Related papers: SPHERE-JEPA: Spherical Prediction with Homogeneous…
In high energy physics, self-supervised learning (SSL) methods have the potential to aid in the creation of machine learning models without the need for labeled datasets for a variety of tasks, including those related to jets -- narrow…
JEPAs often regularize one-view embeddings toward an isotropic Gaussian, implicitly baking Euclidean symmetry into the representation. We show that this is not merely a benign default. For a known structured downstream geometry $H\succ0$,…
Unsupervised 3D scene reconstruction from unstructured image collections remains a fundamental challenge in computer vision, particularly when images originate from multiple unrelated scenes and contain significant visual ambiguity. The…
Self-supervision is often used for pre-training to foster performance on a downstream task by constructing meaningful representations of samples. Self-supervised learning (SSL) generally involves generating different views of the same…
Sparse subspace clustering (SSC), as one of the most successful subspace clustering methods, has achieved notable clustering accuracy in computer vision tasks. However, SSC applies only to vector data in Euclidean space. As such, there is…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We develop a fully intrinsic Bayesian framework for nonparametric regression on the unit sphere based on isotropic Gaussian field priors and the harmonic structure induced by the Laplace-Beltrami operator. Under uniform random design, the…
Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…
Learning efficient representations for decision-making policies is a challenge in imitation learning (IL). Current IL methods require expert demonstrations, which are expensive to collect. Additionally, they are not explicitly trained to…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
This paper investigates the nonparametric regression problem using SVMs with anisotropic Gaussian RBF kernels. Under the assumption that the target functions are resided in certain anisotropic Besov spaces, we establish the almost optimal…
Knowledge graph embedding (KGE) has become a fundamental technique for representation learning on multi-relational data. Many seminal models, such as TransE, operate in an unbounded Euclidean space, which presents inherent limitations in…
In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes.…
Joint-Embedding Predictive Architectures (JEPA) learn view-invariant representations and admit projection-based distribution matching for collapse prevention. Existing approaches regularize representations towards isotropic Gaussian…
The graph embedding (GE) methods have been widely applied for dimensionality reduction of hyperspectral imagery (HSI). However, a major challenge of GE is how to choose proper neighbors for graph construction and explore the spatial…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…
Self-supervised learning (SSL) has made enormous progress and largely narrowed the gap with the supervised ones, where the representation learning is mainly guided by a projection into an embedding space. During the projection, current…
Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…