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:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.
arXiv:2607. 03798v1 Announce Type: cross Abstract: Symmetry is everywhere in nature and society.
arXiv:2608. 10016v1 Announce Type: cross Abstract: Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, sensing modalities, model architectures, latent dimensionalities, and local learning objectives.
arXiv:2510. 14217v2 Announce Type: replace Abstract: The spectral properties of feature embeddings offer critical insights into model generalization and representation quality.
arXiv:2606. 03270v1 Announce Type: cross Abstract: Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs.
arXiv:2601. 16622v2 Announce Type: replace-cross Abstract: Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems.
Foundation models have sparked a revolution via a pretraining-adaptation paradigm, with recent efforts extending this success to graphs. Unlike other modalities, graphs contain rich structural patterns, yet their structural transferability remains poorly understood.
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.
arXiv:2509. 22468v2 Announce Type: replace-cross Abstract: High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce.
arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.
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.
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.