aiqbench analysis
This research introduces GRALIS, a novel framework that unifies coalition-based and gradient-based explainability methods for deep neural networks into a single estimator with rigorous mathematical guarantees. By leveraging the Riesz Representation Theorem, the work provides closed-form completeness corrections and finite-sample bounds that address inherent limitations in existing post-hoc XAI techniques like SHAP and Integrated Gradients. The study advances the theoretical foundation of model interpretability by establishing exact correspondences between different attribution functionals, offering a more robust tool for analyzing complex AI decision-making processes.
GRALIS: Fusing Coalition and Gradient Attribution with Closed-Form Conservation Error and Finite-Sample Guarantees
arXiv:2605.05480v3 Announce Type: replace-cross Abstract: The main post-hoc XAI methods for deep networks -- GradCAM, SHAP, LIME, Integrated Gradients -- originate from heterogeneous theoretical foundations and are not naturally comparable within a single representation. A recent benchmark also finds their coalition-based members (GradCAM, KernelSHAP, LIME) and gradient-based members (Integrated Gradients and variants) empirically complementary, each outperforming the other on different faithfulness metrics, with method selection as the only proposed remedy (Gevaert et al., 2022). This work presents GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), which fuses these two mechanisms -- a Shapley coalition weight and locality kernel, and a continuous Integrated-Gradients-style conditioned path -- into a single estimator, and equips it with two certified guarantees neither mechanism supplies alone: an exact, closed-form completeness deficit (an order-d interaction is attributed at a factor 1/d of its true value under Shapley weights and a multilinear F) and a finite-sample bound, O(1/sqrt(m)) + O(1/k^2), for the actual self-normalized ratio the algorithm returns. This fusion is underpinned by a representation-theoretic result: every additive, linear, continuous attribution functional admits a unique canonical representation via the Riesz Representation Theorem, proved componentwise (feature by feature) rather than as one form shared across features or methods. This class includes SHAP, IG and LIME, but not nonlinear functionals such as standard GradCAM or attention maps. Seven theorems further establish an exact correspondence with Shapley Interaction Values, affine-regime correspondences with the Hoeffding/Sobol decomposition, and a minimum-variance multi-scale extension. A preliminary experimental illustration on breast histology imaging is included; extended validation is in a companion paper (Fanale, 2026).
Abstract:The main post-hoc XAI methods for deep networks -- GradCAM, SHAP, LIME, Integrated Gradients -- originate from heterogeneous theoretical foundations and are not naturally comparable within a single representation. A recent benchmark also finds their coalition-based members (GradCAM, KernelSHAP, LIME) and gradient-based members (Integrated Gradients and variants) empirically complementary, each outperforming the other on different faithfulness metrics, with method selection as the only proposed remedy (Gevaert et al., 2022). This work presents GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), which fuses these two mechanisms -- a Shapley coalition weight and locality kernel, and a continuous Integrated-Gradients-style conditioned path -- into a single estimator, and equips it with two certified guarantees neither mechanism supplies alone: an exact, closed-form completeness deficit (an order-d interaction is attributed at a factor 1/d of its true value under Shapley weights and a multilinear F) and a finite-sample bound, O(1/sqrt(m)) + O(1/k^2), for the actual self-normalized ratio the algorithm returns. This fusion is underpinned by a representation-theoretic result: every additive, linear, continuous attribution functional admits a unique canonical representation via the Riesz Representation Theorem, proved componentwise (feature by feature) rather than as one form shared across features or methods. This class includes SHAP, IG and LIME, but not nonlinear functionals such as standard GradCAM or attention maps. Seven theorems further establish an exact correspondence with Shapley Interaction Values, affine-regime correspondences with the Hoeffding/Sobol decomposition, and a minimum-variance multi-scale extension. A preliminary experimental illustration on breast histology imaging is included; extended validation is in a companion paper (Fanale, 2026).
Retitled and substantially revised: rebalanced abstract/introduction/contributions/conclusions, new related-work positioning, main text restructured for length, several proofs moved to appendix. Results unchanged
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
I.2.6; I.5.1; G.3
arXiv:2605.05480 [cs.LG]
(or arXiv:2605.05480v3 [cs.LG] for this version)
Full text under the publisher's open licence · 291 words
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