Vision-Language Models (VLMs) exhibit puzzling failures in multi-object visual tasks, such as hallucinating non-existent elements or failing to identify the most similar objects among distractions. While these errors mirror human cognitive constraints, such as the "Binding Problem", the internal mechanisms driving them in artificial systems remain poorly understood. Here, we propose a mechanistic insight by analyzing the representational geometry of open-weight VLMs (Qwen, InternVL, Gemma), comparing methodologies to distill "concept vectors" - latent directions encoding visual concepts. We validate our concept vectors via steering interventions that reliably manipulate model behavior in both simplified and naturalistic vision tasks (e.g., forcing the model to perceive a red flower as blue). We observe that the geometric overlap between these vectors strongly correlates with specific error patterns, offering a grounded quantitative framework to understand how internal representations shape model behavior and drive visual failures.

Correlation Clustering (CC) is a natural formulation of clustering in combinatorial optimization, which uses a graph representation of the input and does not require a pre-specified number of clusters. Given n objects and a pairwise similarity function, the goal is to cluster the objects so that similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its versatility, existing CC algorithms suffer from significant scalability issues and are inherently transductive: i.e., the algorithm must be executed from scratch for any new problem instance. In this work, we bridge this gap by leveraging Graph Neural Networks (GNNs) to solve Inductive Correlation Clustering, a novel generalization of the CC problem designed to handle unseen graph instances. By learning to exploit common structural patterns and node features during training, our framework generalizes to new graphs drawn from the same distribution with minimal computational overhead with respect to standard algorithms. We demonstrate the effectiveness and scalability of our approach through extensive experiments. Our framework not only excels in the inductive setting, e.g., lowering the inference time up to 5 order of magnitude, while maintaining an approximation ratio within 10% of the best baseline solution, but also achieves competitive results on standard (transductive) CC benchmarks. Finally, we showcase a practical application of our framework as a learnable pooling mechanism for graph classification. Our results indicate that our method serves as an efficient pooling layer, enhancing the ability of GNNs to capture hierarchical structural information in networks.

Link Prediction is a foundational task in Graph Representation Learning, supporting applications like link recommendation, knowledge graph completion, and graph generation. Graph Neural Networks (GNNs) have shown promising results in this domain and are widely used for learning graph representations from data. However, not all GNNs can represent edge direction and not all training strategies support the learning of directed graph representations. For this reason, Neural Directed Link Prediction (NDLP) has been divided into three sub-tasks. Models that perform well in distinguishing uncorrelated samples of positive and negative directed edges (the general DLP task) do not necessarily capture edge directionality and bidirectionality (two additional tasks). While many models can be trained to perform well on any of the sub-tasks, most fail to perform well across them all. In this work, we propose three novel training strategies that adress the three sub-tasks simultaneously and can be applied to any autoencoder-based GNN without motifying its architecture. Our first strategy, the Multi-Class Framework for Neural Directed Link Prediction (MC-NDLP) maps NDLP to a Multi-Class training objective. The second and third strategies adopt a Multi-Task perspective, either with a Multi-Objective (MO-NDLP) or a Scalarized (S-NDLP) approach. We show that these training strategies allow many models to achieve higher or more balanced performance across the three NDLP sub-tasks. The flexibility offered by our proposed training strategies provides a powerful means for improving the capabilities of NDLP models to advance the state of Neural Directed Link Prediction.

Edge-level explainers for Graph Neural Networks (GNNs) aim to identify the most crucial edges that influence the model's predictions in a node classification task. Benchmarking these explainers is particularly challenging due to the extensive search space of potential explanations and the absence of reliable ground truths for edge importance. Moreover, the evaluation methods which are prominent in the literature rely on assumptions about which subgraphs in the input data influence the classification of a node, yet they provide no guarantee that the model has effectively learned the intended behavior. In this paper, we address these limitations by introducing a white-box GNN model together with a theoretical analysis to identify which edges are truly important, i.e., when removed, they can alter the classification. We demonstrate the effectiveness of this framework on both synthetic and real-world node classification tasks, using metrics that account for the inherent imbalance between the few relevant edges and the many irrelevant ones. Our evaluation reveals two recurring issues in current explainability methods: the frequent misidentification of unimportant edges as important ones, and numerical instability in some attribution techniques. To address these issues, we propose two corrective strategies that significantly enhance the reliability of edge-level attributions: a post-processing method to refine edge rankings and a rescaling of model weights to stabilize numerical outputs. Our work provides valuable insights into the strengths and weaknesses of existing GNN explainers and presents practical solutions to advance the fine-grained explainability of graph-based models.

