arXiv AI
Jul 7
Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks
arXiv:2607. 03798v1 Announce Type: cross Abstract: Symmetry is everywhere in nature and society.
Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs
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arXiv Machine Learning
Sep 1
Rotational Equivariance in Machine Learning: A Comprehensive Tutorial
arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
arXiv Machine Learning
Jun 2
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
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 Machine Learning
Jun 17
Variational autoencoders with latent high-dimensional steady geometric flows for dynamics
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 AI
Jun 10
Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport
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.
Hugging Face Trending Papers
Aug 12
Reducing Symmetry Increase in Equivariant Neural Networks
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv Machine Learning
Aug 13
Reducing Symmetry Increase in Equivariant Neural Networks
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
arXiv Machine Learning
Jul 22
GEqTrain: A Configuration-Driven Framework for Retargeting Equivariant Graph Neural Networks Across 3D Scientific Tasks
arXiv:2607. 19083v1 Announce Type: new Abstract: Equivariant graph neural networks provide a powerful modeling language for three-dimensional scientific data, but their reuse is often limited by implementations tied to specific tasks, outputs, and training regimes.
arXiv Machine Learning
Oct 9
Exact SO(3)-Equivariant Isotropic Kernels for Rotation-Robust Neural Dynamics
The paper introduces the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model designed to predict vector-valued partial differential equations in a rotation‑robust manner. IKNO constructs local interactions from rotation‑invariant scalar quantities and vector directions that transform consistently with the data, ensuring that rotating input positions and velocities results in a correspondingly rotated predicted velocity change. Experiments on three‑dimensional Navier–Stokes dynamics show that IKNO achieves numerical precision consistency, matches the forecasting accuracy of a larger rotation‑aware Tensor Field Network, and outperforms a parameter‑matched graph simulator.
arXiv AI
Jun 3
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
arXiv Machine Learning
Jul 31
Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization
arXiv:2607. 27767v1 Announce Type: new Abstract: Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs.
arXiv AI
Jun 3
Are Common Substructures Transferable? Riemannian Graph Foundation Model with Neural Vector Bundles
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.