While football analytics has changed the way teams and analysts assess performance, there remains a communication gap between machine learning practice and how coaching staff talk about football. Coaches and practitioners require actionable insights, which are not always provided by models. To bridge this gap, we show how to build wordalizations (a novel approach that leverages large language models) for shots in football. Specifically, we first build an expected goals model using logistic regression. We then use the co-efficients of this regression model to write sentences describing how factors (such as distance, angle and defensive pressure) contribute to the model's prediction. Finally, we use large language models to give an entertaining description of the shot. We describe our approach in a model card and provide an interactive open-source application describing shots in recent tournaments. We discuss how shot wordalisations might aid communication in coaching and football commentary, and give a further example of how the same approach can be applied to other actions in football.

Reasoning is a cognitive ability which allows humans to solve problems with previously unseen combinations of constraints. For a long time, it has been debated whether artificial neural networks can obtain such generalization skills or whether they can only learn to detect superficial patterns Fodor and Pylyshyn [1988], Marcus [2003, 2018] without being able to generalize to novel combinations of constraints. With the arrival of Large Language Models (LLMs) specially trained for reasoning Guo et al. [2025], Jaech et al. [2024], it became harder and harder to claim that these models can only detect superficial patterns. Nevertheless, the exact mechanism by which they are able to solve tasks that typically require reasoning is largely unknown and the robustness of the solving process is also not understood. In this contribution, we focus on a restricted class of problems that require reasoning, concretely on solving Boolean formulas in CNF form. This could be viewed as a prototypical task where the goal is to solve problems with novel combinations of constraints, and where detecting superficial patterns seen during training would be insufficient. It has already been demonstrated that Graph Neural Networks (GNNs) can successfully learn to solve such problems and generalize to larger problems Selsam et al. [2018], even though they are still not competitive when compared to state of the art SAT solvers. Understanding the underlying mechanisms GNNs employ to successfully solve problems, as well as their limitations, would offer significant practical and theoretical value.

We introduce a novel loss function, Covariance Loss, which is conceptually equivalent to conditional neural processes and has a form of regularization so that is applicable to many kinds of neural networks. With the proposed loss, mappings from input variables to target variables are highly affected by dependencies of target variables as well as mean activation and mean dependencies of input and target variables. This nature enables the resulting neural networks to become more robust to noisy observations and recapture missing dependencies from prior information. In order to show the validity of the proposed loss, we conduct extensive sets of experiments on real-world datasets with state-of-the-art models and discuss the benefits and drawbacks of the proposed Covariance Loss.

Conformal prediction and scenario optimization constitute two important classes of statistical learning frameworks to certify decisions made using data. They have found numerous applications in control theory, machine learning and robotics. Despite intense research in both areas, and apparently similar results, a clear connection between these two frameworks has not been established. By focusing on the so-called vanilla conformal prediction, we show rigorously how to choose appropriate score functions and set predictor map to recover well-known bounds on the probability of constraint violation associated with scenario programs. We also show how to treat ranking of nonconformity scores as a one-dimensional scenario program with discarded constraints, and use such connection to recover vanilla conformal prediction guarantees on the validity of the set predictor. We also capitalize on the main developments of the scenario approach, and show how we could analyze calibration conditional conformal prediction under this lens. Our results establish a theoretical bridge between conformal prediction and scenario optimization.

This study used machine learning algorithms to identify actors and extract the age of actors from images taken randomly from movies. The use of images taken from Arab movies includes challenges such as non-uniform lighting, different and multiple poses for the actors and multiple elements with the actor or a group of actors. Additionally, the use of make-up, wigs, beards, and wearing different accessories and costumes made it difficult for the system to identify the personality of the same actor. The Arab Actors Dataset-AAD comprises 574 images sourced from various movies, encompassing both black and white as well as color compositions. The images depict complete scenes or fragments thereof. Multiple models were employed for feature extraction, and diverse machine learning algorithms were utilized during the classification and prediction stages to determine the most effective algorithm for handling such image types. The study demonstrated the effectiveness of the Logistic Regression model exhibited the best performance compared to other models in the training phase, as evidenced by its AUC, precision, CA and F1score values of 99%, 86%, 85.5% and 84.2% respectively. The findings of this study can be used to improve the precision and reliability of facial recognition technology for various uses as with movies search services, movie suggestion algorithms, and genre classification of movies.

