The paper introduces ONDA, a graph learning framework that uses operator‑valued information waves to enable effective long‑range propagation in graph neural networks. ONDA evolves stalk‑valued representations through second‑order dynamics governed by learned sheaf transport operators, combining wave‑like propagation with expressive local geometry. Experiments on challenging benchmarks show that ONDA consistently outperforms scalar wave propagation, diffusive sheaf baselines, and state‑of‑the‑art models, demonstrating the advantage of coupling wave dynamics with matrix‑valued transport.
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.
The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.
arXiv:2608.29892v1 Announce Type: new Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv:2608.30152v1 Announce Type: new Abstract: Graph positional encodings are widely used in graph neural networks and graph Transformers, yet it remains unclear when the code itself can identify no...
arXiv:2607. 21607v1 Announce Type: cross Abstract: Graph Neural Networks propagate information through local message passing, but the graph topologies themselves can silently prevent any amount of training from solving long-range tasks.
Deep Neural Sheaf Diffusion (DNSD) is a new graph neural network architecture that replaces the sheaf Laplacian with a sheaf adjacency operator to keep informative signals across many layers. It also uses normalization, odd nonlinearities, and gating, and replaces scalar attention with matrix-valued edge functions. Experiments show DNSD outperforms existing GNNs and Neural Sheaf Diffusion on both synthetic long‑range and real‑world graph benchmarks, achieving up to 30 percentage‑point gains in accuracy.
arXiv:2606. 10071v1 Announce Type: cross Abstract: We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework that equips each node with a time-varying orthogonal frame and compares node states only after explicit transport between local coordinate systems.
The paper introduces a graph-recurrent neural network (GRNN) that learns emergent collective dynamics directly from trajectory data, without requiring explicit microscopic equations of motion. The GRNN combines gated recurrent memory with graph message passing, allowing local hidden states to capture information beyond instantaneous observables and to propagate spatially. The authors validate the approach on the semiclassical Holstein model, successfully reproducing temporal and spatial correlations and dynamical scaling during domain coarsening of charge-density-wave order.
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.
arXiv:2607. 27891v1 Announce Type: cross Abstract: Temporal graph learning is commonly organized around the evolution of node states or the encoding of interaction histories.
arXiv:2608. 09031v1 Announce Type: new Abstract: Graph neural networks typically propagate information through repeated message-passing layers, coupling the distance over which information travels with the number of nonlinear transformations applied.