arXiv:2602. 08785v2 Announce Type: replace Abstract: Generalization and approximation capabilities of message passing graph neural networks (MPNNs) are often studied by defining a compact metric on a space of input graphs under which MPNNs are equicontinuous.
arXiv:2407. 02025v5 Announce Type: replace-cross Abstract: Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions.
arXiv:2607. 26699v1 Announce Type: new Abstract: We investigate message-passing graph neural networks with random node features.
arXiv:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.
We investigate message-passing graph neural networks with random node features. Random node features are known to enhance the expressiveness of graph neural networks (GNNs) both theoretically and empirically.
arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.
arXiv:2608. 16097v1 Announce Type: new Abstract: Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences.
arXiv:2412. 19419v2 Announce Type: replace-cross Abstract: Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges.
arXiv:2606. 26873v1 Announce Type: cross Abstract: Graphs provide a natural language for relational data in chemistry, biology and optimisation.
arXiv:2605. 21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing.
arXiv:2601. 23207v2 Announce Type: replace-cross Abstract: Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge.
arXiv:2511. 02003v2 Announce Type: replace Abstract: We present the bulk--boundary decomposition as a new framework for understanding the training dynamics of deep neural networks.