Deploying Graph Neural Networks in safety-critical domains is hindered by their lack of interpretability, despite their state-of-the-art performance across numerous domains. Self-explainable architectures grounded in formal logic have emerged as a promising path toward transparency, but existing approaches are confined to unary predicates, making them blind to relational properties between nodes and the information carried by edges. We introduce PLEX (Polyadic Logic EXplainable GNN), a self-explainable GNN built upon Polyadic Graded Modal Logic, designed to overcome these limitations. PLEX adopts a hierarchical dual-logic architecture that learns ternary predicates, enabling explicit modeling of edge attributes and pairwise node interactions, capabilities entirely absent in monadic predecessors. We evaluate PLEX across graph classification, node classification, and link prediction benchmarks, where it matches the predictive accuracy of black-box models and consistently surpasses monadic logic-based models. Moreover, the richer logical language does not come at the cost of interpretability: we show that greater expressivity can actually reduce the number of logical rules needed, yielding models that are simultaneously more accurate and more transparent.

Co-clustering refers to the simultaneous clustering of rows and columns in a data matrix, uncovering joint patterns between two distinct sets, such as documents and terms or users and products. Traditional co-clustering algorithms typically rely on discrete optimization techniques based on enumeration, which can limit both scalability and flexibility. In this paper, we introduce a differentiable programming approach to co-clustering that enables the continuous optimization of co-partitions using graph neural networks. Our method is grounded in an associative co-clustering quality measure that is independent of the number of clusters and dynamically adjusts this parameter by jointly considering both partitions. By leveraging automatic differentiation and graph neural networks, our approach scales to very large datasets while maintaining high-quality co-cluster structures. We evaluate our method using different types of graph neural networks and initialization strategies. Furthermore, when compared with recent state-of-the-art methods for co-clustering and graph clustering, our approach achieves competitive or superior results in terms of accuracy. Most importantly, it is the only algorithm that successfully completes on the largest benchmark dataset.

Graph Neural Networks achieve strong performance across diverse graph-based tasks, but their black-box nature remains a major obstacle in domains where interpretability is crucial. Prototype-based self-explainable GNNs mitigate this issue by grounding predictions in comparison with learned patterns. However, existing methods either restrict prototypes to training subgraphs, thereby limiting expressiveness, or learn latent prototypes that lack interpretable counterparts in graph space. We introduce a hybrid self-explainable graph classifier that integrates optimal transport, prototype grounding, and symbolic logic to produce faithful and human-readable explanations. We learn prototypes as point clouds in the embedding space and compare them to input graphs using partial optimal transport. To recover semantic meaning in graph space, each prototype point is anchored to a representative ego-network extracted from the training graphs. These similarity scores are then processed by a transparent logic layer that distills the model’s decisions into human-interpretable logical rules. Experiments on molecular and synthetic benchmarks show that our method achieves competitive predictive performance while producing interpretable, example-based explanations grounded in real graph structures.

Multi-Target Prediction (MTP) aims to predict a class for multiple targets from a single input instance. In this paper, we focus on the general ordinal outputs setting, where targets may have different numbers of ordered classes. This scenario is under-explored yet critical for human-centered applications such as educational assessment or psychological profiling. In these domains, targets span multiple aspects of an evaluation, and capturing latent relationships between seemingly independent targets is essential for deriving meaningful user profiles. Beyond prediction accuracy, it is crucial that the resulting profiles are interpretable, as these applications directly impact humans. We introduce IMPACT, a novel method that extends existing binary MTP frameworks (such as CD-BPR) to the multi-class domain through a newly designed loss function. Rooted in a Bayesian modeling framework, IMPACT jointly embeds user profiles and targets within a shared vector space, providing theoretical rigor while explicitly optimizing for both predictive accuracy and interpretability. Furthermore, IMPACT offers a geometric interpretation of the embedding learning dynamics, giving insight into how the model captures relationships between users and targets and providing an intuitive understanding of profile formation in the latent space. Experimental results show that IMPACT outperforms state-of-the-art approaches in terms of profile interpretability while maintaining competitive prediction accuracy. An ablation study highlights the contribution of each component, demonstrating the benefits of extending the framework to multiple ordered classes, the Bayesian formulation, and the geometric interpretability in enhancing both performance and transparency.

