Search arXivSearch

arXiv · 2507.13090

MUPAX: Multidimensional Problem Agnostic eXplainable AI

Abstract

Robust XAI techniques should ideally be simultaneously deterministic, model agnostic, and guaranteed to converge. We propose MULTIDIMENSIONAL PROBLEM AGNOSTIC EXPLAINABLE AI (MUPAX), a deterministic, model agnostic explainability technique, with guaranteed convergency. MUPAX measure theoretic formulation gives principled feature importance attribution through structured perturbation analysis that discovers inherent input patterns and eliminates spurious relationships. We evaluate MUPAX on an extensive range of data modalities and tasks: audio classification (1D), image classification (2D), volumetric medical image analysis (3D), and anatomical landmark detection, demonstrating dimension agnostic effectiveness. The rigorous convergence guarantees extend to any loss function and arbitrary dimensions, making MUPAX applicable to virtually any problem context for AI. By contrast with other XAI methods that typically decrease performance when masking, MUPAX not only preserves but actually enhances model accuracy by capturing only the most important patterns of the original data. Extensive benchmarking against the state of the XAI art demonstrates MUPAX ability to generate precise, consistent and understandable explanations, a crucial step towards explainable and trustworthy AI systems. The source code will be released upon publication.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vincenzo Dentamaro, Felice Franchini, Giuseppe Pirlo, Irina Voiculescu. 2025-07-17. MUPAX: Multidimensional Problem Agnostic eXplainable AI. https://arxiv.org/abs/2507.13090

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG