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: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...
The paper introduces a Nested Inductive Bias framework that uses a two‑stage diffeomorphic composition to pull back non‑Euclidean target geometries onto symmetric positive definite (SPD) manifolds. This approach allows the construction of curvature‑aligned Riemannian classifiers that respect both matrix constraints and the intrinsic relational geometry of data. Empirical results on kinematic, signal processing, and synthetic benchmarks show that class separability degrades when metric curvature does not match the data distribution, and the authors also propose the Rational Conformal Metric (RCM) for robust vectorized architectures.
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:2609.21039v1 Announce Type: new Abstract: A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matri...
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.
The paper introduces an unsupervised framework that merges manifold learning with rank‑based interpretable graph embeddings to address the Geometric and Interpretability Gaps in visual representation learning. By first analyzing contextual information on the dataset manifold and then producing sparse, self‑explainable embeddings, the method achieves dimensionality reduction while preserving or improving performance in image retrieval and semi‑supervised Graph Convolutional Network classification. Experiments across varied datasets confirm that these context‑aware representations maintain high downstream effectiveness.
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:2609.35436v2 Announce Type: replace Abstract: Recently, deep neural networks on manifold-valued representations have garnered significant attention across various machine learning applications....