Document Visual Question Answering (DocVQA) often leverages Retrieval-Augmented Generation (RAG), where late-interaction encoders are commonly used to identify document pages relevant to a user query, before answer generation by a Large Vision-Language Model (LVLM). Existing approaches typically retrieve a fixed top-k number of pages regardless of query complexity, which increases LVLM latency and may degrade answer accuracy. We introduce ViSAR (Visual Semantic Activation Retrieval), a training-free adaptive-k retrieval method for late-interaction visual document retrieval. ViSAR operates directly in the embedding space to construct a query-conditioned page-level similarity matrix that highlights query-relevant semantics and dynamically determines the number of pages to retrieve. Across multiple encoders and LVLMs, ViSAR retrieves compact, query-adapted page sets that reduce RAG latency by up to 58.7%, while maintaining or improving answer accuracy compared with fixed top-k and adaptive retrieval heuristics. Furthermore, we show that the similarity matrix structure correlates with answer accuracy, suggesting future directions for retrieval quality-aware document understanding.

Network science has been a rapidly evolving field to study systems made of interactions between entities. Studying the structure of such networks reveals indeed the underlying mechanisms of these systems, and has been proven successful in many domains, such as sociology, biology, or geography. Recently, connections between network science and signal processing have emerged, making the use of a wide variety of tools possible to study networks. In this chapter, a focus is made on a methodology introduced to transform a graph into a collection of signals, using a multidimensional scaling technique: by projecting a distance matrix representing relations between vertices of the graph as points in a Euclidean space, it is possible to interpret coordinates of vertices in this space as signals, and take advantage of this dual representation to develop new tools for the study of networks. Deeper considerations of this methodology are proposed, by strengthening the connections between the obtained signals and the common graph structures. A robust inverse transformation method is next described, taking into account possible changes in the signals. Establishing a robust duality between graphs and signals opens up new perspectives, as classical signal processing tools, such as spectral analysis or filtering, are made available for the study of the structure of networks.

Graph neural networks (GNN) are complex Machine Learning models that solve various graph tasks such as node classification, graph classification or link prediction. Due to their complexity, they are treated as black boxes, and how they perform their prediction is difficult to understand. In recent years, explainers for Machine Learning models have been introduced, among them methods based on game theory. These methods try to explain the decision by computing the importance of the features by considering them as players of a cooperative game who cooperate in order to make the decision. A player's impact on the decision is measured by his marginal contribution to a coalition of players. Different measures built on this principle exist, and they differ in the axioms they satisfy. In this article, we consider two such measures that we adapt to explain GNN.

Statistical anomaly detection is critical across various domains, including healthcare, finance, industry, and cybersecurity. While supervised methods often achieve high performance, the limited availability of labeled data requires effective unsupervised techniques. In this paper, we introduce Dataset Sampling Iterative Learning (DSIL), a novel iterative learning framework for unsu-pervised anomaly detection leveraging generative modeling with diffusion. Our approach progressively refines an unlabeled dataset by identifying and removing anomalies, effectively approximating a semi-supervised setup. We demonstrate the efficiency of our framework with Diffusion Time Estimation (DTE). Furthermore, it enables better explainability through a novel approach of noised-feature discovery. Extensive experiments against unsupervised methods on both synthetic and real-world datasets demonstrate improved state-of-the-art performance. Finally, we suggest a novel usage of existing metrics to evaluate the explainability of anomaly detection models.

