Link Prediction is a foundational task in Graph Representation Learning, supporting applications like link recommendation, knowledge graph completion and graph generation. Graph Neural Networks have shown the most promising results in this domain and are currently the de facto standard approach to learning from graph data. However, a key distinction exists between Undirected and Directed Link Prediction: the former just predicts the existence of an edge, while the latter must also account for edge directionality and bidirectionality. This translates to Directed Link Prediction (DLP) having three sub-tasks, each defined by how training, validation and test sets are structured. Most research on DLP overlooks this trichotomy, focusing solely on the "existence" sub-task, where training and test sets are random, uncorrelated samples of positive and negative directed edges. Even in the works that recognize the aforementioned trichotomy, models fail to perform well across all three sub-tasks. In this study, we experimentally demonstrate that training Neural DLP (NDLP) models only on the existence sub-task, using methods adapted from Neural Undirected Link Prediction, results in parameter configurations that fail to capture directionality and bidirectionality, even after rebalancing edge classes. To address this, we propose three strategies that handle the three tasks simultaneously. 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 approaches adopt a Multi-Task perspective, either with a Multi-Objective (MO-DLP) or a Scalarized (S-DLP) strategy. Our results show that these methods outperform traditional approaches across multiple datasets and models, achieving equivalent or superior performance in addressing the three DLP sub-tasks.

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.

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 subsymbolic, 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, 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, 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.

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.

Intelligent systems in the real world often use machine learning (ML) algorithms to process various types of data. However, graph data present a unique challenge due to their complexity. Graphs are powerful data representations that can naturally describe many real-world scenarios where the focus is on the connections among numerous entities, such as social networks, knowledge graphs, drug-protein interactions, traffic and communication networks, and more [9]. Unlike text, audio, and images, graphs are embedded in an irregular domain, which makes some essential operations of existing ML algorithms inapplicable [17]. GML applications seek to make predictions, or discover new patterns, using graph-structured data as feature information: for example, one might wish to classify the role of a protein in a biological interaction graph, predict the role of a person in a collaboration network, or recommend new friends in a social network.

Deep Learning (DL) models have become the go-to method for addressing numerous Computer Vision (CV) tasks, such as image classification. Unlike traditional approaches that require manual feature extraction, DL streamlines the development of end-to-end pipelines that seamlessly integrate images as inputs to the learning process, thereby automating feature extraction and enhancing overall efficiency. This automation enables the training of DL models over extensive image datasets, which subsequently leads to enhanced model accuracy. However, the "black-box" nature of DL models presents challenges, as Machine Learning (ML) practitioners often struggle to understand the chain of transformations that a DL model adopts to map an image into the final prediction. This lack of transparency is considered to be hampering the adoption of DL models in real-world scenarios, due to a plethora of reasons: lack of trust from domain experts, impossibility of thorough debugging from practitioners, lack of compliance to legal requirements regarding explainability, and potential systemic bias in the trained model [18]. The research field of eXplainable Artificial Intelligence (XAI) tackles this problem by trying to provide more insights about the inner decision process of ML models [11]. However, most XAI techniques for CV are post-hoc: they are applied on trained ML models, and typically try to correlated portions of the image to the resulting label by means of input perturbation or maskings [29, 31, 33]. A few other approaches try to modify the training procedure itself, hoping to gain more control over the model's internals, while at the same time maintaining competitive classification performances. With this in mind, we remark how the standard DL pipeline for image classification trains the model to learn a mapping from images to labels.

We present a new effective and scalable framework for training GNNs in supervised node classification tasks, given graph-structured data. Our approach increasingly refines the weight update operations on a sequence of path graphs obtained by linearizing random spanning trees extracted from the input network. The path graphs are designed to retain essential topological and node information of the original graph. At the same time, the sparsity of these path graphs enables a much lighter GNN training which, besides scalability, helps mitigate classical training issues, like over-squashing and over-smoothing. We carry out an extensive experimental investigation on a number of real-world graph benchmarks, where we apply our framework to graph convolutional networks, showing simultaneous improvement of both training speed and test accuracy, as compared to well-known baselines.

Most methods for explaining black-box classifiers (e.g., on tabular data, images, or time series) rely on measuring the impact that the removal/perturbation of features has on the model output. This forces the explanation language to match the classifier features space. However, when dealing with graph data, in which the basic features correspond essentially to the adjacency information describing the graph structure (i.e., the edges), this matching between features space and explanation language might not be appropriate. In this regard, we argue that (i) a good explanation method for graph classification should be fully agnostic with respect to the internal representation used by the black-box; and (ii) a good explanation language for graph classification tasks should be represented by higher-order structures, such as motifs. The need to decouple the feature space (edges) from the explanation space (motifs) is thus a major challenge towards developing actionable explanations for graph classification tasks. In this paper we introduce GRAPHSHAP, a Shapley-based approach able to provide motif-based explanations for black-box graph classifiers, assuming no knowledge whatsoever about the model or its training data: the only requirement is that the black-box can be queried at will. Furthermore, we introduce additional auxiliary components such as a synthetic graph dataset generator, algorithms for subgraph mining and ranking, a custom graph convolutional layer, and a kernel to approximate the explanation scores while maintaining linear time complexity. Finally, we test GRAPHSHAP on a real-world brain-network dataset consisting of patients affected by Autism Spectrum Disorder and a control group. Our experiments highlight how the classification provided by a black-box model can be effectively explained by few connectomics patterns.

A great variety of natural and artificial systems can be represented as networks of elementary structural entities coupled by relations between them. The abstraction of such systems as networks helps us understand, predict and optimize their behaviour [1, 2]. In this sense, node and graph embeddings have been established as standard feature representations in many learning tasks for graphs and complex networks [3, 4]. Node embedding methods map each node of a graph into a low-dimensional vector, that can be then used to solve downstream tasks such as edge prediction, network reconstruction and node classification. Node embeddings have proven successful in achieving low-dimensional encoding of static network structures, but many real-world networks are inherently dynamic, with interactions among nodes changing over time [5]. Time-resolved networks are also the support of important dynamical processes, such as epidemic or rumor spreading, cascading failures, consensus formation, etc. [6] Time-resolved node embeddings have been shown to yield improved performance for predicting the outcome of dynamical processes over networks, such as information diffusion and disease spreading [7]. In this paper we propose a representation learning model that performs an implicit tensor factorization on different higher-order representations of time-varying graphs.