This article deals with the cake cutting problem. In this setting, there exists two notions of fair division: proportional division (when there are n players, each player thinks to get at least 1/n of the cake) and envy-free division (each player wants to keep his or her share because he or she does not envy the portion given to another player). Some results are valid for proportional division but not for envy-free division. Here, we introduce and study a scale between the proportional division and the envy-free division. The goal is to understand where is the gap between statements about proportional division and envy-free division. This scale comes from the notion introduced in this article: k-proportionality. When k = n this notion corresponds to the proportional division and when k = 2 it corresponds to envy-free division. With k-proportionality we can understand where some difficulties in fair division lie. First, we show that there are situations in which there is no k-proportional and equitable division of a pie with connected pieces when k $\le$ n -1. This result was known only for envy-free division, ie k = 2. Next, we prove that there are situations in which there is no Pareto-optimal k-proportional division of a cake with connected pieces when k $\le$ n -1. This result was known only for k = 2. These theorems say that we can get an impossibility result even if we do not consider an envy-free division but a weaker notion. Finally, k-proportionality allows to give a generalization with a uniform statement of theorems about strong envy-free and strong proportional divisions.

Abstract-- In Social Robot Navigation (SRN), the availability of meaningful metrics is crucial for evaluating trajectories from human-robot interactions. In the SRN context, such interactions often relate to resolving conflicts between two or more agents. Correspondingly, the shares to which agents contribute to the resolution of such conflicts are important. This paper builds on recent work, which proposed a Responsibility metric capturing such shares. We extend this framework in two directions: First, we model the conflict buildup phase by introducing a time normalization. Second, we propose the related Engagement metric, which captures how the agents' actions intensify a conflict. In a comprehensive series of simulated scenarios with dyadic, group and crowd interactions, we show that the metrics carry meaningful information about the cooperative resolution of conflicts in interactions. They can be used to assess behavior quality and foresightedness. We extensively discuss applicability, design choices and limitations of the proposed metrics.

Human-machine interaction is increasingly important in industry, and this trend will only intensify with the rise of Industry 5.0. Human operators have skills that need to be adapted when using machines to achieve the best results. It is crucial to highlight the operator's skills and understand how they use and adapt them [18]. A rigorous description of these skills is necessary to compare performance with and without robot assistance. Predicate logic, used by Vergnaud within Piaget's scheme concept, offers a promising approach. However, this theory doesn't account for cognitive system constraints, such as the timing of actions, the limitation of cognitive resources, the parallelization of tasks, or the activation of automatic gestures contrary to optimal knowledge. Integrating these constraints is essential for representing agent skills understanding skill transfer between biological and mechanical structures. Cognitive architectures models [2] address these needs by describing cognitive structure and can be combined with the scheme for mutual benefit. Welding provides a relevant case study, as it highlights the challenges faced by operators, even highly skilled ones. Welding's complexity stems from the need for constant skill adaptation to variable parameters like part position and process. This adaptation is crucial, as weld quality, a key factor, is only assessed afterward via destructive testing. Thus, the welder is confronted with a complex perception-decision-action cycle, where the evaluation of the impact of his actions is delayed and where errors are definitive. This dynamic underscores the importance of understanding and modeling the skills of operators.

Multi-robot mapping with neural implicit representations enables the compact reconstruction of complex environments. However, it demands robustness against communication challenges like packet loss and limited bandwidth. While prior works have introduced various mechanisms to mitigate communication disruptions, performance degradation still occurs under extremely low communication success rates. This paper presents UDON, a real-time multi-agent neural implicit mapping framework that introduces a novel uncertainty-weighted distributed optimization to achieve high-quality mapping under severe communication deterioration. The uncertainty weighting prioritizes more reliable portions of the map, while the distributed optimization isolates and penalizes mapping disagreement between individual pairs of communicating agents. We conduct extensive experiments on standard benchmark datasets and real-world robot hardware. We demonstrate that UDON significantly outperforms existing baselines, maintaining high-fidelity reconstructions and consistent scene representations even under extreme communication degradation (as low as 1% success rate).

While Large Language Models have significantly advanced Text2SQL generation, a critical semantic gap persists where syntactically valid queries often misinterpret user intent. To mitigate this challenge, we propose GBV-SQL, a novel multi-agent framework that introduces Guided Generation with SQL2Text Back-translation Validation. This mechanism uses a specialized agent to translate the generated SQL back into natural language, which verifies its logical alignment with the original question. Critically, our investigation reveals that current evaluation is undermined by a systemic issue: the poor quality of the benchmarks themselves. We introduce a formal typology for "Gold Errors", which are pervasive flaws in the ground-truth data, and demonstrate how they obscure true model performance. On the challenging BIRD benchmark, GBV-SQL achieves 63.23% execution accuracy, a 5.8% absolute improvement. After removing flawed examples, GBV-SQL achieves 96.5% (dev) and 97.6% (test) execution accuracy on the Spider benchmark. Our work offers both a robust framework for semantic validation and a critical perspective on benchmark integrity, highlighting the need for more rigorous dataset curation.

