Group or cluster structure on explanatory variables in machine learning problems is a very general phenomenon, which has attracted broad interest from practitioners and theoreticians alike. In this work we contribute an approach to sparse learning under such group structure, that does not require prior information on the group identities. Our paradigm is motivated by the Laplacian geometry of an underlying network with a related community structure, and proceeds by directly incorporating this into a penalty that is effectively computed via a heat-flow-based local network dynamics. The proposed penalty interpolates between the lasso and the group lasso penalties, the runtime of the heat-flow dynamics being the interpolating parameter. As such it can automatically default to lasso when the group structure reflected in the Laplacian is weak. In fact, we demonstrate a data-driven procedure to construct such a network based on the available data. Notably, we dispense with computationally intensive pre-processing involving clustering of variables, spectral or otherwise. Our technique is underpinned by rigorous theorems that guarantee its effective performance and provide bounds on its sample complexity. In particular, in a wide range of settings, it provably suffices to run the diffusion for time that is only logarithmic in the problem dimensions. We explore in detail the interfaces of our approach with key statistical physics models in network science, such as the Gaussian Free Field and the Stochastic Block Model. Our work raises the possibility of applying similar diffusion-based techniques to classical learning tasks, exploiting the interplay between geometric, dynamical and stochastic structures underlying the data.

Artificial intelligence (AI) systems increasingly inform medical decision-making, yet concerns about algorithmic bias and inequitable outcomes persist, particularly for historically marginalized populations. This paper introduces the concept of Predictive Representativity (PR), a framework of fairness auditing that shifts the focus from the composition of the data set to outcomes-level equity. Through a case study in dermatology, we evaluated AI-based skin cancer classifiers trained on the widely used HAM10000 dataset and on an independent clinical dataset (BOSQUE Test set) from Colombia. Our analysis reveals substantial performance disparities by skin phototype, with classifiers consistently underperforming for individuals with darker skin, despite proportional sampling in the source data. We argue that representativity must be understood not as a static feature of datasets but as a dynamic, context-sensitive property of model predictions. PR operationalizes this shift by quantifying how reliably models generalize fairness across subpopulations and deployment contexts. We further propose an External Transportability Criterion that formalizes the thresholds for fairness generalization. Our findings highlight the ethical imperative for post-hoc fairness auditing, transparency in dataset documentation, and inclusive model validation pipelines. This work offers a scalable tool for diagnosing structural inequities in AI systems, contributing to discussions on equity, interpretability, and data justice and fostering a critical re-evaluation of fairness in data-driven healthcare.

This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample coverage guarantees and fast convergence rates of the oracle estimator. In heteroscedastic settings, we forgo these non-asymptotic guarantees to gain statistical efficiency, proposing a local $k$--nearest--neighbor method without conformal calibration that is adaptive to the geometry of each particular nonlinear space. Both procedures work with any regression algorithm and are scalable to large data sets, allowing practitioners to plug in their preferred models and incorporate domain expertise. We prove consistency for the proposed estimators under minimal conditions. Finally, we demonstrate the practical utility of our approach in personalized--medicine applications involving random response objects such as probability distributions and graph Laplacians.

Every day, multinational firms process thousands of transactions, each of which must adhere to tax regulations that vary by jurisdiction and are often nuanced. The determination of product and service tax codes, such as HSN or SAC is a major use case in Tax compliance. An accurate determination of such codes is imperative to avoid any tax penalties. This paper proposes a domain-adaptive small language model (SLM) with an encoder-decoder architecture for the enhanced prediction of product and service tax codes. In this approach, we address the problem of predicting hierarchical tax code sequences using unstructured product and services data. We employ an SLM based upon encoder-decoder architecture as this enables sequential generation of tax codes to capture the hierarchical dependencies present within the tax codes. Our experiments demonstrate that encoder-decoder SLMs can be successfully applied to the sequential prediction of structured tax codes, a domain that remains comparatively unexplored in current NLP research. In this paper, we demonstrate the superior performance of the domain-adaptive encoder-decoder SLMs over flat classifiers when applied to the Harmonized System of Nomenclature (HSN), and achieve superior results compared to decoder-only and encoder-only architectures for structured sequence generation tasks. This approach can also be scaled to other government-mandated tax commodity codes, such as United Nations Standard Products and Services Codes (UNSPSC), or Brazil's Nomenclatura Comum do Mercosul (NCM).

