arXiv:2607. 19514v1 Announce Type: new Abstract: Geometric architectures are often justified by internal mechanisms such as rotations, yet task performance alone cannot show whether those mechanisms drive predictions.
arXiv:2608. 02558v1 Announce Type: new Abstract: Sheaf Neural Networks (SNNs) generalize message passing by replacing scalar edge weights of standard Graph Neural Networks (GNNs) with learnable, edge-dependent restriction maps between node stalks.
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: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.
arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv:2601. 21207v4 Announce Type: replace-cross Abstract: Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures.
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:2607. 09967v1 Announce Type: cross Abstract: Many neural networks operations have a multiplicative nature rather than additive: halving or doubling a norm are analogous relatively but require unequal optimization distances when taking linear steps.
Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn graph representations. However, their discriminative...
arXiv:2609.17061v1 Announce Type: cross Abstract: Message-passing Graph Neural Networks (GNNs) iteratively propagate and aggregate local neighborhood information followed by global readout to learn g...
The study investigates how to automatically predict the build orientation for selective laser melting (SLM) of dental parts using supervised machine learning. Researchers trained two different neural network backbones—ResNet‑50 on multi‑view images and PointNeXt‑S on point clouds—on about 2,400 patient‑specific parts, evaluating 13 different ways to represent the up‑axis (six classical SO(3) parameterizations and seven unit‑sphere representations). They found that applying test‑time augmentation (TTA) over 21 known rotations consistently reduced angular error, with the octahedral map achieving the lowest mean error (10.6°) on ResNet‑50, while direct S² representations performed best overall but may be influenced by label noise.
arXiv:2608. 06031v1 Announce Type: new Abstract: Dynamic graph prompting freezes a pre-trained temporal backbone and adapts it to label-scarce downstream tasks using lightweight prompts.