Agent-Based Models (ABMs) are powerful tools for studying emergent properties in complex systems. In ABMs, agent behaviors are governed by local interactions and stochastic rules. However, these rules are, in general, non-differentiable, limiting the use of gradient-based methods for optimization, and thus integration with real-world data. We propose a novel framework to learn a differentiable surrogate of any ABM by observing its generated data. Our method combines diffusion models to capture behavioral stochasticity and graph neural networks to model agent interactions. Distinct from prior surrogate approaches, our method introduces a fundamental shift: rather than approximating system-level outputs, it models individual agent behavior directly, preserving the decentralized, bottom-up dynamics that define ABMs. We validate our approach on two ABMs (Schelling's segregation model and a Predator-Prey ecosystem) showing that it replicates individual-level patterns and accurately forecasts emergent dynamics beyond training. Our results demonstrate the potential of combining diffusion models and graph learning for data-driven ABM simulation.

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random spanning trees suitably transformed into path graphs which, despite their simplicity, are shown to retain essential topological and node information of the original input graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also improves accuracy in subsequent test phases, especially under small training set regimes, which are of great practical importance, as in many real-world scenarios labels may be hard to obtain. In these settings, our framework yields very good results as it effectively counters the training deterioration caused by overfitting when the training set is small. Our method also addresses common issues like over-squashing and over-smoothing while avoiding under-reaching phenomena. Although our framework is flexible and can be deployed in several types of GNNs, in this paper we focus on graph convolutional networks and carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we achieve simultaneous improvement of training speed and test accuracy over a wide pool of representative baselines.

Determining whether an algorithmic decision-making system discriminates against a specific demographic typically involves comparing a single point estimate of a fairness metric against a predefined threshold. This practice is statistically brittle: it ignores sampling error and treats small demographic subgroups the same as large ones. The problem intensifies in intersectional analyses, where multiple sensitive attributes are considered jointly, giving rise to a larger number of smaller groups. As these groups become more granular, the data representing them becomes too sparse for reliable estimation, and fairness metrics yield excessively wide confidence intervals, precluding meaningful conclusions about potential unfair treatments. In this paper, we introduce a unified, size-adaptive, hypothesis‑testing framework that turns fairness assessment into an evidence‑based statistical decision. Our contribution is twofold. (i) For sufficiently large subgroups, we prove a Central‑Limit result for the statistical parity difference, leading to analytic confidence intervals and a Wald test whose type‑I (false positive) error is guaranteed at level $\alpha$. (ii) For the long tail of small intersectional groups, we derive a fully Bayesian Dirichlet–multinomial estimator; Monte-Carlo credible intervals are calibrated for any sample size and naturally converge to Wald intervals as more data becomes available. We validate our approach empirically on benchmark datasets, demonstrating how our tests provide interpretable, statistically rigorous decisions under varying degrees of data availability and intersectionality.

As deep learning systems become pervasive, the demand for trustworthy and transparent AI continues to grow. Traditional feature attribution methods, however, often lack robustness and alignment with human reasoning. This tutorial moves beyond feature attribution by introducing participants to two complementary interpretability paradigms: Concept-Based Explainable AI (C-XAI) and Mechanistic Interpretability. C-XAI provides explanations grounded in high-level, human-interpretable concepts, bridging the gap between model reasoning and human understanding. In parallel, mechanistic interpretability--a quickly emerging field--focuses on reverse-engineering neural networks to uncover and disentangle the internal mechanisms that give rise to human-understandable representations. Through interactive coding sessions and hands-on exercises, attendees will gain practical experience implementing, evaluating, and comparing a variety of C-XAI and mechanistic interpretability techniques. By the end of the tutorial, participants will be equipped with a modern interpretability toolbox and a deeper understanding of how to apply them in real-world scenarios.

Node representations, or embeddings, are low-dimensional vectors that capture node properties, typically learned through unsupervised structural similarity objectives or supervised tasks. While recent efforts have focused on explaining graph model decisions, the interpretability of unsupervised node embeddings remains underexplored. To bridge this gap, we introduce DiSeNE (Disentangled and Self-Explainable Node Embedding), a framework that generates self-explainable embeddings in an unsupervised manner. Our method employs disentangled representation learning to produce dimension-wise interpretable embeddings, where each dimension is aligned with distinct topological structure of the graph. We formalize novel desiderata for disentangled and interpretable embeddings, which drive our new objective functions, optimizing simultaneously for both interpretability and disentanglement. Additionally, we propose several new metrics to evaluate representation quality and human interpretability. Extensive experiments across multiple benchmark datasets demonstrate the effectiveness of our approach.

