We present an approach for analyzing message passing graph neural networks (MPNNs) based on an extension of graphon analysis to a so called graphon-signal analysis. AMPNN is a function that takes a graph and a signal on the graph (a graph-signal) and returns some value. Since the input space of MPNNs is non-Euclidean, i.e., graphs can be of any size and topology, properties such as generalization are less well understood for MPNNs than for Euclidean neural networks. We claim that one important missing ingredient in past work is a meaningful notion of graph-signal similarity measure, that endows the space of inputs to MPNNs with a regular structure. We present such a similarity measure, called the graphon-signal cut distance, which makes the space of all graph-signals a dense subset of a compact metric space - the graphon-signal space.

Theorem 1. Minimizing the expected loss Suppose we have T -dimensional features. Anchor nodes serve as fixed reference points within a simplicial complex, anchoring its structure and providing stability. Furthermore, anchor nodes can also represent important entities. Figure S2: Comparison of TSNE plots of representations learned by various encoders. CCA-SSG methods can not capture higher-order information and show similar artifacts. For example, the two clusters on the bottom and one from the right (corresponding to classes 1,2,3) are students from the same year but in different divisions.

The failure to learn common neighbor demonstrates GAE's severe limitation for link prediction.

Large robot fleets are now common in warehouses and other logistics settings, where small control gains translate into large operational impacts. In this article, we address task scheduling for lifelong Multi-Agent Pickup-and-Delivery (MAPD) and propose a hybrid method that couples learning-based global guidance with lightweight optimization. A graph neural network policy trained via reinforcement learning outputs a desired distribution of free agents over an aggregated warehouse graph. This signal is converted into region-to-region rebalancing through a minimum-cost flow, and finalized by small, local assignment problems, preserving accuracy while keeping per-step latency within a 1 s compute budget. On congested warehouse benchmarks from the League of Robot Runners (LRR) with up to 500 agents, our approach improves throughput by up to 10% over the 2024 winning scheduler while maintaining real-time execution. The results indicate that coupling graph-structured learned guidance with tractable solvers reduces congestion and yields a practical, scalable blueprint for high-throughput scheduling in large fleets.

As the use of AI in society grows, addressing emerging biases is essential to prevent systematic discrimination. Several bias detection methods have been proposed, but, with few exceptions, these tend to ignore transparency. Instead, interpretability and explainability are core requirements for algorithmic fairness, even more so than for other algorithmic solutions, given the human-oriented nature of fairness. We present ABIDE (Argumentative BIas detection by DEbate), a novel framework that structures bias detection transparently as debate, guided by an underlying argument graph as understood in (formal and computational) argumentation. The arguments are about the success chances of groups in local neighbourhoods and the significance of these neighbourhoods. We evaluate ABIDE experimentally and demonstrate its strengths in performance against an argumentative baseline.

Machine learning models are integrated into many real-world applications. Since these models contain artifacts of potentially sensitive training data, this raises concerns about data confidentiality and user privacy. The ability to remove specific training data from a model has emerged as a key mechanism to enforce, for instance, the "right to be forgotten" promoted by the European GDPR law [17] or the "right to erase" in the Canadian CPPA legislation [29]. Approximate machine unlearning aims to find efficient mechanisms, avoiding the cost of learning a new model from scratch over the training dataset deprived of the sensitive data. Privacy is not the only application of machine unlearning. It has been proven useful as a defense against backdoor attacks by annihilating the influence of the poisoned training data [45, 38], or to improve fairness by removing data that induce biases in the training set. Another scenario is the derivation of a restricted public model from a powerful private model learned on some sensitive data [12]. The accuracy of the public model should be on par with or slightly degraded compared to the private model.

We introduce a logical language for reasoning about quantized aggregate-combine graph neural networks with global readout (ACR-GNNs). We provide a logical characterization and use it to prove that verification tasks for quantized GNNs with readout are (co)NEXPTIME-complete. This result implies that the verification of quantized GNNs is computationally intractable, prompting substantial research efforts toward ensuring the safety of GNN-based systems. We also experimentally demonstrate that quantized ACR-GNN models are lightweight while maintaining good accuracy and generalization capabilities with respect to non-quantized models.