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.
By Rachid Caich, Yassine Abbahaddou
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.
By Mingsong Yan, Zhida Wang, Sui Tang
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.
By R\'emi Bourgerie, \v{S}ar\={u}nas Girdzijauskas, Viktoria Fodor
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.
By Dennis Chemnitz, Maximilian Engel, Christian Kuehn, Sara-Viola Kuntz
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...
By Chen Zeng, Qiao Wang
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...
By Pingbing Ming, Han Wang
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
By Jose Marie Antonio Mi\~noza, Erika Fille T. Legara, Christopher P. Monterola
arXiv:2509. 12484v2 Announce Type: replace Abstract: We propose a novel neural network architecture, called Non-Trainable Modification (NTM), for computing Nash equilibria in stochastic differential games (SDGs) on graphs.
By Ruimeng Hu, Jihao Long, Haosheng Zhou
arXiv:2607. 11289v1 Announce Type: cross Abstract: Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs.
By Ahmed Boughammoura
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.
By Md Sadek Hossain Asif, Tanzila Khan, Md. Mosaddek Khan
The paper presents a new formulation of the Schr"odinger bridge problem on graphs that incorporates state costs via a Feynman‑Kac tilt, eliminating the need for learned control or temporal‑difference penalties. The resulting cost‑augmented bridge is solved exactly by alternating two endpoint rescalings, each requiring only a sparse matrix‑exponential application, and the method scales linearly with network size. Experiments on a protein‑folding model and a large road‑network demonstrate that the exact bridge reduces expected energy barriers and matches target distributions within sampling error.
By Akshay Balsubramani
arXiv:2512.12767v2 Announce Type: replace-cross
Abstract: Training recurrent neuronal networks consisting of excitatory (E) and inhibitory (I) units with additive noise for working memory computation...
By Thiparat Chotibut, Oleg Evnin, Weerawit Horinouchi