explains the empirical observation: across all local attribution methods (LRP, IG, Grad-CAM), importance scores fluctuate dramatically between patients with identical diagnoses, reflecting both model variance and data noise.
We the term "faithful" denote how closely the produced attribution maps reflect the features the model has learned and utilizes to arrive decisions, with attribution quality quantified using perturbation based metrics such as Insertion AUC, Deletion AUC, and Sufficiency.
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To solve this problem, global attribution methods that highlight locations of important features seen through-
out training data have been proposed. SAGE (Shapley Additive Global importancE) Covert et al. (2020)
directly measures the contribution of features to the model's prediction by introducing features into arbi-
trary subsets and calculating their Shapley values, but scales exponentially with dimensionality. Chan &
Veas 2024) use a gradient-based approach to rank features based on gradient descent, updating a feature's
weight. Wu et al. (2020)'s framework learns global explanations by identifying which feature detectors are most critical for each class, then testing how well those detectors respond to semantic concepts, with Graziani et al. )0200) extending this to medicine, proposing a framework to explain attribute pixel-level values to user-defined concepts. Global Attribution Mapping (GAM) Tbrahim et al. (2019) captures het- erogeneous patterns across subpopulations of local explanations clustered on distance metrics to arrive at a singular global explanation. Although faithful, this relies on local atlributions computed individually on input data, which is time-consuming and computationally expensive. As the algorithm also computes the distance matrix for all input samples, the time complexity is quadratic the number of samples, making it unsuitable for large datasets.
2.1
KANs for attribution
With KANs being proposed as interpretable networks, there have been applications in medicine. Dong ct al. 2025 used a KAN-based Graph Convolutional Networks (GCNs) for AD diagnosis on the ADNI dataset, with their GCN-KAN achieving & classification accuracy of 62.6% over standard GCNs at 57.4%. They score each ROT's importance by summing the absolute spline coefficients from the KAN layer edges connected that ROI. Although their GCN-KAN identified the hippocampus, inferior parietal gyrus, and amygdala relevant regions for AD, the approach does not work voxel-level gramularity. Knottenbelt et al. 2025 proposed CoxKAN, KAN-based framework for interpretable survival analysis with Cox proportional hazards regression, and pruned their network using the Li-norm on the edge-function of their KAN.
KANs have a structure where the flow of information throughout the network can be interpreted and input contributions can be quantified. By tracing the model's decision through the flow of information back to a specific input or set of inputs, it can be made possible identify and rank the features influencing the model. In Liu et al.] (2025), the authors utilize L1 norms to score each layer. The individual L1 norm for each activation Hi.j defined as |orsh Nr Exin Oij (ar"")) is calculated, where oi is the learnable univariate
function on the edge from input j to output i, z²(") denotes the j-th feature value from the s-th data sample, N₂ is the total number of samples.
KAN 2.0 Liu et al. (2024) states that this would not effectively capture the global relationships of the edge with the rest of the network, due to L1 norms capturing just the local information. To solve this, the authors propose recursive scoring method utilizing standard deviations of activations on the edges and nodes. They consider an L-layer KAN with width [ng, R1, nnl: Ei,, as the standard deviation of activations (1,4,)) edge, and NL, as the standard deviation on the (I, node. They score nodes as AI, and edges BL.s recursively as follows: all output node scores are set to 1; ie., AL, = 1 for all i. For (= L, - 1,..., BLnd, A1-1, Σド= B This iterative compulation propagates attribution scores from B1-1, At.j N441.
the
the output layer to the input layer, capturing the activity of each node. We are looking to score each input with respect to the output, i.e., how much each input contributes to the prediction of the model. We are also looking to find which combinations of edges carry an input's influence to the output, so a path-based attribution is required. Hence, an attribution method that propagates edge scores throughout the network to compule the contribution of each input is necessary.
3 Methodology
3.1 Edge-Scoring
KANs have a structure in which each edge comprises a function with a lincar base term and nonlinearly modulated spline component, with addition or multiplication at the nodes. A meaningful edgo-scoring metric must therefore reflect the influence of this function under data activations. For each edge from input node
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to output node o, the contribution can depend on both the learned base weight and the projection of the input through spline basis expansion whose coefficients are learned during training. Several edge-scoring metrics can be used to quantify edge importance in this setting, Examples include the L2 magnitude of the combined base and spline activations, formally defined on edge Es,o as:
B B
2
E
1
Σ Bu,i,
Waplinee 0,4,
+ Whase 6(x0.))
(1)
where Br is the activation of the e-th spline basis for input i in sample b, Wappiiue is the associated spline weight, W Whase is the base weight from to o, and b(.) is the base activation function (e.g. SiLU). Several other metries can also be used to compute the edge-score, such as the L1 norm Liu et al. (2025), standard- deviation, maximun of base and spline contributions, among several others, defined over the parameters in Eqn. 1 Each of these metrics captures different aspects of edge behavior, such total activation energy, sparsily, variability, or peak response, and the choice of metric would be dataset-dependent, based on the nature of the data being analyzed.
In our experiments, we evaluate multiple such scoring functions both independently and in combination with the proposed path-based aggregation framework. These choices are not. presented as theoretically optimal; rather, they serve as representative instantiations illustrating how different notions of edge importance interact with path-level attribution. Importantly, the proposed framework can be used in tandem with any suitable alternative edge-scoring function that captures the contribution of the readily applied depending on the dataset, architecture, or analysis objective.
3.2 Path-based Attribution
The formulae in Sec. 3.1 capture just the local influence of the function on the edge, and hence, do not account for the contributions of edges downstream in the network. Even if the edge has a strong local influence, it can be cancelled out by an edge later on in the network Liu et al. (2025). To account for the behaviourdownstrrem contribution of edges towards scoring the contribution of the input, we propose a path-basod attribution method. To prevent an explosion of the edgo-score, we normalize the score with the tanh function, with motivation from Liu et al. (2025). We score the paths as the absolute of the tanh of the product of edge-scores on the path. The input is scored as sum of all paths from the respective input node to the output node. If there are several output nodes, all the scores from the specific input node to all the output nodes are averaged. Formally, the importance score of an input feature in an L-layer Bolmogorov-Arold Network (KAN) with n output nodes can be expressed as the average over all oulput neurons of the sum over all possible paths Pi-+o from input i to output neuron o:
imp; = Σ
II 0=1 PEP CEP
Σ
aell where a. tanh (anh(F.)) (Fa).
(2)
Here, the product is taken over all edges along the path p from input neuron i to output neuron o, and Ee is the edge-score at edge e. For multiclass settings, the importance scores imp; can be obtained by averaging contributions across class-specific output neurons o, as in Equ. 2 While the proposed path-based attribution framework is agnostic to the choice of local edge-scoring function, our experimental evaluation considers multiple edge-scoring metrics as described in Sec. [.T] These include norm-based, variability-based, and max-basod mcasures, all of which are compatible with the proposed framework and are asscssed empirically across datasets. For reporting and visualization, we use magnitude- (unsigned) edge scores to provide consistent measure of how strongly an edge is utilized under data-driven activations. Importantly, none of the evaluated edge-scoring metrics is presented as theoretically optimal or universally superior. Instead, the choice of edge-scoring function is treated as datasset-dependent,, and our results illustrate how different scoring rules interact with path-level aggregation under varying data characteristics. The proposed framework remains agnostic to this choice and can accommodate suitably alternative metrics without modification.
The non-linear functions in a KAN lee on its respective edges, with simple addition or multiplication per- formed at the nodes. This means the influence of an input variable factorizes naturally along directed paths
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Figure 1: The proposed path factorization avoids double counting in KAN attribution. From left to right: Flow of information bottom-to-top; multi-layer KAN showing two different sets of subpaths (orange and blue) to the output node, with example function scores on edges. Decomposition shows how shared subpath factors identically into both paths, with distinguishing contributions arising only from unique sub-paths A and B; P and Q. The multiplicative factorization ensures that overlapping edges contribute uniformly without additive redundancy, preserving the relative importance of cach input.
from itself the output. While KAN computation graphs are not path disjoint, different inputs often traverse overlapping subnetworks due to shared spline edges. Under these architectural assumptions, where each edge applies a learned function to its input,path-dise path-disjoint and each node sums incoming signals, the network output is expressed as a path expansion:
Σ T
Σ
II
II ae.
