Caterina Graziani

Silvia Beddar-Wiesing, Giuseppe Alessio D'Inverno, Caterina Graziani et al.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.

Michelangelo Diligenti, Francesco Giannini, Stefano Fioravanti et al.

Knowledge Graph Embeddings (KGE) have become a quite popular class of models specifically devised to deal with ontologies and graph structure data, as they can implicitly encode statistical dependencies between entities and relations in a latent space. KGE techniques are particularly effective for the biomedical domain, where it is quite common to deal with large knowledge graphs underlying complex interactions between biological and chemical objects. Recently in the literature, the PharmKG dataset has been proposed as one of the most challenging knowledge graph biomedical benchmark, with hundreds of thousands of relational facts between genes, diseases and chemicals. Despite KGEs can scale to very large relational domains, they generally fail at representing more complex relational dependencies between facts, like logic rules, which may be fundamental in complex experimental settings. In this paper, we exploit logic rules to enhance the embedding representations of KGEs on the PharmKG dataset. To this end, we adopt Relational Reasoning Network (R2N), a recently proposed neural-symbolic approach showing promising results on knowledge graph completion tasks. An R2N uses the available logic rules to build a neural architecture that reasons over KGE latent representations. In the experiments, we show that our approach is able to significantly improve the current state-of-the-art on the PharmKG dataset. Finally, we provide an ablation study to experimentally compare the effect of alternative sets of rules according to different selection criteria and varying the number of considered rules.

Giang Pham, Rebecca Finetti, Caterina Graziani et al.

Alkaptonuria (AKU) is an ultra-rare autosomal recessive metabolic disorder caused by mutations in the HGD (Homogentisate 1,2-Dioxygenase) gene, leading to a pathological accumulation of homogentisic acid (HGA) in body fluids and tissues. This leads to systemic manifestations, including premature spondyloarthropathy, renal and prostatic stones, and cardiovascular complications. Being ultra-rare, the amount of data related to the disease is limited, both in terms of clinical data and literature. Knowledge graphs (KGs) can help connect the limited knowledge about the disease (basic mechanisms, manifestations and existing therapies) with other knowledge; however, AKU is frequently underrepresented or entirely absent in existing biomedical KGs. In this work, we apply a text-mining methodology based on PubTator3 for large-scale extraction of biomedical relations. We construct two KGs of different sizes, validate them using existing biochemical knowledge and use them to extract genes, diseases and therapies possibly related to AKU. This computational framework reveals the systemic interactions of the disease, its comorbidities, and potential therapeutic targets, demonstrating the efficacy of our approach in analyzing rare metabolic disorders.

Martin Carrasco, Caio F. Deberaldini Netto, Vahan A. Martirosyan et al.

The expressive power of graph neural networks (GNNs) is typically understood through their correspondence with graph isomorphism tests such as the Weisfeiler-Leman (WL) hierarchy. While more expressive GNNs can distinguish a richer set of graphs, they are also observed to suffer from higher generalization error. This work provides a theoretical explanation for this trade-off by linking expressivity and generalization through the lens of coloring algorithms. Specifically, we show that the number of equivalence classes induced by WL colorings directly bounds the GNNs Rademacher complexity -- a key data-dependent measure of generalization. Our analysis reveals that greater expressivity leads to higher complexity and thus weaker generalization guarantees. Furthermore, we prove that the Rademacher complexity is stable under perturbations in the color counts across different samples, ensuring robustness to sampling variability across datasets. Importantly, our framework is not restricted to message-passing GNNs or 1-WL, but extends to arbitrary GNN architectures and expressivity measures that partition graphs into equivalence classes. These results unify the study of expressivity and generalization in GNNs, providing a principled understanding of why increasing expressive power often comes at the cost of generalization.