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:2511. 11046v3 Announce Type: replace-cross Abstract: Graph neural networks (GNNs) have become an indispensable tool for analyzing relational data.
arXiv:2502. 16533v3 Announce Type: replace-cross Abstract: Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing.
arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.
The paper introduces Topological Attention (Top‑A), a multi‑head attention mechanism that extends standard diagonal edge maps by allowing off‑diagonal, edge‑conditioned communication across attention heads. By isolating the transport primitive through quiver representations, the authors show that standard multi‑head attention only implements diagonal edge maps, whereas Top‑A learns additional cross‑head routes while preserving the original same‑head paths. Experiments on relational reasoning, heterogeneous graph learning, and algorithmic reasoning demonstrate that cross‑head transport is most beneficial when tasks require interaction‑dependent transformations, whereas heterophily alone does not provide a systematic advantage.
The paper introduces RGC‑Net, a Reservoir‑Based Graph Convolutional Network that combines fixed‑random reservoir dynamics with a structured convolutional framework for graph learning. It addresses limitations of existing reservoir‑based GNNs by adding a leaky integrator for better feature retention and a robust, adaptable architecture for graph classification and generation. Experiments demonstrate state‑of‑the‑art performance on classification and generative tasks, including dynamic brain connectivity, with faster convergence and reduced over‑smoothing.
arXiv:2608. 02128v1 Announce Type: new Abstract: Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers.
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
arXiv:2608. 04381v1 Announce Type: cross Abstract: Self-supervised learning on graphs is largely shaped by contrastive methods that depend on carefully designed augmentations, and by generative methods that reconstruct node attributes in the input space.
The paper introduces an asynchronous message‑passing framework for Graph Neural Networks to mitigate oversquashing, a problem where distant nodes cannot effectively communicate due to structural bottlenecks. Unlike conventional synchronous updates, the method updates a centrality‑guided batch of nodes at each layer, allowing information to propagate sequentially and reducing the need for increased channel capacity. Experiments on six standard and two long‑range graph classification benchmarks show notable performance gains, including 5 % improvement on REDDIT‑BINARY and 4 % on Peptides‑struct.
Training Graph Neural Networks on large graphs is challenged by the memory cost of storing all node representations across layers. We show that several existing scalable approaches can be written as structured modifications of the GNN propagation matrix, providing a unified perspective that exposes their respective limitations.
arXiv:2607. 17570v1 Announce Type: new Abstract: Graph foundation models (GFMs) with global attention are increasingly used to represent mixed-integer linear programs (MILPs), aiming to capture structure beyond the locality of standard graph neural networks.
arXiv:2609.06668v1 Announce Type: new Abstract: Multimodal graphs couple node attributes in different modalities, such as text and images, with relational structure, enabling topological structure an...