(3)
PEP(L-t) PEP
Consider the illustrative toy-example in Fig. the factorization gives:
For two paths and Q that share common subpath S
II aee
II
ae
II ae PEPis
II ae eEQ
II aee
II ae eEQis
(4)
where the shared product Ie Or factored identically both paths as common multiplicative scalar rather than accumulating additively. As result, the distinguishing contribution of each path arises only from the edges unique to that path, i.c. from Heep, Oe versus Ile Qg- Overlaps are therefore factored in uniformly, propagating the same multiplicative weight to every traversing path, avoiding bias due to double- counting. The measure is non-negative and bounded, producing overlap-neutral attribution that is consistent with the multilayer KAN architectures used in our experiments. The path scoring accounts for downstream effects of the edge on the rest of the network, where any cancellation upstream results in lower relevance, activity and weights downstream. This is similar relevance propagation attribution methods such as DeepLIFT Shrikumar et al. (2017) and Layer-wise Relevance Propagation Bach et al. (2015). The input score is then converted to percentage- wise contribution to highlight individual contributions of each input node. This level of granularity is useful for domains such medical imaging, where regional interpretability is desired. Although the path-based formulation in Eqn. 2 captures both local edge influence and downstream interactions, computing these scores by explicitly enunerating all input-oulpul paths is not feasible for deep or moderately wide KANs, since the number of possible paths grows exponentially with network depth. Therefore, an efficient propagation mechanism is required obtain the same path-aggrogated importance values without enumerating paths directly. We introduce such an efficient matrix- based computation in the following section.

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3.3 Efficient Path-based Attribution
For a computationally elficient allribution framework, we compute the same inpul-score using matrix multi- plication. Let (( E R4xxd-1 be the edge importance matrix for layer 4, where do is the input dimensionality and n is the number of output ncurons. Then, the propagated importance matrix M is:
M a a (I- (1) E Ruxdo
(5)
The importance of the i-th input neuron simplisies to imp; = - Ma.. This matrix-based calculation scales linearly with the number of edges, O (E didi-1): which same as chained matrix multiplication
compared to the exponential complexity of the naive path enumeration, O di): making it feasible for deeper and wider models with numerous paths. This makes the scoring approach practical for high- dimensional neuroimaging data. For example, a structural MRI volume of size 91 109 91 yields do 902,629 voxels. For KAN with layer widths d1 256, d2 = 128, and d3 64, the efficient batrix-based propagation
= 256 902,629 + 128 256 + 64 128 ~ 2.31 x 10a which is significantly
smaller than naive path enumeration (IT d.) = 902,629 256 128 64 ~ 1.89 x 10 an increase of more than four orders of magnitude, making exhaustive path computation infeasible. This comparison highlights the necessity of the efficient matrix- basod formulation for voxcl-level global attribution in high- dimensional neuroimaging settings. Once the inputs have been attributed and scored, they are then converted to percentage-wiee contributions to highlight individual contributions of each input node, at input-level granularity. This resolution is very important in brain imaging due to the requirement of high granularity, such that individual brain regions are highlighted to carry out accurate medical inferences.
4 Experimental Setup
The datasets utilized in this study include the volumetric public OASIS-1 dataset Marcus et al. (2007) to evaluate the framework's performance on 3D volumetric data, the middle sagittal slice from the ADNI dataset Jack Jr et al. (2008), selected to analyze the volume on 2D-slice data, and the Mendeley coronal-slice MRI collection Yakkundi (2023). We choose the middle sagittal slice as passes through key midline brain structures (e.g., corpus callosum, cingulate gyrus, ventricles), which are highly informative for Alzheimer's pathology, while reducing dimensionality compared to full 3D volumes Odimayo et al. (2024) Hoang et al.) (2023). All three datasets comprise sMRI scans of cognitively normal individuals, subjects with mild cognitive impairment (MCI), and patients diagnosed with AD, These cohorts provide a progression of disease states and are established benchmarks for Alzheimer's prediction on neural networks. OASIS consists of 436 volumes of shape 91 x 109 x 91. ADNI consists of 592 volumes, from which we extract the sagittal slice and crop it to 184 x 152. The Mendeley data cohort consists of 6400 samples of coronal slices. Class imbalance is handled by the usage of weighted Cross- Entss-y loss. Standard preprocessing procedures such as skull-stripping |mmth Smith al. (2004), intensity normalization Tustison al. (2010), and affine registration Avants et al. (2009, were applied to ensure anatomical consistency and comparability across scans. We use these datasets with well-defined diagnostic categories to rigorously test how KANs capture structural differences associated with cognitive decline. As a Conccep,-, we also test the attribution frameworks on a 10-class MNIST classification.
All experiments were conducted on machine with Nvidia A100 GPU, and the path- attribution framework is applied post-hoc on fully trained models to generate global attribution maps, showing the contribution of specific inputs towards the models decision. The maps are quantitatively assessed using Insertion AUC (InsAUC), Deletion AUC (DelAUC) Petsiuk et al. (2018), and Sufficiency (Suff) metrics DeYoung et al. (2020). InSAUC measures how the model's confidence increases as the most important features (voxels) identified by the altribution are progressively added to a blank input. DelAUC assesses how quickly the model's confidence decreases as these important features are removed, indicating the extent to which the model relics on these features for its decision. Suff measures whether the top-ranked features alone are sufficient to maintain the model's predictive performance. This allows for an assessment of whether the network identifies clinically meaningful features for differentiating between healthy and diseased individuals.
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Further, to interpret model attributions and assess their relevance, we performed region-of-interest (ROI) analyses on the attribution ion maps generated across 15 independent runs. Two anatomical atlases were used for comprehensive grey and white matter coverage: the Brainnetome (BN) Atlas Fan et al. (2016) and the Johns Hopkins University (JHU) ICBM-DTI White Matter Atlas Mori et al. (006 Please refer Appendix
A.I for more details on model up, training and analysis.
5 Results and Discussions
We train a KAN on the datasets and achieve test accuracies of 93. 93.24%, 81.85% and 91. 91.25% respectively, on the OASIS-I, ADNI and Mendeley test sets. We also train the KAN on MNIST classification as a Proof- of- Concept (PoC) and achieve test accuracy of 99.4%. Using the proposed path-based attribution, we obtain Insertion AUC of 0.865 + 0.049, Deletion AUC of 0.282 + 0.020, and Sufficiency of 0.068 + 0.064 On ADNI, the method achieves an Insertion AUC of 0.758
the OASIS dataset as indicated in Table I + 0.044, Deletion AUC of 0.380 + 0.051, and Sufficiency of 0.209 + 0.143. For the Mendeley cohort, we report an Insertion AUC of 0.791 + 0.016, Deletion AUC of 0.463 + 0.099, and Sufficiency of 0.226 + 0.033. On MNIST, the results are Insertion AUC 0.964 + 0.003, Deletion AUC 0.393 + 0.022, and Sufficiency 0.072 = 0.015. These values indicate that path attributions consistently rank features that affect model confidence under both insertion and deletion perturbations. We compare against global attribution methods from GAM, KAN, and KAN 2.0, while also reporting results for the proposed path-attribution framework paired with selected edge-scoring functions to illustrate its behaviour, under different scoring choices. It is to be noted that, although this framework has been applied for the pathology of Alzheimer's in this study on 3D-volumetric and 2D-slice data, it can be applied to other neurological conditions and problems involving interpreting KANs where global, population-lovel pattern identification across subjects and data is required.