Proprietary data is a valuable asset used to develop predictive algorithms that benefit a wide range of users, including customers, business owners, and decision-makers. Consequently, there is a growing interest in developing safe and robust techniques for sharing, learning models, and distributing predictions across a wide spectrum of potential stakeholders. However, a structured process to assess the value of data assets, and thus enabling collaborations among stakeholders, remains largely unexplored. This is particularly challenging when the data to be shared has a networked structure, where increasing the shared data samples potentially connects information observed by different data owners, providing new knowledge that is unavailable to any data owner individually. Here, we propose E-GraDE, a framework that assists organizations in assessing the value of their networked data to better address graph machine learning tasks. This framework includes a step-by-step analysis of the requirements of different stakeholders, such as the accuracy or fairness requisites of the models, ensuring a fair evaluation process and stronger alignment in the development of a data federation consortium. Additionally, we propose an approach to estimate the value of networked data to be shared while disclosing only a small fraction of the original information. We support our approach with extensive computational experiments, analysing each part of it through simulated use cases.

We investigate the problem of online collaborative filtering under no-repetition constraints, whereby users need to be served content in an online fashion and a given user cannot be recommended the same content item more than once. We start by designing and analyzing an algorithm that works under biclustering assumptions on the user-item preference matrix, and show that this algorithm exhibits an optimal regret guarantee, while being fully adaptive, in that it is oblivious to any prior knowledge about the sequence of users, the universe of items, as well as the biclustering parameters of the preference matrix. We then propose a more robust version of this algorithm which operates with general matrices. Also this algorithm is parameter free, and we prove regret guarantees that scale with the amount by which the preference matrix deviates from a biclustered structure. To our knowledge, these are the first results on online collaborative filtering that hold at this level of generality and adaptivity under no-repetition constraints. Finally, we complement our theoretical findings with simple experiments on real-world datasets aimed at both validating the theory and empirically comparing to standard baselines. This comparison shows the competitive advantage of our approach over these baselines.

Modern Machine Learning (ML) has significantly advanced various fields; yet, the challenge of understanding complex models, often referred to as the "black box problem", remains a barrier to their widespread adoption, particularly in critical domains such as medical diagnosis and financial services. Explainable AI (XAI) addresses this challenge by augmenting ML models' outputs with interpretable information to facilitate human understanding of their internal decision processes. Despite the proliferation of explainers in recent years, covering a wide range of ML tasks and explanation types, there is no consensus on what constitutes a good explanation, leaving ML practitioners without clear guidance for selecting appropriate explainers. We argue that explanation quality quantification is the enabling factor for informed explainer choices, but many proposed explanation evaluation criteria are either narrow in scope or closer to desired properties than quantifiable metrics. This paper addresses this gap by proposing a standardized set of metrics for quantitatively evaluating explanations across diverse explanation types and ML tasks. We describe in detail the metrics of Effective Compactness, Rank Quality Index and Stability, designed to assess quantitatively explanation quality for various types of explanations (attributions, counterfactuals and rules) across different ML tasks (classification, regression and anomaly detection). We then present an exhaustive benchmarking framework for tabular-based ML, comprising open datasets, trained models, and state-of-the-art explainers. For each (data, model, explainer) tuple, we measure the time of the explanation production, apply our metrics and collect the results, highlighting correlations and trade-offs between desired properties. The resulting framework allows us to quantitatively rank explainers suitable for specific ML scenarios and select the most appropriate one based on the user's requirements.

Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a latent vector space, allowing their use for various graph tasks. Despite their success, only few studies have focused on explaining node embeddings locally. Moreover, global explanations of node embeddings remain unexplored, limiting interpretability and debugging potentials. We address this gap by developing human-understandable explanations for dimensions in node embeddings. Towards that, we first develop new metrics that measure the global interpretability of embedding vectors based on the marginal contribution of the embedding dimensions to predicting graph structure. We say that an embedding dimension is more interpretable if it can faithfully map to an understandable sub-structure in the input graph - like community structure. Having observed that standard node embeddings have low interpretability, we then introduce DINE (Dimension-based Interpretable Node Embedding), a novel approach that can retrofit existing node embeddings by making them more interpretable without sacrificing their task performance. We conduct extensive experiments on synthetic and real-world graphs and show that we can simultaneously learn highly interpretable node embeddings with effective performance in link prediction.

