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arXiv:2607. 22381v1 Announce Type: new Abstract: Curvature notions on graphs, particularly Ollivier-Ricci and Forman, have emerged as powerful tools for addressing fundamental issues in Graph Neural Networks (GNNs) such as oversmoothing and oversquashing, but rely almost exclusively on local edge-level comparisons and therefore fail to certify how information actually propagates over long distances.
arXiv:2606. 26662v1 Announce Type: cross Abstract: Graph Neural Differential Equations (GNDEs) model continuous-time graph dynamics by parameterizing Neural ODE velocity fields with Graph Neural Networks.
The paper introduces SheafDEQ, a subhomogeneous deep-equilibrium architecture that uses adaptive neural-sheaf propagation to allow richer, edge-dependent transformations in implicit graph neural networks while guaranteeing a unique equilibrium. The authors prove that SheafDEQ’s equilibrium is globally reachable from any positive initialization and remains contractive even with bounded communication staleness. Experiments demonstrate that SheafDEQ outperforms fixed-propagation implicit baselines on tasks such as Sums, MNIST Terrain, Coordinates, and community detection, especially as graph connectivity becomes increasingly heterophilic.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
arXiv:2609.14977v1 Announce Type: cross Abstract: Finite element stress fields often exhibit strong local non-smoothness, where stress concentrations near holes, notches, and loading regions induce s...
arXiv:2609.00528v1 Announce Type: new Abstract: We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy su...