arXiv:2608.22874v1 Announce Type: cross Abstract: Neurobiological studies and representation learning have observed that representations of objects belonging to the same category in high-dimensional...
arXiv:2511. 08307v2 Announce Type: replace-cross Abstract: Generative models, such as large language models or text-to-image diffusion models, can generate relevant responses to user-given queries.
arXiv:2409. 18804v3 Announce Type: replace-cross Abstract: Denoising Diffusion Probabilistic Models (DDPM) are powerful state-of-the-art methods used to generate synthetic data from high-dimensional data distributions and are widely used for image, audio, and video generation as well as many more applications in science and beyond.
arXiv:2609.13920v1 Announce Type: cross Abstract: Persistent Gaussian perturbations have been shown to prevent asymptotic oversmoothing in recurrent Graph Neural Networks (GNNs) by ensuring a positiv...
arXiv:2606. 08721v1 Announce Type: new Abstract: Modern neural classifiers commonly rely on linear readouts, yet predictive metrics alone do not characterize the class-wise geometry of the representations on which such readouts operate.
arXiv:2607. 10592v1 Announce Type: new Abstract: Many geometric statistics and manifold learning pipelines routinely produce observations -- such as tangent vectors or local frames -- whose natural home is a varying family of fibers attached to different points of a base manifold, rather than a single shared vector space.
arXiv:2606. 19036v1 Announce Type: new Abstract: Sparse Mixture-of-Experts (SMoE) architectures are now widely deployed in state-of-the-art language and vision models, where conditional routing allows scaling to very large networks.
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
The paper develops a theory for relocating a finite number of compact sets in ℝ^n to arbitrary target domains using diffeomorphisms of ℝ^n. It proves that any such collection can be embedded differentiably into ℝ^{n+1} so that the images become linearly separable. The authors apply this result to show that compact datasets in ℝ^n can be made linearly separable by width‑n deep neural networks with Leaky‑ReLU, ELU, or SELU activations, and that mutually disjoint compact datasets can be separated in ℝ^{n+1} by a width‑(n+1) DNN.
This review discusses how neuroimaging data can be represented as symmetric positive-definite (SPD) matrices and analyzed using the Riemannian geometry of the SPD manifold. It surveys the evolution from modality-specific SPD representations to geometric shallow and deep learning methods, emphasizing how these approaches maintain structural constraints while integrating modern AI techniques. The paper frames SPD matrix learning as a bridge between classical geometric statistics and contemporary machine learning in neuroimaging and brain‑computer interface research.
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:2606. 02047v1 Announce Type: cross Abstract: We introduce Convex Distance Operator Transport (CDOT), the first convex optimal transport framework that aligns distributions across heterogeneous domains by jointly preserving feature correspondence and intrinsic geometric structure.