Graph Neural Networks (GNNs) have demonstrated strong performance in molecular interaction prediction, but their interpretability remains limited, especially in domain-specific applications like ligand-receptor modeling. This paper presents a model-agnostic explainer for GNN-CLS, a specialized GNN model designed to predict interactions between molecules and olfactory receptor proteins. The proposed method uses cooperative game theory to identify influential molecular substructures and receptor sequence regions, offering faithful and theoretically grounded explanations of model predictions. This approach enhances transparency by revealing which features drive predictive outcomes, helping bridge the gap between model performance and chemical insight. The contributions include a formal framework for relevance attribution and interaction analysis, positioning this work at the intersection of explainable AI and computational chemistry.

We address the challenge of identifying the most influential graph structures in the decisions of Graph Neural Networks (GNNs). To tackle this, we propose a novel approach for evaluating the importance of subgraphs in GNN decisions, with a particular emphasis on calculating Shapley values. Unlike existing methods that impose rigid, predefined constraints on subgraph shapes (e.g., egographs or individual nodes), our approach remains flexible, accommodating arbitrary subgraph structures. Our method begins by analyzing activation rules within the representation spaces generated by the GNN, followed by computing Shapley values for these rules to quantify their contributions to model decisions. Using these Shapley values, we produce both instance-level and model-level explanations, offering deeper insights into the reasoning processes of GNNs. Extensive empirical studies across diverse datasets and comparisons with state-of-the-art methods highlight the effectiveness of our approach in delivering interpretable and robust explanations.

Graphs are complex, non-Euclidean structures that require specialized models, such as Graph Neural Networks (GNNs), Graph Transformers, or kernel-based approaches, to effectively capture their relational patterns. This inherent complexity makes explaining GNNs decisions particularly challenging. Most existing explainable AI (XAI) methods for GNNs focus on identifying influential nodes or extracting subgraphs that highlight relevant motifs. However, these approaches often fall short of clarifying how such elements contribute to the final prediction. To overcome this limitation, logic-based explanations aim to derive explicit logical rules that reflect the model's decision-making process. Current logic-based methods are limited to post-hoc analyzes and are predominantly applied to graph classification, leaving a significant gap in intrinsically explainable GNN architectures. In this paper, we explore the potential of integrating logic reasoning directly into graph learning. We introduce LogiX-GIN, a novel, self-explainable GNN architecture that incorporates logic layers to produce interpretable logical rules as part of the learning process. Unlike post-hoc methods, LogiX-GIN provides faithful, transparent, and inherently interpretable explanations aligned with the model's internal computations. We evaluate LogiX-GIN across several graph-based tasks and show that it achieves competitive predictive performance while delivering clear, logic-based insights into its decision-making process.

The ever-increasing evolution of Deep Learning methods has enabled their use in many areas, including cybersecurity. With the exponential growth in the volume of data circulating in computer networks, their security is a paramount necessity. Nowadays, network security is mainly pursued using preventive techniques but also by detecting intrusions as soon as possible, when they occur. Different types of Machine Learning and Deep Leaning models have been recently studied for network intrusion detection, but surprisingly, although Network Intrusion Detection Systems (NIDSs) scrutinize flow data exchanges on a network, graph-based models have been little explored so far. We propose in this article to consider the relevance of Graph Neural Network (GNNs) to detect intrusions and also to explain them. For this purpose, we adapt the GNNExplainer method, that is, the pioneer method for explaining GNN decisions, to edge-level classification models.

We study the real economic activity in the Bitcoin blockchain that involves transactions from/to retail users rather than between organizations such as marketplaces, exchanges, or other services. We first introduce a heuristic method to classify Bitcoin players into three main categories: Frequent Receivers (FR), Neighbors of FR, and Others. We show that most real transactions involve Frequent Receivers, representing a small fraction of the total value exchanged according to the blockchain, but a significant fraction of all payments, raising concerns about the centralization of the Bitcoin ecosystem. We also conduct a weekly pattern analysis of activity, providing insights into the geographical location of Bitcoin users and allowing us to quantify the bias of a well-known dataset for actor identification.

