Related papers: SPHERE-JEPA: Spherical Prediction with Homogeneous…
Large Language Models (LLMs) obey consistent scaling laws -- empirical power-law fits that predict how loss decreases with compute, data, and parameters. While predictive, these laws are descriptive rather than prescriptive: they…
This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We…
We develop a unified framework for distributed inference, semantic communication, and exploration in spatial networks by integrating stochastic geometry with information geometry - a direction that has not been explored in prior literature.…
Semi-supervised learning (SSL) is a machine learning methodology that leverages unlabeled data in conjunction with a limited amount of labeled data. Although SSL has been applied in various applications and its effectiveness has been…
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and…
This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed…
Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of scientific and engineering fields. Numerous methods exist for distributional comparison but kernel Stein's method has…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
Self-supervised learning (SSL) has emerged as a powerful strategy for representation learning under limited annotation regimes, yet its effectiveness remains highly sensitive to many factors, especially the nature of the target task. In…
This paper establishes error bounds for the convergence of a piecewise linear approximation of the constrained optimal smoothing problem posed in a reproducing kernel Hilbert space (RKHS). This problem can be reformulated as a Bayesian…
We study the complexity of smoothed agnostic learning, recently introduced by~\cite{CKKMS24}, in which the learner competes with the best classifier in a target class under slight Gaussian perturbations of the inputs. Specifically, we focus…
Most machine learning methods require tuning of hyper-parameters. For kernel ridge regression with the Gaussian kernel, the hyper-parameter is the bandwidth. The bandwidth specifies the length scale of the kernel and has to be carefully…
Self-supervised learning (SSL) has recently advanced through non-contrastive methods that couple an invariance term with variance, covariance, or redundancy-reduction penalties. While such objectives shape first- and second-order statistics…
Graph Representation Learning (GRL) is a fundamental task in machine learning, aiming to encode high-dimensional graph-structured data into low-dimensional vectors. Self-Supervised Learning (SSL) methods are widely used in GRL because they…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
Traditional semi-supervised learning (SSL) assumes that the feature distributions of labeled and unlabeled data are consistent which rarely holds in realistic scenarios. In this paper, we propose a novel SSL setting, where unlabeled samples…
Motivated by the need to address the degeneracy of canonical Laplace learning algorithms in low label rates, we propose to reformulate graph-based semi-supervised learning as a nonconvex generalization of a \emph{Trust-Region Subproblem}…
Given a Riemannian manifold $M$ and an $L^2$-normalized Laplacian eigenfunction $\psi$ on $M$ with eigenvalue $\lambda^2$, a general problem in analysis is to understand how the mass of $\psi$ distributes around $M$. There are different…
Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two…
Semi-supervised learning faces significant challenges in realistic scenarios where labeled data is scarce and unlabeled data follows unknown, arbitrary distributions. We formalize this critical yet under-explored paradigm as Universal…