arXiv research

This work refines Cover's theory for binary classification on low-dimensional data.

Diffusion models adapt to low-dimensional data regardless of coefficient choices.

Improved likelihood-free inference by localizing and refining low-dimensional approximations.

Generative models learn complex data from low-dimensional manifolds.

A new BO method tackles high-dimensional optimization without reconstruction.

Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of Hölder functions on low-dimensional manifolds using deep ReLU networks. Suppose $n$ training data are sampled from a Hölder function in $\mathc…

The paper shows diffusion models can converge faster to a target distribution with low-dimensional structure.

This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].

LASE improves local network structure visualization by targeting locally low-dimensional regions.

Proves Kastler-Kalau-Walze theorem for spectral Einstein functional on low-dimensional manifolds.

We consider the ability of deep neural networks to represent data that lies near a low-dimensional manifold in a high-dimensional space. We show that deep networks can efficiently extract the intrinsic, low-dimensional coordinates of such data. We first show that the first two layers of a deep network can exactly embed…

We study low-dimensional representations of matrix groups over general rings, by considering group actions on CAT(0) spaces, spheres and acyclic manifolds.

Kernel models learn low-dimensional predictive subspaces from input data.

Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a low-dimensional subspace nearly isometrically, known as the restricted isometric property in compressed sensing. In th…

Paper adapts DDPM to low-dimensional structures in image distributions.

The local linear embedding algorithm (LLE) is a non-linear dimension-reducing technique, widely used due to its computational simplicity and intuitive approach. LLE first linearly reconstructs each input point from its nearest neighbors and then preserves these neighborhood relations in the low-dimensional embedding. W…

The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. S…

This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…

The paper analyzes side effects of learning from low-dimensional data embedded in a Euclidean space.

Paper solves globally optimal k-means for low dimensional data.

This article sketches various ideas in contact geometry that have become useful in low-dimensional topology. Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle attachments, an…

We develop a method to summarize causal models with cycles in cubic time.

Cryo-em images are found to be low-dimensional.

This paper improves causal inference using deep neural networks for low-dimensional covariates.

New research shows DDPM can adapt to data's intrinsic low dimensionality efficiently.

Two-layer networks trained on low-dimensional subspaces are vulnerable to adversarial examples.

Unified framework for high-dimensional bandit problems with low-dimensional structures.

Unified framework for 3D and 4D manifold and knot theory.

This paper improves diffusion models for low-dimensional data.

Projective DP-SGD reduces privacy error by identifying low-dimensional gradient subspaces.

ConvResNets approximate Besov functions and classify on low-dimensional manifolds.

The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden parameters by utilizing distance metrics that consider the set of attributes as…

In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a response variable. This helps in solving the prediction problem with a low-dimensional…

We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback--Leibler divergence …

New embeddings capture local structure in complex networks.

Study shows how diffusion models learn on low-dimensional manifolds.

A scalable method for accurate inference of low-dimensional parameters in high-dimensional linear regression.

We prove a Livsic type theorem for cocycles taking values in groups of diffeomorphisms of low-dimensional manifolds. The results hold without any localization assumption and in very low regularity. We also obtain a general result (in any dimension) which gives necessary and sufficient conditions to be a coboundary.

UAPCA projects uncertain data to low dimensions using GMMs.

Novelty search in low-dimensional space improves sample efficiency in exploration tasks.

Agents collaborate to reduce regret in a multi-agent linear bandit problem with side information.

Extends dimension reduction to data-driven settings without gradients.

Paper explores how Rectified Flow adapts to low-dimensional data.

New algorithms extract low-dimensional representations from sequential data, revealing insights into complex processes.

New method identifies differences between groups in low-dimensional data representations.

The paper proves compactness of scalar-flat metrics on low-dimensional manifolds with umbilic boundary.

Paper provides statistical guarantees for GANs estimating Hölder space densities.

Study on low-dimensional adversarial perturbations in classification models.