Regulators, researchers, and practitioners recognize the urgency of explainability in artificial intelligence systems, including the ones based on machine learning for graph-structured data. Despite the large number of proposals, however, a common understanding of what constitutes a good explanation is still lacking: different explainers often arrive at different conclusions on the same problem instance, making it hard for practitioners to choose among them. Furthermore, explainers often produce explanations through opaque logic hard to understand and assess -- ironically mirroring the black box nature they aim to elucidate. Recent proposals in the literature for benchmarking graph-based explainers typically involve embedding specific logic into data, training a black-box model, and then empirically assessing how well the explanation matches the embedded logic, i.e., they test truthfulness to the data. In contrast, we propose a true-to-the-model axiomatic framework for auditing explainers in the task of node classification on graphs. Our proposal hinges on the fundamental idea that an explainer should discern if a model relies on a particular feature for classifying a node. Building on this concept, we develop three types of white-box classifiers, with clear internal logic, that are relevant in real-world applications. We then formally prove that the set of features that can induce a change in the classification correctly corresponds to a ground-truth set of predefined important features. This property allows us to use the white-box classifiers to build a testing framework. We apply this framework to both synthetic and real data and evaluate various state-of-the-art explainers, thus characterizing their behavior. Our findings highlight how explainers often react in a rather counter-intuitive fashion to technical details that might be easily overlooked. Our approach offers valuable insights and recommended practices for selecting the right explainer given the task at hand, and for developing new methods for explaining graph-learning models.

Cycling is an outdoor activity with massive health benefits, and an effective solution for sustainable urban transport. Despite these benefits and the recent rising popularity of cycling, most countries still have a negligible uptake. This uptake is especially low for women: there is a largely unexplained, persistent gender gap in cycling. To understand the determinants of this gender gap in cycling at scale, here we use massive, automatically-collected data from the tracking application Strava on outdoor cycling for 61 cities across the United States, the United Kingdom, Italy and the Benelux area. While Strava data is particularly well-suited to describe the behavior of regular cyclists and its generalizability to occasional cyclists requires further investigation, the size of these data and their characteristics represent an unprecedented opportunity for the literature on cycling. Leveraging the associated gender and usage information, we first quantify the emerging gender gap in recreational cycling at city-level. A comparison of cycling rates of women across cities within similar geographical areas—where the penetration of Strava is assumed to be comparable—unveils a broad range of gender gaps. On a macroscopic level, we link this heterogeneity to a variety of urban indicators and provide evidence for traditional hypotheses on the determinants of the gender-cycling-gap. We find a positive association between female cycling rate and urban road safety. On a microscopic level, we identify female preferences for street-specific features in the city of New York. Assuming that the determinants of the gender-cycling-gap are similar across regular and occasional cyclists, our study suggests that enhancing the quality of the dedicated cycling infrastructure may be a way to make urban environments more accessible for women, thereby making urban transport more sustainable for everyone.

Convolutional Neural Networks (CNNs) are nowadays the model of choice in Computer Vision, thanks to their ability to automatize the feature extraction process in visual tasks. However, the knowledge acquired during training is fully sub-symbolic, and hence difficult to understand and explain to end users. In this paper, we propose a new technique called HOLMES (HOLonym-MEronym based Semantic inspection) that decomposes a label into a set of related concepts, and provides component-level explanations for an image classification model. Specifically, HOLMES leverages ontologies, web scraping and transfer learning to automatically construct meronym (parts)-based detectors for a given holonym (class). Then, it produces heatmaps at the meronym level and finally, by probing the holonym CNN with occluded images, it highlights the importance of each part on the classification output. Compared to state-of-the-art saliency methods, HOLMES takes a step further and provides information about both where and what the holonym CNN is looking at. It achieves so without relying on densely annotated datasets and without forcing concepts to be associated to single computational units. Extensive experimental evaluation on different categories of objects (animals, tools and vehicles) shows the feasibility of our approach. On average, HOLMES explanations include at least two meronyms, and the ablation of a single meronym roughly halves the holonym model confidence. The resulting heatmaps were quantitatively evaluated using the deletion/insertion/preservation curves. All metrics were comparable to those achieved by GradCAM, while offering the advantage of further decomposing the heatmap in human-understandable concepts. In addition, results were largely above chance level, thus highlighting both the relevance of meronyms to object classification, as well as HOLMES ability to capture it. The code is available at https://github.com/FrancesC0de/HOLMES .