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Predictive tasks on relational databases are critical in real-world applications spanning e-commerce, healthcare, and social media. To address these tasks effectively, Relational Deep Learning (RDL) encodes relational data as graphs, enabling Graph Neural Networks (GNNs) to exploit relational structures for improved predictions. However, existing RDL methods often overlook the intrinsic structural properties of the graphs built from relational databases, leading to modeling inefficiencies, particularly in handling many-tomany relationships. Here we introduce RELGNN, a novel GNN framework specifically designed to leverage the unique structural characteristics of the graphs built from relational databases. At the core of our approach is the introduction of atomic routes, which are simple paths that enable direct single-hop interactions between the source and destination nodes. Building upon these atomic routes, RELGNN designs new composite message passing and graph attention mechanisms that reduce redundancy, highlight key signals, and enhance predictive accuracy. RELGNN is evaluated on 30 diverse real-world tasks from RELBENCH (Fey et al., 2024), and achieves state-of-the-art performance on the vast majority of tasks, with improvements of up to 25%. 

Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes, in the form of features or time-series data. Modern representation learning techniques employ both the connectivity and attribute information of the nodes to produce embeddings in an unsupervised manner. In this context, deriving embeddings that preserve the geometry of the network and the attribute vectors would be highly desirable, as they would reflect both the topological neighborhood structure and proximity in feature space. While this is fairly straightforward to maintain when only observing the connectivity or attribute information of the network, preserving the geometry of both types of information is challenging. A novel tensor factorization approach for node embedding in attributed networks is proposed in this paper, that preserves the distances of both the connections and the attributes. Furthermore, an effective and lightweight algorithm is developed to tackle the learning task and judicious experiments with multiple state-of-the-art baselines suggest that the proposed algorithm offers significant performance improvements in downstream tasks. 

Knowledge graphs (KGs) are powerful tools that codify relational behaviour between entities in knowledge bases. KGs can simultaneously model many different types of subject-predicate-object and higher-order relations. As such, they offer a flexible modeling framework that has been applied to many areas, including biology and pharmacology – most recently, in the fight against COVID-19. The flexibility of KG modeling is both a blessing and a challenge from the learning point of view. In this paper we propose a novel coupled tensor-matrix framework for KG embedding. We leverage tensor factorization tools to learn concise representations of entities and relations in knowledge bases and employ these representations to perform drug repurposing for COVID-19. Our proposed framework is principled, elegant, and achieves 100% improvement over the best baseline in the COVID-19 drug repurposing task using a recently developed biological KG. 

Tensor decomposition models have proven to be effective analysis tools in various applications, including signal processing, machine learning, and communications, to name a few. Canonical polyadic decomposition (CPD) is a very popular model, which decomposes a higher order tensor signal into a sum of rank 1 terms. However, when the tensor size gets big, computing the CPD becomes a lot more challenging. Previous works proposed using random (generalized) tensor sampling or compression to alleviate this challenge. In this work, we propose using a regular tensor sampling framework instead. We show that by appropriately selecting the sampling mechanism, we can simultaneously control memory and computational complexity, while guaranteeing identifiability at the same time. Numerical experiments with synthetic and real data showcase the effectiveness of our approach.