5.1 Comparative Analysis
Table 1 compares the proposed bashd attribution framework against represcntative global attribution and edge-scoring approaches derived from GAM, KAN, and KAN 2.0. For GAM, we adopt local attribution scoring via Integrated Gradients (TG), which performed better than simple gradients Tbrahim et al. (2019). We include the L2 norm (Eq. D. and the maximum of the base and spline contributions of the KAN edge function as two examples of edge-scoring metrics, denoted as Path-Attr. + L2 and Path-Attr. + mar. These choices serve as representative examples of edge-scoring strategies within the proposed framework. Statistical significance was evaluated using two-sided paired Wilcoxon signed-rank test over 15 random seeds, applied independently for each dataset, metric, and method comparison. For the proposed framework, we additionally report, for each dataset-metric metric pair, the best-performing path-attribution variant to reflect the framework's upper-bound capability under the considered scoring functions. It can be observed that the path-attribution framework achieves statistically significant improvements over baseline methods on Mendeley and on MNIST, where the task is comparatively simple and base model accuracy is high. Tn contrast, performance on Insertion AUC against GAM statistically indistinguishable on OASIS and ADNI, are Deletion AUC comparisons against KAN and Sufficiency comparisons against GAM on OASIS and KAN on ADNI, other than which, the proposed framework is significantly better than baselines. Within the proposed framework itself, quantitative differences across edge-scoring norms are also observed: L2 attains the highest path-attribution Insertion AUC on all datasets (OASIS: 0.865, ADNI: 0. 0.758, Mendeley: 0.791, MNIST: 0.964), while competing norms produce consistently lower insertion scores by margins of 0.009-0..02 suggesting that, for these datasets, attribution mass accumulated under L2 leads to larger increases prediction confidence during feature insertion. For Deletion AUC, the minimum values shift across datasets: L2 on OASIS, L1 ADNI and Mendeley, and STD on MNIST, suggesting dataset-dependen differences in how rapidly model confidence decreases under feature removal. Similarly, for Sufficiency, the lowest scores are achieved by STD on OASIS, MAX on ADNI, and L2 on Mendeley and MNIST, suggesting differences across datasets in the proportion of features required to retain predictive performance. Overall, the results indicate that the advantages of the proposed path-attribution framework are dataset- and metric-dependent, with clearer improvements emerging in settings where attribution signals are more pronounced. In cases where differences are statistically insignificant, the results suggest comparable explanatory performance between methods rather than defintiiv superiority of any single approach.
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Nevertheless, the results in T demonstrate that path-based multilayer attributions provide competitive and often improved performance relative to established attribution baselines, without observable degradation across the evaluated settings. These findings support the use of path-based attribution as an interpretability tool in both neuroimaging- focuuss focused and general prediction tasks, contingent on adequate underlying model performance.
Table 1:
Comparison of metrics along with the best performing edge-scoring metric in tandem with the proposed framework.
variants against baselines. Included are two example edge-scoring
Dataset
Method
InsAUC f (+ std)
DelAUC & (# std)
Suff (= std)
(Accuracy, AUC)
Path-Attr. (best)
12: 0.865 + 0.049
12: 0.282 + 0.020
std: 0.042 + 0.068
Path-Attr. + 12
0.865 = 0.049
0.282 + 0.020
0.068 + 0.064
Path-Attr. + max
0.837 = 0.015
0.331 + 0.080
0.103 + 0.076
OASIS
GAM IG
0.860 + 0.048
0.366 0.161
0.046 + 0.071
(Acc: 93.24%,
KAN 2.0
0.845 = 0.030
0.354 = 0.101
0.087 0.073
AUC: 95.74)
KAN
0.839 + 0.042
0.287 + 0.024
0.072 0.058
Path-Attr. (best)
12: 0.758 + 0.044
11: 0.310 + 0.081
max: 0.201 + 0.134
Path-Attr. + 12
0.758 = 0.044
0.380 0.051
0.209 + 0.143
Path-Attr. + max
0.749 = 0.059
0.364 0.041
0.201 0.134
ADNI (Ace: 81.85%,
GAM IG
0.746 + 0.026
0.506 0.048
0.269 + 0.136
KAN 2.0
0.716 = 0.033
0.439 = 0.034
0.326 + 0.124
AUC: 91.30)
KAN
0.666 = 0.016
0.376 + 0.075
0.221 + 0.029
Path-Attr. (best)
12: 0.791 + 0.016
11: 0.296 + 0.053
12: 0.226 0.033
Path-Attr. + 12
0.791 = 0.016
0.463 0.099
0.226 + 0.033
Path-Attr. + max
0.773 + 0.012
0.513 + 0.067
0.265 + 0.093
Mendeley (Ace: 91.25%,
GAM IG
0.767 = 0.037
0.399 + 0.090
0.293 + 0.113
KAN 2.0
0.781 + 0.019
0.554 + 0.027
0.301 + 0.034
AUC: 96.62)
KAN
0.710 = 0.080
0.401 + 0.053
0.444 + 0.102
Path-Attr. (best)
12: 0.964 + 0.003
std: 0.114 + 0.007
12: 0.052 0.015
Path-Attr. + 12
0.964 = 0.003
0.293 = 0.022
0.052 + 0.015
Path-Attr. + max
0.944 + 0.004
0.269 + 0.009
0.161 + 0.015
MNIST (Ace: 99.41%,
GAM + IG
0.956 = 0.004
0.380 + 0.008
0.103 + 0.013
KAN 2.0
0.911 + 0.010
0.326 + 0.111
0.412 + 0.164
AUC: 99.89)
KAN
0.924 = 0.012
0.240 + 0.012
0.111 + 0.015
Statistical Significance:
< 0.05
p< 0.01
p 2 0.05
5.2 Visual Comparisons
The side-by-side heatmaps of the attribution maps are presented in Table 2 where the middle slice is plotted along the sagittal axis for OASIS and ADNI, and the coronal slice is presented for the Mendeley Dataset, along with the MNIST global attribution maps. The KAN, KAN 2.0, and GAM plots are presented alongside the proposed path-based attribution approach. Although the general regions identified by all approaches appear to be similar, there are differences in the magnitude and number of regions highlighted. The KAN approach has lot of area highlighted downstream path interactions are not considered. KAN 2.0 sees some regions that are highlighted by our approach and GAM not highlighted, as some functions that contribute equally without a large standard deviation are suppressed.
It can be observed in the ADNI maps that the slice provides a visualization of midline structures such as the corpus callosum, cingulate gyrus, thalamic region, and the ventricular cavity, all of which exhibit different tissue intensity patterns. Several of these structures are known to exhibit degeneration in AD. The smooth high-intensity band near the center corresponds to dense white-matter tracts of the corpus callosum

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Walterfang et al. (2014). while surrounding regions with moderate intensity reflect gray-matter cortical areas. The darker cavities near the center and lower portions of the image represent cerebrospinal fluid (CSF) spaces, primarily the lateral and third ventricles. Even though volumetric and ROI-level analyses are not feasible on this single slice, it remains structurally informative due to the inclusion of midline anatomy that captures the general morphological organization of the brain.
The Mendeley attributions show the coronal mid-slice showing pronounced activations along the medial tem- poral regions, particularly surrounding the hippocampal and parahippocampal arcas Echávarri et al. (2011) and extending around the periventricular zones. Highlighted regions are also visible across the cortical ribbon, outlining the gyral-sulcal boundaries along the outer cerebrum. The central midline region-corresponding primarily to the thalamus, corpus callosum, and basal ganglia struclures-appears comparatively subdued, with minimal activation intensity. This lower response suggests that the discriminative emphasis in this slice arises more from cortical and medial temporal morphometry than from deep gray matter contrast.