We present Match Chat, a real-time, agent-driven assistant designed to enhance the tennis fan experience by delivering instant, accurate responses to match-related queries. Match Chat integrates Generative Artificial Intelligence (GenAI) with Generative Computing (GenComp) techniques to synthesize key insights during live tennis singles matches. The system debuted at the 2025 Wimbledon Championships and the 2025 US Open, where it provided about 1 million users with seamless access to streaming and static data through natural language queries. The architecture is grounded in an Agent-Oriented Architecture (AOA) combining rule engines, predictive models, and agents to pre-process and optimize user queries before passing them to GenAI components. The Match Chat system had an answer accuracy of 92.83% with an average response time of 6.25 seconds under loads of up to 120 requests per second (RPS). Over 96.08% of all queries were guided using interactive prompt design, contributing to a user experience that prioritized clarity, responsiveness, and minimal effort. The system was designed to mask architectural complexity, offering a frictionless and intuitive interface that required no onboarding or technical familiarity. Across both Grand Slam deployments, Match Chat maintained 100% uptime and supported nearly 1 million unique users, underscoring the scalability and reliability of the platform. This work introduces key design patterns for real-time, consumer-facing AI systems that emphasize speed, precision, and usability that highlights a practical path for deploying performant agentic systems in dynamic environments.

One of the main goals of robotics and intelligent agent research is to enable natural communication with humans in physically situated settings. While recent work has focused on verbal modes such as language and speech, non-verbal communication is crucial for flexible interaction. We present a framework for generating pointing gestures in embodied agents by combining imitation and reinforcement learning. Using a small motion capture dataset, our method learns a motor control policy that produces physically valid, naturalistic gestures with high referential accuracy. We evaluate the approach against supervised learning and retrieval baselines in both objective metrics and a virtual reality referential game with human users. Results show that our system achieves higher naturalness and accuracy than state-of-the-art supervised models, highlighting the promise of imitation-RL for communicative gesture generation and its potential application to robots.

We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs. These games model a broad class of graph-structured multi-agent systems arising in finance, robotics, energy, and social dynamics, where agents interact locally under uncertainty. The NTM architecture imposes a graph-guided sparsification on feedforward neural networks, embedding fixed, non-trainable components aligned with the underlying graph topology. This design enhances interpretability and stability, while significantly reducing the number of trainable parameters in large-scale, sparse settings. We theoretically establish a universal approximation property for NTM in static games on graphs and numerically validate its expressivity and robustness through supervised learning tasks. Building on this foundation, we incorporate NTM into two state-of-the-art game solvers, Direct Parameterization and Deep BSDE, yielding their sparse variants (NTM-DP and NTM-DBSDE). Numerical experiments on three SDGs across various graph structures demonstrate that NTM-based methods achieve performance comparable to their fully trainable counterparts, while offering improved computational efficiency.

Understanding user intents from UI interaction trajectories remains a challenging, yet crucial, frontier in intelligent agent development. While massive, datacenter-based, multi-modal large language models (MLLMs) possess greater capacity to handle the complexities of such sequences, smaller models which can run on-device to provide a privacy-preserving, low-cost, and low-latency user experience, struggle with accurate intent inference. We address these limitations by introducing a novel decomposed approach: first, we perform structured interaction summarization, capturing key information from each user action. Second, we perform intent extraction using a fine-tuned model operating on the aggregated summaries. This method improves intent understanding in resource-constrained models, even surpassing the base performance of large MLLMs.

This paper addresses the problem of collaborative formation control for multi-agent systems with limited resources. We consider a team of robots tasked with achieving a desired formation from arbitrary initial configurations. To reduce unnecessary control updates and conserve resources, we propose a distributed event-triggered formation controller that relies on inter-agent distance measurements. Control updates are triggered only when the measurement error exceeds a predefined threshold, ensuring system stability. The proposed controller is validated through extensive simulations and real-world experiments involving different formations, communication topologies, scalability tests, and variations in design parameters, while also being compared against periodic triggering strategies. Results demonstrate that the event-triggered approach significantly reduces control efforts while preserving formation performance.