The subjective evaluation of early stage engineering designs, such as conceptual sketches, traditionally relies on human experts. However, expert evaluations are time-consuming, expensive, and sometimes inconsistent. Recent advances in vision-language models (VLMs) offer the potential to automate design assessments, but it is crucial to ensure that these AI ``judges'' perform on par with human experts. However, no existing framework assesses expert equivalence. This paper introduces a rigorous statistical framework to determine whether an AI judge's ratings match those of human experts. We apply this framework in a case study evaluating four VLM-based judges on key design metrics (uniqueness, creativity, usefulness, and drawing quality). These AI judges employ various in-context learning (ICL) techniques, including uni- vs. multimodal prompts and inference-time reasoning. The same statistical framework is used to assess three trained novices for expert-equivalence. Results show that the top-performing AI judge, using text- and image-based ICL with reasoning, achieves expert-level agreement for uniqueness and drawing quality and outperforms or matches trained novices across all metrics. In 6/6 runs for both uniqueness and creativity, and 5/6 runs for both drawing quality and usefulness, its agreement with experts meets or exceeds that of the majority of trained novices. These findings suggest that reasoning-supported VLM models can achieve human-expert equivalence in design evaluation. This has implications for scaling design evaluation in education and practice, and provides a general statistical framework for validating AI judges in other domains requiring subjective content evaluation.

Gaussian processes (GPs) are crucial in machine learning for quantifying uncertainty in predictions. However, their associated covariance matrices, defined by kernel functions, are typically dense and large-scale, posing significant computational challenges. This paper introduces a matrix-free method that utilizes the Non-equispaced Fast Fourier Transform (NFFT) to achieve nearly linear complexity in the multiplication of kernel matrices and their derivatives with vectors for a predetermined accuracy level. To address high-dimensional problems, we propose an additive kernel approach. Each sub-kernel in this approach captures lower-order feature interactions, allowing for the efficient application of the NFFT method and potentially increasing accuracy across various real-world datasets. Additionally, we implement a preconditioning strategy that accelerates hyperparameter tuning, further improving the efficiency and effectiveness of GPs.

Unlearnable data (ULD) has emerged as an innovative defense technique to prevent machine learning models from learning meaningful patterns from specific data, thus protecting data privacy and security. By introducing perturbations to the training data, ULD degrades model performance, making it difficult for unauthorized models to extract useful representations. Despite the growing significance of ULD, existing surveys predominantly focus on related fields, such as adversarial attacks and machine unlearning, with little attention given to ULD as an independent area of study. This survey fills that gap by offering a comprehensive review of ULD, examining unlearnable data generation methods, public benchmarks, evaluation metrics, theoretical foundations and practical applications. We compare and contrast different ULD approaches, analyzing their strengths, limitations, and trade-offs related to unlearnability, imperceptibility, efficiency and robustness. Moreover, we discuss key challenges, such as balancing perturbation imperceptibility with model degradation and the computational complexity of ULD generation. Finally, we highlight promising future research directions to advance the effectiveness and applicability of ULD, underscoring its potential to become a crucial tool in the evolving landscape of data protection in machine learning.

The increasing availability of traffic data from sensor networks has created new opportunities for understanding vehicular dynamics and identifying anomalies. In this study, we employ clustering techniques to analyse traffic flow data with the dual objective of uncovering meaningful traffic patterns and detecting anomalies, including sensor failures and irregular congestion events. We explore multiple clustering approaches, i.e. partitioning and hierarchical methods, combined with various time-series representations and similarity measures. Our methodology is applied to real-world data from highway sensors, enabling us to assess the impact of different clustering frameworks on traffic pattern recognition. We also introduce a clustering-driven anomaly detection methodology that identifies deviations from expected traffic behaviour based on distance-based anomaly scores. Results indicate that hierarchical clustering with symbolic representations provides robust segmentation of traffic patterns, while partitioning methods such as k -means and fuzzy c-means yield meaningful results when paired with Dynamic Time Warping. The proposed anomaly detection strategy successfully identifies sensor malfunctions and abnormal traffic conditions with minimal false positives, demonstrating its practical utility for real-time monitoring. Real-world vehicular traffic data are provided by Autostrade Alto Adriatico S.p.A. Keywords.

A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is constructed that allows approximating such functions with any degree of accuracy. A physical interpretation of such a model is given and possible methods for its training are discussed. The proposed model can be considered as a simple alternative to possible $p$-adic models based on neural network architecture.