CGF can outperform the GMI cuts for certain distributions.

The performance of algorithms, methods, and models tends to depend heavily on the distribution of cases on which they are applied, this distribution being specific to the applicative domain. After performing an evaluation in several domains, it is highly informative to compute a (weighted) mean performance and, as shown in this paper, to scrutinize what happens during this averaging. To achieve this goal, we adopt a probabilistic framework and consider a performance as a probability measure (e.g., a normalized confusion matrix for a classification task). It appears that the corresponding weighted mean is known to be the summarization, and that only some remarkable scores assign to the summarized performance a value equal to a weighted arithmetic mean of the values assigned to the domain-specific performances. These scores include the family of ranking scores, a continuum parameterized by user preferences, and that the weights to consider in the arithmetic mean depend on the user preferences. Based on this, we rigorously define four domains, named easiest, most difficult, preponderant, and bottleneck domains, as functions of user preferences. After establishing the theory in a general setting, regardless of the task, we develop new visual tools for two-class classification.

Ranking methods or models based on their performance is of prime importance but is tricky because performance is fundamentally multidimensional. In the case of classification, precision and recall are scores with probabilistic interpretations that are both important to consider and complementary. The rankings induced by these two scores are often in partial contradiction. In practice, therefore, it is extremely useful to establish a compromise between the two views to obtain a single, global ranking. Over the last fifty years or so,it has been proposed to take a weighted harmonic mean, known as the F-score, F-measure, or $F_β$. Generally speaking, by averaging basic scores, we obtain a score that is intermediate in terms of values. However, there is no guarantee that these scores lead to meaningful rankings and no guarantee that the rankings are good tradeoffs between these base scores. Given the ubiquity of $F_β$ scores in the literature, some clarification is in order. Concretely: (1) We establish that $F_β$-induced rankings are meaningful and define a shortest path between precision- and recall-induced rankings. (2) We frame the problem of finding a tradeoff between two scores as an optimization problem expressed with Kendall rank correlations. We show that $F_1$ and its skew-insensitive version are far from being optimal in that regard. (3) We provide theoretical tools and a closed-form expression to find the optimal value for $β$ for any distribution or set of performances, and we illustrate their use on six case studies.

The application of machine learning (ML) methods, a subfield of artificial intelligence (AI), to the solution of electromagnetic boundary value problems (BVPs) is currently a highly active area of research. Deep neural networks such as neural operators (Kovachki et al. 2023) and physics-informed neural networks, in which information about the BVP (and possibly measurement data) is integrated into the loss function of the network, often aim to replace traditional numerical methods such as the finite element (FE) method, compare, for example, with (Guo et al. 2025; Rezende and Schuhmann 2025). This work addresses an orthogonal problem: How can AI methods be used to reduce the time required to set up electromagnetic simulation models, rather than solving the numerical models themselves? The focus is thus on the assisted generation of simulation models, whereby the numerical scheme itself remains unaffected. A conceptually related direction has recently emerged in the computational fluid dynamics (CFD) community.

A.1 Proof of Theorem 1 Theorem 1. (MDI are Shapley values) F or all feature X The other way around is trivial. A.4 Proof of Theorem 4 Theorem 4. If a variable is locally irrelevant at x with respect to Y , then Imp The proof stems from the definition of the local irrelevance.

Then, we derive a local MDI importance measure of variable relevance, which has a very natural connection with the global MDI measure and can be related to a new notion of local feature relevance. We further link local MDI importances with Shapley values and discuss them in the light of related measures from the literature.

Developing benchmark datasets for low-resource languages poses significant challenges, primarily due to the limited availability of native linguistic experts and the substantial time and cost involved in annotation. Given these challenges, Maithili is still underrepresented in natural language processing research. It is an Indo-Aryan language spoken by more than 13 million people in the Purvanchal region of India, valued for its rich linguistic structure and cultural significance. While sentiment analysis has achieved remarkable progress in high-resource languages, resources for low-resource languages, such as Maithili, remain scarce, often restricted to coarse-grained annotations and lacking interpretability mechanisms. To address this limitation, we introduce a novel dataset comprising 3,221 Maithili sentences annotated for sentiment polarity and accompanied by natural language justifications. Moreover, the dataset is carefully curated and validated by linguistic experts to ensure both label reliability and contextual fidelity. Notably, the justifications are written in Maithili, thereby promoting culturally grounded interpretation and enhancing the explainability of sentiment models. Furthermore, extensive experiments using both classical machine learning and state-of-the-art transformer architectures demonstrate the dataset's effectiveness for interpretable sentiment analysis. Ultimately, this work establishes the first benchmark for explainable affective computing in Maithili, thus contributing a valuable resource to the broader advancement of multilingual NLP and explainable AI.

This paper presents Gym-TORAX, a Python package enabling the implementation of Reinforcement Learning (RL) environments for simulating plasma dynamics and control in tokamaks. Users define succinctly a set of control actions and observations, and a control objective from which Gym-TORAX creates a Gymnasium environment that wraps TORAX for simulating the plasma dynamics. The objective is formulated through rewards depending on the simulated state of the plasma and control action to optimize specific characteristics of the plasma, such as performance and stability. The resulting environment instance is then compatible with a wide range of RL algorithms and libraries and will facilitate RL research in plasma control. In its current version, one environment is readily available, based on a ramp-up scenario of the International Thermonuclear Experimental Reactor (ITER).