arXiv:2607. 08987v1 Announce Type: new Abstract: Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures.
arXiv:2608. 08704v1 Announce Type: cross Abstract: Kernel spectral clustering with a single bandwidth can be inadequate for data exhibiting multiple characteristic pairwise-distance scales, a problem particularly prevalent in the high-dimensional regime.
arXiv:2607. 00556v1 Announce Type: cross Abstract: While recent advancements like the Poincar\'e ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold.
arXiv:2410. 09737v2 Announce Type: replace Abstract: A popular way to improve the expressive power of graph neural networks (GNNs) is to use Laplacian eigenvectors as additional node features, since they can serve both as structural identifiers and global coordinates of nodes.
arXiv:2607. 08783v1 Announce Type: cross Abstract: Manifold-valued measurements are prevalent in various machine learning tasks.
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
arXiv:2607. 25295v2 Announce Type: replace Abstract: Tensorial multi-view clustering (TMC) has achieved strong performance due to its ability to capture high-order correlations across multiple views.
While recent advancements like the Poincaré ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold. Furthermore, standard hyperbolic networks treat spatial transformations of the same object as distinct hierarchical concepts, leading to redundant parameter usage and vanishing signals.
arXiv:2510. 02308v2 Announce Type: replace Abstract: Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis.
arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
arXiv:2607. 19305v2 Announce Type: replace-cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
arXiv:2607. 19305v1 Announce Type: cross Abstract: Deep neural networks on manifold-valued representations have attracted growing interest, but many basic components remain tied to specific manifolds, rely on Euclidean approximations, or require costly and numerically fragile geometric operations.
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.