Table 2: Visual comparisons with example attribution maps
Dataset
KAN
KAN 2.0
GAM
Ours
OASIS
ADNI
Mendeley
5.2.1 Medical Insights from the OASIS Attribution Maps
The mapped ROI inferences the OASIS volume grey matter from the Brainnetome atlas follows. The bilateral dorsal caudate nuclei (dCa R and dCa L) were the most important region pair observed in Fig. 2c Prior studies have reported candate nucleus atrophy in AD, supporting its involvement in disease progression Jiji et al. (2013). The regions have mean attribution importance of 0.75911.114
(Cocfficient of Variation (CV) = 18.91%) and 0.687=0.109 (CV = 15.87%) respectively. As seen in Fig. the bilateral medial prefrontal cortex (A10m R: 0.571 CV = 2.76%; A10m L: 0.568 CV 3.39%), left angular gyrus (A39rv L: 0.487#0.026, CV 5.38%), and left cuneus (cCunG L: 0.458-0.031, CV = 6.85%) all show perfect consistency. The medial prefrontal regions showed the highest stability, and convergence of default mode network regions with frontostriatal structures is consistent with established
AD neurobiology. Bilateral superior temporal regions (TE10//TE12 T. 0.672+00003: TF1.0/ TE100/TE.. 1.2 R: 0.5 0.501+0.040) also were fully consistent, indicating temporal lobe involvement in AD Castellano et al. (0224). Near-perfect consistency was observed for the right inferior parietal cortex (A40c R: 0.461 The right hippocampus (cHipp R) appeared 66.7% of runs with high stability when present (CV 2.90%, range 0.433-0.476). The top grey matter ROIs comprisod prefrontal cortex (4 ROIs: bilatcral A10m, A10I R, A13 L), subcortical regions (2 ROIs: bilateral caudate), parietal cortex (4 ROIs: A39rv L, A40c R/L,
A40rv R), temporal cortex (2 ROIs: bilateral TE1.0/TE1.2) posterior cortex (1 ROI: cCunG_ L), and medial temporal lobe (1 ROI: cHipp_R) Independent OASIS studies identified overlapping anatomical regions with our findings: Castellano et al. (2024) identified temporal and frontal regions as critical for classification; Kim et al. (2024) identified visual cort, caudate and hippocampus as AD contributors.
The top white matter ROIs identified from the JHU atlas were as follows. The body of corpus callosum (importance 2.331) and genu of corpus callosum (importance 2.167) emerged as the highest-ranked commissural structures, as seen in Fig. 2b Corpus callosum atrophy in AD reflects interhemispheric
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(a) Axial view
(b) Sagittal view
(c) Coronal view
Top ROIs identified through attribution analysis in (a) axial, (b) sagittal, and (c) coronal views, showing gray matter (GM) and white matter (WM) regions most contributive model predictions. The regions primarily highlighted in the maps were body and genu of the Corpus Callosum, Bilateral posterior thalamic radiation, the prefrontal, parietal, temporal and posterior cortex
Figure 2:
commissural fiber degeneration secondary to cortical neuronal loss Tomimoto et al. (2004). The splenium of corpus callosum (importance = 1.236) showed third-highest. importance; posterior callosal regions show particular vulnerability in AD due to their connect ions with temporal and parietal cortices Kamal et al. (2021). Association fiber tracts demonstrated substantial importance scores. Bilateral posterior thalamic radiation (left: 0.866, right: 0.847) ranked among the top white matter regions of interest, consistent with established involvement of thalamic relay structures in AD populations Biesbroek al. (2024). Bilateral anterior corona radiata (left: 0.848, right: 0.762) and bilateral superior corona radiata (left: 0.709, right: 0.632) were also identified among the ROls seen in Fig. 2a The corona radiata comprises projection fibers connecting cortical regions through the internal capsule to subcortical structures; compromised white matter within corona radiata tracts has been reported in AD population. The middle cerebellar peduncle (importance = 0.660) emerged with moderate importance, reflecting potential cerebellar involvement in cognitive processing deficits. Bilateral posterior corona radiata (left: 0.546, right: 0.531) completed the set of significant white matter tracts identified. Collectively, these white matter tract findings reflect regions that are previously reported to be affected in AD. This convergence across highlighted grey and white matter ROIs suggests the biological relevance and plausibility of our attributed regions with respect to established AD pathology.
5.3 Limitations
To analyze the performance our framework on 2D inputs, the ADNI experiments utilize only the middle sagittal slice rather than full 3D volumes. A limitation of the proposed framework is its dependence on model performance; attribution maps are only meaningful learned reliable decision function, which is 93.24%, 81.85% and 91.25% accurate the OASIS, ADNI and Mendeley datasets. The framework currently does not provide inherently faithful class-conditional global attribution maps in fully connected KANss. Because edge functions are Iearned jointly across the full training dist ributtinoo and we analyze just the trained model without relying on input-data post-hoc, restricting path aggregation to individual output neurons does not guarantee disentangled or class-specific explanations. As result, the attribution maps produced are global and cumulative, reflecting the complete Icarned behavior of the model rather than class-wist patterns. The framework also sensitive architectural choices, such network depth and width, the choice of edge-scoring function, and to the quality of the trained model. Tn
the extent that the underlying model has
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particular, the method is most effective in deeper networks where meaningful information flow can be traced across multiple layers.
6 Broader Impact Statement
The proposed path-based attribution framework is intended as research and decision-support tool for understanding population-level information flow in trained models, rather than as a standalone diagnostic system. In medical imaging contexts, a primary ethical concern is the risk of automation bias, where clinicians or practitioners may place undue trust. attribution maps and interpret them as ground-truth biomarkers. Such over-reliance could lead to inappropriate clinical conclusions, particularly if the underlying model has learned spurious correlations or datasel-specific artifacts. Accordingly, the attribution maps produced by this framework should be interpreted as suggestive explanations that support hypothesis generation, model auditing, and exploratory analysis, and not as definitive evidence for clinical decision-making. Any clinical use must occur in conjunction with established diagnostic protocols and expert judgment. Furthermore, this study relies on widely used public neuroimaging datasets, including OASIS, ADNI, and Mendeley, which are known to exhibit demographic and socioeconomic biases and to underrepresent certain populations. Because the proposed method derives global attributions from the training distribution, the resulting maps may underrepresent mischaracterize patterns present. in underrepresented demographic groups. As a. result, conclusions drawn from these attribution maps should be contextualized with respect to the populations which the models were trained. Validation on more diverse, real-world cohorts is necessary before considering any clinical translation. Finally, global attribution methods, including the one proposed in this work, do not eliminate the need for careful dataset curation, robust model evaluation, and interdisciplinary collaboration. When used appropriately, the framework can aid researchers in identifying systematic model dependencies and potential biases, but attribution maps should be interpreted carefully, while also considering the broader context of clinical and scientific evidence.
7 Conclusion
We introduced path-based attribution framework for Kolmogorov-Amood Networks that generates global, population-lvvel importance maps by tracing information flow through the network's explicit edge structure. The proposed framework produces faithful attribution maps that rellect intrinsic network properties learned during training. The efficient matrix- based implementation scales linearly with network depth, making the approach practical for high-dimensional neuroimaging applications. Our evaluation across three publicly available AD classification datasets (OASIS, ADNI, Mendeley) and MNIST shows that the proposed method consistently performs competitively against existing global attribution approaches in attribution metrics. The attribution maps identify clinically meaningful brain regions including the bilateral caudate nuclei, medial prefrontal cortex, and default mode network structures, with high consistency across multiple runs and concordance with established AD neurobiology literature. Higher Insertion AUC and lower Deletion AUC values also show that our method accurately identifies the most informative features for model predictions.
This work addresses a present gap in medical AI interpretability by providing voxel-level global attributions for KAN-based neuroimaging models. The ability to generate population-level importance maps as network- intrinsic propertics supports the identification of biomarkers across patient populations, assisting clinical validation and regulatory approval of Al systems. By bridging the gap between model interpretability and medical knowledge, our framework can facilitate trust and transparency in Al-assisted diagnosis.
Several promising directions emerge from this work. Extending the framework to multi-class classification with ways to generate disentangled class-wise maps would broaden its applicability. Applying the meth to other medical imaging modalities and domains beyond medicine, such as on tabular data, would validate generalizability. Exploring ways to generate classwise attribution maps and bettering KAN performance on a larger scale data is one of our ongoing works. Finally, developing interactive visualization tools that allow clinicians and users to explore path-level attributions could enhance trust. in KAN-based systems.
