Related papers: Neuc-MDS: Non-Euclidean Multidimensional Scaling T…
This paper investigates the self-similar solutions of the Einstein-axion-dilaton configuration from type IIB string theory and the global SL(2,R) symmetry. We consider the Continuous Self Similarity (CSS), where the scale transformation is…
A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As…
In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the…
We investigate scaling ansatz with texture zeros within the framework of linear seesaw mechanism. In this variant of seesaw mechanism a simplified expression of effective neutrino mass matrix $m_\nu$ containing two Dirac type matrices…
A new framework based on Boltzmann equation which is genuinely multidimensional and mesh-less is developed for solving Euler's equations. The idea is to use the method of moment of Boltzmann equation to operate in multidimensions using…
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of convexity-concavity and relative smoothness of the payoff…
Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…
We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG). DNN-MG is a novel neural network-based technique for the simulation of the Navier-Stokes equations that combines an adaptive geometric multigrid…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
TSNE and UMAP are two of the most popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings. However, while attempts have been made to improve on TSNE's computational complexity, no existing…
While supervised stereo matching and monocular depth estimation have advanced significantly with learning-based algorithms, self-supervised methods using stereo images as supervision signals have received relatively less focus and require…
We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…
Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…
It has become standard to use gradient-based dimensionality reduction (DR) methods like tSNE and UMAP when explaining what AI models have learned. This makes sense: these methods are fast, robust, and have an uncanny ability to find…
This paper proposes Neural-MMGS, a novel neural 3DGS framework for multimodal large-scale scene reconstruction that fuses multiple sensing modalities in a per-gaussian compact, learnable embedding. While recent works focusing on large-scale…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
In this paper we present a new model and an algorithm for unsupervised clustering of 2-D data such as images. We assume that the data comes from a union of multilinear subspaces (UOMS) model, which is a specific structured case of the much…
The maximum mean discrepancy and Wasserstein distance are popular distance measures between distributions and play important roles in many machine learning problems such as metric learning, generative modeling, domain adaption, and…
In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on computing constrained minimizers of functionals - or,…
Cross-entropy loss has long been the standard choice for training deep neural networks, yet it suffers from interpretability limitations, unbounded weight growth, and inefficiencies that can contribute to costly training dynamics. The…