arXiv research

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

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

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

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

New method detects low-dimensional manifolds within bounds.

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

A low-rank tensor model simplifies multi-dimensional Markov chains.

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

Generative models learn complex data from low-dimensional manifolds.

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…

Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.

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…

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

Shallow diffusion models learn hidden low-dimensional structures effectively.

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…

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…

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].

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.

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

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

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

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…

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

New embeddings capture local structure in complex networks.

Study symplectic structures on low dimensional 2-step nilmanifolds.

Proposes GPLFR for predicting high-dimensional outputs with few data.

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

This paper improves diffusion models for low-dimensional data.

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.

High-dimensional representations often have a lower dimensional underlying structure. This is particularly the case in many decision making settings. For example, when the representation of actions is generated from a deep neural network, it is reasonable to expect a low-rank structure whereas conventional structures l…

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

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…

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

The paper classifies special geometric shapes in 2D and 3D.

Low-dimensional structure in images helps deep learning models generalize better.

Paper connects free-energy and low-degree hardness in high-dimensional statistics.

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

UAPCA projects uncertain data to low dimensions using GMMs.

NPMD uses CNNs to optimize policies on low-dimensional manifolds, reducing sample complexity.

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…

Kernel-spectral embedding learns low-dim. structures from noisy data.

Finding rare information hidden in a huge amount of data from the Internet is a necessary but complex issue. Many researchers have studied this issue and have found effective methods to detect anomaly data in low dimensional space. However, as the dimension increases, most of these existing methods perform poorly in de…

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

We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that…

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…