Most post-hoc explainability methods for graph classification analyze the model's internal representations rather than explicitly capturing its reasoning process. These approaches typically rely on perturbations, gradients, or optimization techniques to infer important features but do not approximate the decision-making function itself. In this paper, we propose a novel approach that directly models the GNN's decision function using a Transparent Explainable Logic Layer (TELL). This logic-based approximation enables both instance-level and global-level explanations, offering insights into how node embeddings contribute to predictions. Unlike conventional methods, our approach derives explanations that are structurally aligned with the model's decision process rather than being externally imposed. Through experiments on synthetic and real-world graph classification tasks, we show that our method produces faithful, sparse, and stable explanations, outperforming existing techniques.

Pattern mining addresses the challenge of automatically identifying interpretable and discriminative patterns within data. Recent approaches, leveraging differentiable approach through neural autoencoder with class recovery, have achieved encouraging results but tend to fall short as the magnitude of the noise and the number of underlying features increase in the data. Empirically, one can observe that the number of discovered patterns tend to be limited in these challenging contexts. In this article, we present a differentiable binary model that integrates a new regularization technique to enhance pattern coverage. Besides, we introduce an innovative pattern decoding strategy taking advantage of non-negative matrix factorization (NMF), extending beyond conventional thresholding methods prevalent in existing approaches. Experiments on four real-world datasets exhibit superior performances of DiffVersify in terms of the ROC-AUC metric. On synthetic data, we observe an increase in the similarity between the discovered patterns and the ground truth. Finally, using several metrics to finely evaluate the quality of the patterns in regard to the data, we show the global effectiveness of the approach.

Explainable AI seeks to unveil the intricacies of black box models through post-hoc strategies or self-interpretable models. In this paper, we tackle the problem of building layers that are intrinsically explainable through logic rules. In particular, we address current state-of-the-art methods’ lack of fidelity and expressivity by introducing a transparent explainable logic layer (TELL). We propose to constrain a feed-forward layer with positive weights, which, combined with particular activation functions, offer the possibility of a direct translation into logic rules. Additionally, this approach overcomes the limitations of previous models, linked to their applicability to binary data only, by proposing a new way to automatically threshold real values and incorporate the obtained predicates into logic rules. We show that, compared to state-of-the-art, TELL achieves similar classification performances and, at the same time, provides higher explanatory power, measured by the agreement between models’ outputs and the activation of the logic explanations. In addition, TELL offers a broader spectrum of applications thanks to the possibility of its use on real data.

In the field of education, the automatic assessment of student profiles has become a crucial objective, driven by the rapid expansion of online tutoring systems and computerized adaptive testing. These technologies aim to democratize education and enhance student assessment by providing detailed insights into student profiles, which are essential for accurately predicting the outcomes of exercises, such as solving various types of mathematical equations. We aim to develop a model capable of predicting responses to a large set of questions within the Multi-Target Prediction framework while ensuring that this model is explainable, allowing us to quantify student performance in specific knowledge areas. Existing cognitive diagnosis algorithms often struggle to meet the dual requirement of accurately predicting exercise outcomes and maintaining interpretability. To address this challenge, we propose an alternative to the complexity of current advanced machine learning models. Instead, we introduce a direct yet highly effective Bayesian Personalized Ranking algorithm, called CD-BPR, which incorporates interpretability as a core learning objective. Extensive experiments demonstrate that CD-BPR not only performs better in predicting exercise outcomes but also provides superior interpretability of estimated student profiles, thus fulfilling both key requirements.

Graphs are widely used for describing systems made of many interacting components and for understanding the structure of their interactions. Various statistical models exist, which describe this structure as the result of a combination of constraints and randomness. In this article, we introduce edge probability prequential inference, a new approach to perform model selection, which relies on probability distributions on edge ensembles. From a theoretical point of view, we show that this methodology provides a more consistent ground for statistical inference with respect to existing techniques, due to the fact that it relies on multiple realizations of the random variable. It also provides better guarantees against overfitting, by making it possible to lower the number of parameters of the model below the number of observations. Experimentally, we illustrate the benefits of this methodology in two situations: to infer the partition of a stochastic blockmodel and to identify the most relevant model for a given graph between the stochastic blockmodel and the configuration model.