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Acknowledgements
The authors would like to thank the anonymous reviewers and the Action Editor for their valuable feedback, which has siguificantly improved the quality of this manuscript. We are grateful to Priyam Dey for his helpful input towards revision of the manuscript, and K Suryanarayan for his contribution towards Fig. [ This work was also partially supported by EMSTAR (Pratiksha Trust Extra-Mural Support for Transformational Aging Brain Research).
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A Appendix
A.1 Training and Implementation Details for Models and Metrics
All experiments were carried out using the Kolmogorov Arnold Network with weight decay architecture and trained on a CUDA-A100. Dependencies necessary for execution of the framework included PyTorrc 2.5.1+cu121 as the primary deep learning framework. Supporting data processing and analysis were per- formed using NumPy 1.26.4, Pandas 2.2.2, and scikit-learn 1.2.2. Neuroimaging data was handled using NiBabel 5.3.2. Each model was built using a sequence of KANLinear layers, where the connection weights are represented using B-spline functions. Unless stated otherwise, the following spline and training settings were kept the same across all datasets:
grid size: 5 points per input dimension,
spline order: cubic (order 3);
base activation function: SILU,
noise scale: 0.1,
linear and spline scaling factors: 1.0,
grid epsilon: 0.02,
initial spline grid range: [-1,
Spline configuration and initialization. All KAN models cubic B-spline basis functions with five knots per imput dimension, following the configuration recommended in the original KAN implementation Liu et al. (2025). This choice was kept fixed across all experiments to avoid introducing additional hyper- parameter variation. Although this setting provided stable training and sufficient expressivity for the tasks considered in this work, we do not claim that five knots are universally optimal.
Initialization noisc. The noise scale refers to the standard deviation of small additive Gaussian noise applied during spline coelficient initialization. This initialization strategy, adopted from the original KAN implementation, encourages smoother function learning and helps prevent degenerate spline configurations early in training.
Spline grid and scaling across layers. Spline grids are defined over the interval [-1, and input features are scaled accordingly before being passod to the first KAN layer. Subscquent layers operate on the activations produced by preceding KAN layers; these activalions remain within the effective spline support due to the learned base and spline functions, and therefore do not require additional rescaling.
The layer widths were selected reflect the input dimensionality and complexity of each dataset. For OASIS-1, the network width configuration was
[D, 20, 10, 10, 10, 10, 10, 10, 10, 5, 1),
where D denotes the number of input features. This produced an 11-layer network with progressively narrower layers for binary classification.
For ADNN, a larger first hidden layer was used to accommodate its higher input dimensionality: The width configuration was
D. 800, 20, 15, 15, 15, 10, 10, 10, 5. 1].
For the Mendeley dataset, slightly shallower network was used:
[D, 800, 20, 15, 15, 10, 10, 10, 1).
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All models were optimized using AdamW with learning rate of 10-3. An exponential learning rate scheduler was applied by factor of 0.8. The same optimizer and scheduler settings were used for all datasets for reproducibility.
These configurations were sufficient for stable training across datasets and provided a controlled setting for comparing model behaviour. All attribution analyses are performed post hoc on the fully trained models.
Quantitative Analysis Metrics To assess and compare our methods against other attribution methods that capture importance across training data, utilized Insertion and Deletion AUC metrics, with their formal definitons as follows.
Let f(-) denote a trained model, I E I an input, and A(x) an attribution map that induces a ranking of input features. Let Sş C (l.....,d d} denote the set of top-k features according to this ranking. We define rs, as the input where only features in Sy are retained and all others are replaced by a baseline value, and rys, as the input where features in S& are removed and replaced by the baseline. The Insertion AUC is defined as the area under the curve obtained by evaluating ((,,,,)) k increases from 0 to d. The Deletion AUC is defined as the area under the curve obtained by progressively removing the top-ranked features from the input consisting the full set of features. Formally, we evaluate (x for k = 0, 0, d. The Sufficiency metric measures whether the most relevant features alone are sufficient to preserve the model prediction, and is defined as Suff(k) = f(x) f(*s,)- As a Proof-of-Concepl, we also test the attribution frameworks on 10-class MNIST classification.
Atlascs for ROI Analysis To interpret model attributions and further assess their stability, we per- formed region-offinteres. (ROT) analyses on the altribution maps generated across 15 independent runs. Two anatomical atlases were used for comprehensive grey and white matter coverage: the Brainnetome (BN) Atlas Fan et al. (2016) and the Johns Hopkins University (JHU) ICBM-DTI White Matter Atlas Mori ct al. 20060.
The BN Atlas provides a 246-region parcellation of the grey matter at a 2 mm isotropic resolution. It contains both structural and functional connectivity information to define connectivtty-infoned cortical and subcortical ROIs. This atlas enables detailed inference across diverse grey matter regions and aligns well with OASIS Te-weighted MRT volumes (91 x 109 x 91 voxels) after standard MNT registration. ROI- level intensity mcasures and region-basod features were extracted for each subject in native space following co-registration.
The JHU ICBM-DTI Atlas offers a 48-region parcellation of the brain's white matter based on high-quality diffusion tensor imaging acquired in the ICBM-152 template space, also at a 2 mm isotropic resolution. Each region corresponds to a major white matter tract manually delineated using fiber orientation information, ensuring standardized tract identification across subjects. For every OASIS MRI, the JHU atlas was co- registered to native space after MNI transformation extract regional white matter features. This facilitates tract-based ROI inferences for comparative and cross-sectional evaluation of attribution stability within white matter structures.
Together, the BN and JHU atlases provide complementary insights into grey and white matter attribution patterns, allowing for a comprehensive region-level interpretation of the model's behavior across both tissue domains and insights into regions affected by Alzheimer's.
Usage of the Path-Attribution Framework. The proposed path-attribution framework is applied post hoc to a fully trained feedforward network that satisfies the following architectural assumptions: (i) nonlinear transformations are associated with edges, (ii) nodes aggregate incoming signals additively, and (iii) directed paths exist from input features to output neurons. The method requires access only to the trained model parameters, including learned edge functions and base activations, and optionally stored activation itatis used for edge scoring. Access to the original training data is not required. Given such a model, attribution is performed by first computing a scalar importance score for each edge using a predefined edge-scoring function, such as the L1, L2, or max norm of the learned function or its activations. These edge scores are then propagated layer-wise using matrix-based formulation to implicitly accumulate contributions
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Algorithm 1: Path-Based Attribution Framework (Post-hoc)
Input: A well-trained feedforward network satisfying: (i) nonlinear functions are associated with edges, (ii) nodes aggregate incoming signals additively or multiplicatively, (ii)) directed paths exist from input features to output neurons; saved edge functions {0] and trained model parameters.
Let L denote the number of layers, do the input dimensionality, de the width of layer e, and n = dr the number of output neurons,
Output: Global input-level attribution scores s e Rd for each layer f == l.....,, L do Construct the edge-importance matrix ( E idd-de-1 with entries
(6) j,k
tanh E j.b.
F - 5( j.k
where g(-) is a fixed scalar edge-scoring functional; Compute the propagated importance matrix
M + a44) (L-1)) ().1))... (2) E Raxds
which aggregates contributions over all directed paths from inputs to outputs; for each input feature (1....,dg) do) do
8 n
M
Optionally normalize s for visualization or comparison
along all directed paths from input features output neurons, without explicit path enumeration. Because computation graphs need not be path-disjoint, overlapping paths through shared edges are naturally handled by this formulation.
For each input feature, path contributions aggregated across all output neurons; in multi-class settings, this aggregation is performed by averaging over outputs to obtain a global, class-agnostic attribution score. The resulting input-level scores may optionally be normalized for stability or visualization. Finally, these scores are mapped back to the input space (e.g., voxels or pixels) to produce a global altribution map summarizing the model's learned information flow across the training distribution.
A.2 Synthetic Data Test for Proof-of- Concepp
To complement evaluations on real-world datasets, we conduct. a controlled synthetic experiment designed verify whether the proposed path-based global attribution framework can correctly recover known signal regions, whilst ignoring background information.
