Graph neural networks beyond limits: functional expansions and cognitive enrichment

Graph Neural Networks (GNNs) are widely used in domains such as recommendation systems, bioinformatics, and computer vision, as they can model non-Euclidean structures and relational data. Despite this success, many architectures still face issues like over-smoothing, sensitivity to noise or missing data, and a limited ability to handle dynamic graphs. This thesis addresses these challenges by proposing a set of architectural innovations aimed at enhancing the expressiveness and robustness of GNNs in realistic scenarios. First, we introduce a new family of models based on a non-linear expansion of node features, inspired by the Kolmogorov-Arnold representation theorem. This expansion is applied in a differentiable way before the message passing phase, allowing the model to work with a more expressive feature space. The result is an improvement in both robustness to noise and resistance to over-smoothing, without increasing the architectural complexity of the GNN itself. In the second part, we address the problem of homogeneous node representations by introducing a GNN architecture that incorporates temporal, geospatial, and cognitive information through a structured concatenation strategy. This enables the network to adjust its predictions to user behavior, environmental context, or domain knowledge, improving personalization and accuracy. The proposed approaches are evaluated on benchmark graph learning datasets covering different domains, including citation, biological, and social network data, as well as on mobility prediction scenarios. Results demonstrate improvements over existing graph learning approaches, supporting the effectiveness of the proposed methods across different application domains.