England's players were racially abused during their second Test victory over Argentina in San Juan on 12 July. Team officials lodged a complaint to governing body World Rugby over the incident that occurred when the visitors' replacements were warming up in the first half. "While it is clear that an incident took place, we regret that the individuals responsible could not be identified," said World Rugby, adding their investigation included witness statements and video analysis. "Intense efforts were made to identify the small group of five or seven individuals responsible within a crowd of over 20,000 spectators," said Gabriel Travaglini, president of the Union Argentina de Rugby (UAR). "Unfortunately, despite an exhaustive search, it was not possible to identify the perpetrators. "We strongly condemn all acts of racism and stand in solidarity with the England rugby players who felt aggrieved." He added that the UAR would work with World Rugby to educate fans. There have been several recent high-profile cases of discriminatory behaviour in Argentine sport. In 2020, Pablo Matera and Guido Petti, both of whom played in the match in San Juan, were suspended from the team after racist remarks they had made on social media several years earlier were unearthed. In 2024, Chelsea footballer Enzo Fernandez apologised to team-mates after being filmed joining in with a chant that questioned the heritage of France's black and mixed race players. "Rugby completely condemns discriminatory behaviour of any kind," said World Rugby chairman Brett Robinson. "We offer our full support to the players involved and want them to know that rugby stands with them in opposing racism.

However, the epistemological approach differs from that of so-called "grounded cognition". We can summarise this difference as follows: while grounded cognition analyses the experience of a living system from the point of view of an observer, we adopt the point of view of the system itself, defined by the need to preserve the biological properties essential for its survival. Therefore, our proposal implies the idea that the system is self-referential, since it operates with the aim of being able to continue operating. The method is based on an algorithmic schema that we called Environment Generative Operator (EGO) and uses an object language developed for this purpose, that we called E-language. EGO simulates cognitive processes by manipulating E-language strings. Among all the feasible ones, an EGO model called "EGO-P" (Supplementary Material 2) was implemented and tested, achieving the expected objectives. Repositories 2 and 3, as all the others mentioned in the article, can be accessed via the corresponding link in the bibliography. E-language has various mathematical properties. Those useful for this work have been demonstrated and are available in Supplementary Material 1.

RoboCup2025 is currently taking place in Salvador, Brazil. With day one of the main competition complete, things are hotting up across the many different leagues. From soccer to rescue, from industrial to home scenarios, teams are putting their robots through their paces across a variety of tasks and matches. If you would like to catch up on the action from the first day, you can watch the recording of the livestream below. This includes coverage of the teams competing, interviews with participants and organisers, and insights into RoboCup and the various leagues.

Netflix has used artificial intelligence in one of its TV shows for the first time, in a move the streaming company's boss said would make films and programmes cheaper and of better quality. Ted Sarandos, a co-chief executive of Netflix, said the Argentinian science fiction series El Eternauta (The Eternaut) was the first it had made that involved using generative AI footage. "We remain convinced that AI represents an incredible opportunity to help creators make films and series better, not just cheaper," he told analysts on Thursday after Netflix reported its second-quarter results. He said the series, which follows survivors of a rapid and devastating toxic snowfall, involved Netflix and visual effects (VFX) artists using AI to show a building collapsing in Buenos Aires. "Using AI-powered tools, they were able to achieve an amazing result with remarkable speed and, in fact, that VFX sequence was completed 10 times faster than it could have been completed with traditional VFX tools and workflows," he said.

Recent advancements in vision-language models (VLMs) have improved performance by increasing the number of visual tokens, which are often significantly longer than text tokens. However, we observe that most real-world scenarios do not require such an extensive number of visual tokens. While the performance drops significantly in a small subset of OCR-related tasks, models still perform accurately in most other general VQA tasks with only 1/4 resolution. Therefore, we propose to dynamically process distinct samples with different resolutions, and present a new paradigm for visual token compression, namely, VisionThink. It starts with a downsampled image and smartly decides whether it is sufficient for problem solving. Otherwise, the model could output a special token to request the higher-resolution image. Compared to existing Efficient VLM methods that compress tokens using fixed pruning ratios or thresholds, VisionThink autonomously decides whether to compress tokens case by case. As a result, it demonstrates strong fine-grained visual understanding capability on OCR-related tasks, and meanwhile saves substantial visual tokens on simpler tasks. We adopt reinforcement learning and propose the LLM-as-Judge strategy to successfully apply RL to general VQA tasks. Moreover, we carefully design a reward function and penalty mechanism to achieve a stable and reasonable image resize call ratio. Extensive experiments demonstrate the superiority, efficiency, and effectiveness of our method. Our code is available at https://github.com/dvlab-research/VisionThink.

The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient reasoning and computational techniques for such a combined formalism presents a significant challenge. In this paper, we adopt a more straightforward approach aiming at integrating two well-established and computationally well-behaved components: higher-order patterns on one side and fuzzy equivalences expressed through similarity relations based on minimum T-norm on the other. We propose a unification algorithm for higher-order patterns modulo these similarity relations and prove its termination, soundness, and completeness. This unification problem, like its crisp counterpart, is unitary. The algorithm computes a most general unifier with the highest degree of approximation when the given terms are unifiable.