Dataset construction. We generate a synthetic dataset consisting of 10,000 grayscale images of size 40 x 40. Each image contains a filled triangular shape centered in the frame. For 50% of the samples, a srcular/plus-shapee
hole is carved out from a fixed subregion located in the lower portion of the triangle, depicted by the red region in Fig. 3e| while the remaining samples contain no hole. Additionally, the 70% of the triangles are stretched and squeezed, distinguishing between triangles with and without hole, shown in Figs. Abland 3a Importantly, the hole's general location is clearly defined across samples, ensuring that the discriminative signal is spatially localized and known by construction.
denote background noise. The classification task is binary:
Robal-Attributton.. A feedforward KAN trained on this dataset using standard supervised learning until convergence. After training, we apply the proposed path-based attribution method to compute global
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(a) Label
(b) Label O
(c) Triangle with discriminative re- gion
Figure 3: Synthetic experiment sctup: L-R, Label image with the hole, Label image without hole; Theoretical triangle, the red region indicates the discriminative area with holes that attribution methods are expected to highlight.
importance map over input pixels. Since the dalaset is synthelic and the discriminative signal is explicitly defined, the expected behavior of a faithful global attribution method is clear: the attribution map should highlight the entire subregion of the triangle where holes occur, while assigning low importance the rest of the image.
Results and interpretation. The resulting attribution map accurately localizes the predefined hole- containing subregion and assigns negligible importance to pixels outside this area, including other parts of the triangle that are visually salient but irrelevant to the classification task, as observable in Fig. [ This demonstrates that the proposed framework captures the true causal structure of the data-generating process, rather than relying on spurious correlations or global shape cues.
Discussion. This synthetic experiment serves as a proof-of-concept sanity check, illustrating that the proposed global attribution framework can correctly identify signal features when ground truth is known, While such controlled settings do not reflect the full complexity of real-world data, they provide important validation that the method behaves intended and that observed attribution patterns real datasets are not merely artifacts of the evaluation metrics. We emphasize that this experiment is not meant to replace real-data analysis, but to complement it by establishing baseline faithfulness under idealized conditions. To complement this experiment, we also plot the global attribution plot on MNIST as seen in Fig. 5 and we can see the highlighted region focuses on the center, where digits are present, as opposed to the frame. Together with the synthetic experiment, the MNIST plot and the ROI-analysis, we conclude that the proposed framework identify ground-truth regions effectively.
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!
(a) Attributed region generaled the path-attribution method
(b) An overlay of the theoretical tri- angle over the actual triangle overlaid the attributed region
(c) An overlay of the theoretical tri- angle with the discriminative region the actual triangle overlaid the attributed region
Figure 4: L-R: The generated attribution map, Overlaid regular triangle region without boundary distortion (not-noise) perfectly encompassing the highlighted region, Theoretical region and actual region
Figure 5: Global-Attribution Map (Path-Attribation + L2 edge scoring) for the MNIST dataset, the high- lighted region focuses on the center, where digits are present, as opposed to the frame.
A.3 Detailed Analysis Table
Comprehensive comparison of explanation quality metrics across four datasets (OASTS-1, ADNI, Mendeley, and MNIST), evaluating 5 attribution methods applied to KAN and Path-Attr. models. Metrics include Insertion/Delltton AUC (InsAUC/DelAUCC) and Sufficiency (Sulf). Best performance per dalaset and metric appears in bold, if there is no significantly better metric, none are bolded. The base KAN paper uses L1 norms at the input node, and we test it with different scoring functions, listed as KAN + scoring function. Rather than claiming a universally optimal scoring rule, our results empirically compare different edge- scoring functions on their own, in-tandem with Path-Attribttion and against baselines KAN, KAN 2.0 and GAM. Please note that KAN + edge scoring functions other than L1 are not baselines; they have been included for edge-scoring comparisons only.
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Table 3: Comparison of explanation metrics across datasets (mean + SD).
Method
InSAUC
DelAUC
Suff
OASIS (Ace: 93.24%, AUC:
95.74)
KAN + max
0.821
0.004
0.703
1: 0.035
0.099 :: 0.080
Path-Attr.
max
0.837
0.015
0.331
0.080
0.103 - 0.076
GAM
0.860
0.048
0.366
0.161
0.046
0.071
Path-Attr.
0.853
0.029
0.274
0.041 0.057
Attr-Attr.
12
0.865
0.049
0.282
0.020
0.068
1 0.064
Path-Atre std
0.760
0.033
0.218 + 0.004
0.042 - 0.068
Path-Attr.
11 max
0.835
0 03036
0.271 - 0.016
0.082
Σ 0.054
Path-Attr
recursive
0.847
0.019
0.299 0.070
0.087
- 080
KAN
+ 1I
0.839
0.042
0.287 0.024
0.072
1 0.058
KAN
12
0.846 0.017
0.454
0.075
0.066
+ 0.092
KAN
std
0.610 0.070
KAN
11 max
0.092 053
0.013 0.466
188
0.611 0.031
KAN
+ recursive
0.831 0.008
0.070
0.068
1 0.084
ADNI (Ace: 81.85%,
AUC: 91.30)
Path-Attr. + 11 max
0.678
0.025
0.347 1 0.098
0.221 1 0.029
KAN 2.0
0.716 0 030
0.439 = 0.034
0.320 - 0.124
KAN + 12
0.746 0.060
0.364
0.041
0.175 + 0.1
GAM
0.716 0. 0.026
0.506
0.048
0.269
+ 0. 136
Path-Attr.
11
0.698 0.028
0.310
0.081
0.222 0.030
Path-Atte
0.758 0.044
0,380
Path-Attr.
std
0.631 0.021
0,885
0.069
0.211
0.029
Path-Atta max
0.749 O 0.0
0,301
0,041
0.201
+ 0.134
Path-Atte recursive
0.740 O. 0.064
0.356
0.039
0.217
1 0.168
KAN + 11
0.666 U 0.016
0.376
0.U75
0.221
- 0.029
RAN
std
0.631 0.021
0.392
0.058
0.267
1 0.036
KAN
0.745 0.061
0.354
0.040
0.196
- 0. 165
KAN
0.658 0.014
0.309
0.077
0.222 0.030
+ recursive
0.746
0.072
0.336
0.042
0.229
0.174
Mendeley (Ace: 91.25%
AUC: 96.62)
0.781
0.027
Path-Attr. max
0.773 0.012
0.513
0.067
0.265
+ 0.003
Path-Attr. std
0.679 0.065
0.332
0.020
0.261
1 0.073
GAM
0.767 = 0. 0.037
0 399
0.090
0.293
+ 0.113
Atth-Attr.
11
0.649 O 0.080
0. 296
0.053
0.504
0. 103
Path-Attr. 12
0.791 + 0.016
063 0.099
0.226
+ 0.033
Path-Attr.
0.671 0.073
0.300
0.047
0.398
0.087
Path-Attr. recussive
0.778 0.026
0.431
0.097
- 0.096
II
0.730 0.080
0,401 0.053
KAN + 12
0.730 O 0.011
0. 126 0.063
0.484
+ 0.051
KAN + std
0.652 0.074
0,320
0.011
0.351
1 0.132
KAN + max
0.758 0.016
0 444 0.064
0.443
- 0.122
RAN + II max
0.683 0.093
0.372 0.048
0.501
+ 0.049
KAN recursive
0.755 0.032
0. 102
0.124
0.316
= 0.095
MNIST (Ace: 99.41% %, AUC: 99.89)
Path-Attr. +12 12
0,964 0.003
0.293
0.022
0.052 + 0.015
KAN + std
0.906 0.023
168
0.046
0.153 1 0.035
KAN + recursive
0.936 0
250
0.053
0.111
GAM
0.956 0. 0.004
383
0.008
0.103
+ 0.013
KAN 2.0
0.911 0.010
0.326
0.111
0.412
+ 0.364
Path-Attr. II
0.756 = 0.012
0.0
0.113
0,490
1 0.003
Ptth-Attr. std
0.753 0.006
0.114
0.007
0.109
L 0.013
Path-Attr.
