In this work we introduce GreenLightningAI (GLAI), a new architectural block designed as an alternative to conventional Multilayer Perceptrons (MLPs). The central idea is to separate two types of knowledge that are usually entangled during training: (i) structural knowledge, encoded by the stable activation patterns induced by Rectified Linear Unit (ReLU) activations; and (ii) quantitative knowledge, carried by the numerical weights and biases. By fixing the structure once stabilized, GLAI reformulates the MLP as a combination of paths, where only the quantitative component is optimized. This refor-mulation retains the universal approximation capabilities of MLPs, yet achieves a more efficient training process, reducing training time by 40% on average across the cases examined in this study. Crucially, GLAI is not just another classifier, but a generic block that can replace MLPs wherever they are used, from supervised heads with frozen backbones to projection layers in self-supervised learning or few-shot classifiers. Across diverse experimental setups, GLAI consistently matches or exceeds the accuracy of MLPs with an equivalent number of parameters, while converging faster. Overall, GLAI establishes a new design principle that opens a direction for future integration into large-scale architectures such as Transformers, where MLP blocks dominate the computational footprint.

We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations of existing functions that quantify the contribution of a single contributing argument to a topic. Accordingly, we generalize existing contribution function principles for set contribution functions and provide a corresponding principle-based analysis. We introduce new principles specific to set-based functions that focus on properties pertaining to the interaction of arguments within a set. Finally, we sketch how the principles play out across different set contribution functions given a recommendation system application scenario.

We develop a new approximative estimation method for conditional Shapley values obtained using a linear regression model. We develop a new estimation method and outperform existing methodology and implementations. Compared to the sequential method in the shapr-package (i.e fit one and one model), our method runs in minutes and not in hours. Compared to the iterative method in the shapr-package, we obtain better estimates in less than or almost the same amount of time. When the number of covariates becomes too large, one can still fit thousands of regression models at once using our method. We focus on a linear regression model, but one can easily extend the method to accommodate several types of splines that can be estimated using multivariate linear regression due to linearity in the parameters.

In this study, we unveil a new AI model, termed PhyE2E, to discover physical formulas through symbolic regression. PhyE2E simplifies symbolic regression by decomposing it into sub-problems using the second-order derivatives of an oracle neural network, and employs a transformer model to translate data into symbolic formulas in an end-to-end manner. The resulting formulas are refined through Monte-Carlo Tree Search and Genetic Programming. We leverage a large language model to synthesize extensive symbolic expressions resembling real physics, and train the model to recover these formulas directly from data. A comprehensive evaluation reveals that PhyE2E outperforms existing state-of-the-art approaches, delivering superior symbolic accuracy, precision in data fitting, and consistency in physical units. We deployed PhyE2E to five applications in space physics, including the prediction of sunspot numbers, solar rotational angular velocity, emission line contribution functions, near-Earth plasma pressure, and lunar-tide plasma signals. The physical formulas generated by AI demonstrate a high degree of accuracy in fitting the experimental data from satellites and astronomical telescopes. We have successfully upgraded the formula proposed by NASA in 1993 regarding solar activity, and for the first time, provided the explanations for the long cycle of solar activity in an explicit form. We also found that the decay of near-Earth plasma pressure is proportional to r^2 to Earth, where subsequent mathematical derivations are consistent with satellite data from another independent study. Moreover, we found physical formulas that can describe the relationships between emission lines in the extreme ultraviolet spectrum of the Sun, temperatures, electron densities, and magnetic fields. The formula obtained is consistent with the properties that physicists had previously hypothesized it should possess.

As a favorable tool for explainable artificial intelligence (XAI), Shapley value has been widely used to interpret deep learning based predictive models. However, accurate and efficient estimation of Shapley value is difficult since the computation load grows exponentially with the increase of input features. Most existing accelerated estimation methods have to compromise on estimation accuracy with efficiency. In this article, we present EmSHAP(Energy-based model for Shapley value estimation) to estimate the expectation of Shapley contribution function under arbitrary subset of features given the rest. The energy-based model estimates the conditional density in the Shapley contribution function, which involves an energy network for approximating the unnormalized conditional density and a GRU (Gated Recurrent Unit) network for approximating the partition function. The GRU network maps the input features onto a hidden space to eliminate the impact of input orderings. In order to theoretically evaluate the performance of different Shapley value estimation methods, Theorems 1, 2 and 3 analyzed the error bounds of EmSHAP as well as two state-of-the-art methods, namely KernelSHAP and VAEAC. It is proved that EmSHAP has tighter error bound than KernelSHAP and VAEAC. Finally, case studies on two application examples show the enhanced estimation accuracy of EmSHAP.

In formal argumentation, arguments and their relations are typically represented as directed graphs, in which nodes are arguments and edges are argument relationships (typically: attack or support). From these argumentation graphs, inferences about the acceptability statuses or strengths of arguments are drawn. One formal argumentation approach that is gaining increased research attention is Quantitative Bipolar Argumentation (QBA). In QBA, (typically numerical) weights - so-called initial strengths - are assigned to arguments, and arguments are connected by a support and an attack relation. Hence, arguments directly connected to a node through the node's incoming edges can be referred to as attackers and supporters (depending on the relation). Given a Quantitative Bipolar Argumentation Graph (QBAG), an argumentation semantics then infers the arguments' final strengths; intuitively, an argument's attackers tend to decrease its final strength, whereas supporters tend to increase it.