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The concept of Relative Divergence of one Grading Function from another is extended from totally ordered chains to power sets of finite event spaces. Shannon Entropy concept is extended to normalized grading functions on such power sets.…

Probability · Mathematics 2022-07-15 Alexander Dukhovny

We investigate the explanability properties of the recently proposed linear-min-max neural networks. At initialization, they can be interpreted as k-medoids with the infinity norm as a distance. Then, they are trained using subgradient…

Computer Vision and Pattern Recognition · Computer Science 2026-05-05 Ikhlas Enaieh , Olivier Fercoq , García Ángel

Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…

Machine Learning · Statistics 2024-12-04 Wuyue Yang , Liangrong Peng , Guojie Li , Liu Hong

The Information Bottleneck (IB) objective uses information theory to formulate a task-performance versus robustness trade-off. It has been successfully applied in the standard discriminative classification setting. We pose the question…

Machine Learning · Computer Science 2021-01-13 Lynton Ardizzone , Radek Mackowiak , Carsten Rother , Ullrich Köthe

This paper considers the problem of assumptions refinement in the context of unrealizable specifications for reactive systems. We propose a new counterstrategy-guided synthesis approach for GR(1) specifications based on Craig's…

Logic in Computer Science · Computer Science 2018-11-01 Davide G. Cavezza , Dalal Alrajeh

Artificial intelligence models and methods commonly lack causal interpretability. Despite the advancements in interpretable machine learning (IML) methods, they frequently assign importance to features which lack causal influence on the…

Machine Learning · Computer Science 2024-01-29 Francisco Nunes Ferreira Quialheiro Simoes , Mehdi Dastani , Thijs van Ommen

Deep learning methods are achieving ever-increasing performance on many artificial intelligence tasks. A major limitation of deep models is that they are not amenable to interpretability. This limitation can be circumvented by developing…

Machine Learning · Computer Science 2022-07-05 Hao Yuan , Haiyang Yu , Shurui Gui , Shuiwang Ji

Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical…

Machine Learning · Computer Science 2026-04-01 Nir Shlezinger , Santiago Segarra , Yi Zhang , Dvir Avrahami , Zohar Davidov , Tirza Routtenberg , Yonina C. Eldar

In this paper, we improve the known estimates for the invariance entropy of a nonlinear control system. For sets of complete approximate controllability we derive an upper bound in terms of Lyapunov exponents and for uniformly hyperbolic…

Optimization and Control · Mathematics 2014-08-12 Adriano Da Silva , Christoph Kawan

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy

Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…

Artificial Intelligence · Computer Science 2025-12-01 Uri Andrews , Luca San Mauro

Graph Neural Networks (GNNs) have shown remarkable success across various scientific fields, yet their adoption in critical decision-making is often hindered by a lack of interpretability. Recently, intrinsically interpretable GNNs have…

Machine Learning · Computer Science 2025-10-07 Cheng Xin , Fan Xu , Xin Ding , Jie Gao , Jiaxin Ding

The combinatorial basis of entropy by Boltzmann can be written $H= {N}^{-1} \ln \mathbb{W}$, where $H$ is the dimensionless entropy of a system, per unit entity, $N$ is the number of entities and $\mathbb{W}$ is the number of ways in which…

Mathematical Physics · Physics 2009-11-13 Robert K. Niven

In long-horizon tasks, recent agents based on Large Language Models (LLMs) face a significant challenge that sparse, outcome-based rewards make it difficult to assign credit to intermediate steps. Previous methods mainly focus on creating…

Machine Learning · Computer Science 2025-09-12 Jiawei Wang , Jiacai Liu , Yuqian Fu , Yingru Li , Xintao Wang , Yuan Lin , Yu Yue , Lin Zhang , Yang Wang , Ke Wang

Good generative models should not only synthesize high quality data, but also utilize interpretable representations that aid human understanding of their behavior. However, it is difficult to measure objectively if and to what degree…

Machine Learning · Computer Science 2025-04-09 Daniel Galperin , Ullrich Köthe

Background. The reliability paradox describes the empirical observation that cognitive tasks producing robust group-level effects often yield poor between-individual reliability. Existing approaches rely predominantly on the intraclass…

Methodology · Statistics 2026-05-26 Maria Westrin

We consider the problem of learning from demonstrated trajectories with inverse reinforcement learning (IRL). Motivated by a limitation of the classical maximum entropy model in capturing the structure of the network of states, we propose…

Machine Learning · Computer Science 2020-08-19 Tien Mai , Kennard Chan , Patrick Jaillet

Uniform confidence bands for functions are widely used in empirical analysis. A variety of simple implementation methods (most notably multiplier bootstrap) have been proposed and theoretically justified. However, an implementation over a…

Methodology · Statistics 2025-12-23 Shunsuke Imai

We introduce path-sampled integrated gradients (PS-IG), a framework that generalizes feature attribution by computing the expected value over baselines sampled along the linear interpolation path. We prove that PS-IG is mathematically…

Machine Learning · Computer Science 2026-04-17 Firuz Kamalov , Fadi Thabtah , R. Sivaraj , Neda Abdelhamid

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argumentative-consequence relation taking into account the existence of consistent arguments in favor of a conclusion and the…

Artificial Intelligence · Computer Science 2013-03-08 Salem Benferhat , Didier Dubois , Henri Prade