0.944 0.004
0.269
0.009
0.161
+ 0.015
Path-Attr. II
0.917 0,002
0.228
0.007
0.114
+ 0.039
Psth-Attr. recursive
0.938
0.261
0.924 0.012
0.240
0.012
0.111
KAN
+ 12
0.941 0.005
0.208
0.006
0.315
+ 0.015
KAN + max
0.932 0.014
0.256 + 0.024
0.128 1 0.034
KAN- + 11 max
0.930 0.015
0.218 = 0.013
0.062
- 0.016
A.4 Tabulated ROIs identified across 15 runs
Table 4 presents an example set of the top 18 regions overall. Not all presented grey and white matter regions are tabulated, as this is a combined tabulation of both regions, and we see that white matter regions are highlighted with greater magnitude than grey matter regions. We performed a one-dimensional clustering analysis (k-means, k 4) on the mean values across all ROIs. This procodure consistently separated the ROIs into four natural clusters, with an apparent separation between a low-intensity cluster (centered approximately 0.41) and higher-intensity cluster beginning near 0.52.
Regions presented include the corpus callosum, corona radiata, and posterior thalamic radiations, along- side subcortical and temporal regions such as the dorsal caudate and TEI TE1.2 auditory cortex. These structures exhibited both high mean importance values and variability patterns consistent with differences reported in AD populations. Importantly, the retained pattern aligns with established neuroanatomical vulnerability profiles observed in "ezheimers--rcltten cohorts, supporting the biological plausibility of the model's feature ranking.
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This clustering procedure therefore ensures that the retained ROIs represent the prominent and anatomically interpretable contributors to the model, while excluding regions that fall within the lower-intensity portion of the distribution.
Table 4: Example ROIs sorted in descending order of the Mean value.
Rank
ROI label
Mean
SD
CV (%)
1
WM: Body of corpus callosum
2.307
0.751
32.53
2
WM: Genu of corpus callosum
1.986
0.635
31.98
3
WM: Splenium of corpus callosum
1.099
0.333
30.31
WM: Anterior corona radiata L
0.886
0.268
30.24
WM: Posterior thalamic radiation (optic radiation) R
0.836
0.169
20.20
WM: Posterior thalamic radiation (optic radiation) L
0.827
0.209
25.32
GM: dCa R
0.759
0.144
18.91
8
WM: Superior corona radiata L
0.758
0.188
24.86
9
WM: Anterior corona radiata R
0.737
0.154
20.91
10
GM: dCa L
0.687
0.109
15.87
11
GM: TE10/TEE12__
0.672
0.063
9.42
12
WM: Superior corona radiata R
0.640
0.109
16.97
WM: Middle cerebellar pedunele
0.630
0.136
21.61
14
GM: A10m R
0.571
0.016
2.76
15
GM: A10m_
0.568
0.019
3.39
16
WM: Posterior corona radiata L
0.562
0.082
14.67
17
WM: Posterior corona radiata R
0.543
0.095
17.45
18
GM: TE10/TE112 R
0.525
0.030
5.71
22


Reviews:
[{"review_id": "twj2PUk8jn", "reviewer": "Reviewer_3KX1", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The paper focuses on the problem of interpretability/explainability of neural network models in a medical context. Specifically, the paper builds upon the Kolmogorov-Arnold Networks (KAN) and proposes a path-based attribution framework. \n\nThe paper demonstrates that ...\n\n- the proposed method can be scaled to voxel-level rather than ROI-level\n- the proposed method performs well on several metrics for three Alzeheimer's Disease (AD) datasets. \n\nThe paper is generally well-written, well-structured, and easy to follow. The method and math are sound. However, there are no theoretical justification or analysis of the proposed method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "There is no theoretical justification or analysis for the proposed method, but the authors provide empirical evidence showing that the proposed method outperforms competing baseline with a small margin.\n\nThe paper emphasises the significance of the deployed L2-norm as a contribution. However, the significance of this is not entirely clear to me.", "audience_yn": "Yes", "audience_explanation": "The problem of interpreting and explaining decisions from black box models is getting increasingly important for both researchers and practitioners in ML and the medical domain.", "requested_changes": "Overall, the paper is well-written, well-structured and easy to follow. However, I believe there a several areas, where the paper could benefit from a clarification and/or additional discussion.\n\n1) It would be great if the author could add a single paragraph about the \"overall workflow of using the method\". The way I understand the method is as follows. Suppose you want to build a model for AD's given some dataset, then you identify an appropriate architecture for the problem/dataset. When you are happy with your architecture, you reparametrize all edges of the network using the base + split parametrization and retrain the network. Finally, you compute the attribution maps of interest. Is this correct?\n   \n2) The main performance metrics for the experiments are the \"Insertion AUC\", \"Deletion AUC\", and \"Sufficiency\", whose informal definition is repeated twice in section 4.1 and 4.2 It would be great if the author could replace one of the informal descriptions with a proper mathematical definition for clarity.\n   \n3) The proposed method is spline-based, but there is are results or discussion for the sensitivity the results are to the specific spline-configuration (cubic B-splines with 5 knots per dimension). Is 5 knots always sufficient? Moreover, section A.1 mention a \"noise scale\" of 0.1, but it is unclear to me what this refers to.     Finally, Appendix A.1 states that the spline grid is defined to be [-1, 1] and the input is scaled accordingly. But it is unclear to me what happens on the subsequent layers. Please clarify these details.\n   \n4) The paper makes heavy use of the word \"faithful\", but does not provide a clear definition (or a clear reference).\n   \n5) The paper is centered around the application to medical applications (AD) and states that local attributions methods can be useful for \"individual cases, such as tumor detection\", but less so for studying AD. Could you make elaborate a bit on this for the average non-medical ML-audience like me? \n   \n6) It is unclear how the method is deployed for other problems than binary classification. How does the method apply to multi-class classification like the MNIST problem?\n   \n7) It would also be great with a more in-depth discussion of the drawback of the proposed method besides the \"accuracy-constraint\".", "broader_impact_concerns": "None", "additional_comments": "A few minor comments:\n\n- The paper states \"With KANs being proposed as interpretable networks, there have been applications in medicine. Dong et al. (2025) used a KAN-based Graph Convolutional Networks (GCNs) for Alzheimer’s disease diagnosis on the ADNI dataset, with their GCN-KAN achieved 62.6% over standard GCNs at 57.4%.\"\n\t- What are the percentages?  Accuracy or some other metrics?\n\t  \n- \"We use a simple feedforward deep KAN, each with about 6-10 hidden layers and run the attributions on the fully trained model.\"\n\t- Please be more precise :-)\n\t\n- Base activation function seems to change notation from b(x) to sigma(x). Is there any significance to this?\n  \n- \"We score the paths as the absolute of the tanh of the product of edge-scores on the path.\". But there is no absolute value in eq. (2). Am I missing something?", "extra_scores": {}, "extra_text": {}}, {"review_id": "NWdRfeGS6U", "reviewer": "Reviewer_K6ZF", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Here are some key contributions in top of KAN's\n\n* They built a path-based framework to trace exactly how the AI makes decisions\n* Energy-Based Scoring: Used L_2 energy norms to figure out which parts of the AI's internal functions are doing the most work\n* Created a matrix trick so this works on massive 3D brain scans in seconds instead of years\n* Produced super-detailed maps showing exactly which tiny 3D pixels (voxels) the AI is looking at.\n* Showed the AI is actually smart by proving it focuses on the same brain regions doctors already worry about, like the corpus callosum and caudate nuclei.", "claims_and_evidence_yn": "Yes", "claims_explanation": "he claims are solid because the model actually hits high marks, like 93.24% accuracy on the OASIS dataset and 99.4% on MNIST. The authors proved their maps are \"faithful\" using math tests called Insertion and Deletion AUC, where their method consistently beat older ones like GAM and KAN 2.0. This means when the AI says a brain region is important, it’s not just guessing; removing those areas actually tanks the model's confidence.\n\nThe evidence is even more convincing because the AI's internal thoughts match real medical science. It consistently zeroed in on the corpus callosum and caudate nuclei across 15 different test runs, which are exactly the spots doctors look at for Alzheimer's. With a massive testing pool of over 7,400 image acquisitions.", "audience_yn": "Yes", "audience_explanation": "This paper moves the needle on both Kolmogorov-Arnold Network theory and practical AI explainability. It solves a massive bottleneck in neuroimaging by introducing a matrix-based method that handles the huge dimensionality of 3D brain scans, which usually crashes standard path-counting algorithms. Beyond just math, it proves that these newer, flexible networks can actually be trusted in a clinical setting by showing their internal logic aligns perfectly with established human brain anatomy. By turning a black box into a transparent map of medical biomarkers, it provides a blueprint for how AI can gain regulatory approval and clinical trust in high-stakes fields like neuroscience", "requested_changes": "* Explicitly state that the attribution maps are only as reliable as the model's test accuracy, which is currently around 93% for OASIS.\n* Showing separate \"Healthy\" vs. \"Diseased\" patterns would be very helpful the current framework only produces one combined global map", "broader_impact_concerns": "The main ethical concern is the risk of \"automation bias,\" where clinicians might treat the AI’s global importance maps as absolute truth rather than a suggestive tool, potentially leading to misdiagnosis if the model relies on spurious correlations. Since the framework currently lacks class-wise distinction, there is also a risk of misinterpreting general brain aging patterns as specific Alzheimer's pathology.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "jzmOdw6hmo", "reviewer": "Reviewer_74hz", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a path-based attribution framework specifically designed for Kolmogorov-Arnold Networks (KANs) to address the limitations of local, instance-specific interpretability in neuroimaging. The primary contributions include:\n1. Propose a global attribution method that scores network edges using the L2 norm of learned spline and base functions.\n2. Propose an efficient implementation using matrix propagation that reduces computational complexity from exponential to linear relative to network depth, making voxel-level global attribution feasible for high-dimensional data.\n3. Evaluate the proposed framework and compared with baselines methods on three major Alzheimer’s Disease datasets (OASIS, ADNI, Mendeley) comprising.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The technical implementation of path-based attribution framework and its linear scalability is clearly demonstrated and mathematically sound. However, the empirical \"convincingness\" is hampered by\n1. Norm Selection: While the $L_2$ norm performs best on most datasets, the $max$ norm is superior on the ADNI dataset for both DelAUC and Suff. The authors claim $L_2$ is more stable, but the performance gap is not addressed in detail. The author fails to clarify whether norm selection is a dataset-dependent hyperparameter or if there is a theoretical justification for prioritizing $L_2$.\n2. The performance advantage of the \"Path-Attr\" method over existing baselines such as GAM is frequently marginal. For example, Path-Attr + $L_2$ achieved an Insertion AUC (InsAUC) of 0.865, representing a negligible improvement over the second-best approach (GAM + IG) at 0.860. In the absence of rigorous statistical significance testing (e.g., p-values or confidence intervals), it is difficult to verify if these gains represent a robust methodological advancement or are simply the result of experimental noise.", "audience_yn": "Yes", "audience_explanation": "The paper would be of interest for researchers interested in KAN, explainable AI and AD neuroimaging.", "requested_changes": "1. Add significance testing to the results in Table 1 to ensure reported differences are meaningful.\n2. Provide a qualitative or quantitative discussion on why the $max$ norm outperformed $L_2$ on ADNI. Is it due to data-specific biomarkers or preprocessing differences?\n3. Introduce and define the abbreviation “GAM” before its first use.", "broader_impact_concerns": "1. The authors claim that the generated attribution maps \"support clinical validation\" and help gain \"clinical trust\". However, there is a significant risk that clinicians may over-rely on these \"interpretable\" maps, treating them as ground-truth biomarkers rather than decision-support aids. The authors should explicitly state that these maps are intended for research and decision-support, not as standalone diagnostic evidence.\n2. The study relies on well-known public datasets. These cohorts are known to have demographic biases, often underrepresenting certain racial, or socioeconomic groups. Because the proposed method produces a global map based on the training population, this could lead to a diagnostic framework that is less accurate for patients from underrepresented demographics. A broader impact statement should acknowledge these limitations and the need for validation on more diverse, real-world cohorts.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "4SgSPFkwdC", "reviewer": "Reviewer_Rq9g", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors introduce a path-based attribution framework for Kolmogorov-Arnold Networks (KANs) applied to Alzheimer's disease (AD) detection from neuroimaging data as a global attribution method that traces information flow through all computational paths in a trained KAN to generate population-level importance maps.\n\n**Strengths**\n1. Provides global attributions as an intrinsic property of the trained network itself, rather than instance-specific explanations\n2. Scalable to high-dimensional neuroimaging data\n3. Empirically validated on three public AD datasets (OASIS, ADNI, Mendeley), while identifying clinically meaningful regions-of-interest (ROI).\n\n**Weaknesses**\n1. Limited to KAN, which AFAIK is not a widely-adopted classification model for AD\n2. Scales well, but not *that* well, as Section 4.1 only analyzes the middle sagittal slice from the ADNI.\n    + It can be argued that the costly part is training a feed-forward KAN, instead of running the global attribution method. However, this is at least partially because the method isn't well-defined for convolutional/volumetric or other KAN variants, which could be necessary when working with high-dimensional data\n3. Only works for binary classification, but unable to produce class-wise attribution map\n4. Partially supported claims (see below)", "claims_and_evidence_yn": "No", "claims_explanation": "1. The path-based method only marginally outperforms GAM + IG, KAN 1, and KAN 2 in terms of Insertion/Deletion AUC and Sufficiency (Table 1), and the error bar of many methods are overlapping with each other, so the signal isn't very clear.\n\n1. Insertion/Deletion AUC are problematic by themselves, e.g., they forces the model to extrapolate to artificial/unrealistic inputs that are completely out-of-distribution, and they cannot capture the interaction between features because they add/remove each on individually. One alternative is to run generate simulated datasets with known/synthetic signal and noisy features, and see whether the path-based method can identify the signal features correctly.\n\n1. Many design choices are only backed up by informal/heuristic arguments and experiment result. For example, the authors are using L2 instead of L1 edge scoring function because \"[...] this L2 measure avoids underestimating important edges that display a lower variance, penalizes sporadic large activations, and provides a more faithful signal for path-level attribution,\" but it's not uncommon for L1 to outperform L2 in Table 3.\n    + The same goes for tanh normalization, and absolute vs signed edge score magnitudes, which don't even have ablation studies.\n\n1. While KAN achieves test accuracies of 93.24%, 81.85% and 91.25% on OASIS-1, ADNI and Mendeley, we can easily find models that greatly outperforms KAN on test datasets, e.g, a CNN with >99% test accuracy on ADNI: https://www.nature.com/articles/s41598-024-53733-6 . As the authors pointed out themselves, \"[t]he attribution maps would be accurate only if the model is able to accurately perform the task at hand.\"", "audience_yn": "No", "audience_explanation": "The paper is strongly coupled to both KAN (since it relies on the fact that each node only does addition) and neuroimaging data (since the method has many moving parts, e.g., L2 scoring, tanh normalization, absolute edge score magnitudes, and they all had to be handpicked by the authors based on their performance on neuroimaging data). I don't think many individuals in TMLR's audience would be interested in the narrow intersection field between KAN and neuroimaging.", "requested_changes": "1. Expand the scope of the path-based attribution method to domains other than neuroimaging.\n\n1. Clarify the advantage of global attributions over local attributions. In particular, it is known that global attribution is *different* than averaged local attribution, but how is it *better* than the latter? Moreover, how can global attribution reveal biases or spurious correlation in a way that (averaged) local attribution can't?\n\n1. Make Table 3 clearer. The text says \"Best performance per dataset and metric appears in bold\", but some cases the best performance isn't in bold. For example, on the `OASIS` dataset, the best performance is `KAN + l1_max` with `DelAUC = 0.188 ± 0.013` but the bold item is `Path-Attr. + l1` with `DelAUC = 0.274 ± 0.049`, a significantly higher/worse value. Moreover, the `Suff` and `Comp` columns don't have anything in bold, while the `Prec@5` column has two methods both in bold.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)