arXiv research

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

Generative models learn complex data from low-dimensional manifolds.

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

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

This paper improves diffusion models for low-dimensional data.

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

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

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…

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…

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

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…

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

UAPCA projects uncertain data to low dimensions using GMMs.

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

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

Paper provides statistical guarantees for GANs estimating Hölder space densities.

Extracting an understanding of the underlying system from high dimensional data is a growing problem in science. Discovering informative and meaningful features is crucial for clustering, classification, and low dimensional data embedding. Here we propose to construct features based on their ability to discriminate bet…

Scattering networks maximize separation on low-dimensional data.

Extends dimension reduction to data-driven settings without gradients.

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

Two methods factor out prior knowledge from low-dimensional embeddings.

Improved likelihood estimation for singular distributions using deep models.

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

Mercat preserves angles to create accurate low-dimensional embeddings.

Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates better understanding of the underlying processes, and enables their optimization. I…

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

This paper improves conditional multidimensional scaling for incomplete data.

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

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

Sensor data analysis plays a key role in health assessment of critical equipment. Such data are multivariate and exhibit nonlinear relationships. This paper describes how one can exploit nonlinear dimension reduction techniques, such as the t-distributed stochastic neighbor embedding (t-SNE) and kernel principal compon…

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …

Wasserstein Autoencoders improve model efficiency and interpretability for low-dimensional data.

Optimizes optimal transport distances using low-dimensional embeddings.

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…

The paper explores how regularization can improve multi-objective learning with high-dimensional data.

A new framework detects anomalies in structured data.

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach…

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

Study on low-dimensional adversarial perturbations in classification models.

The study explains transformer scaling laws using statistical and approximation theories.

New model for high rank matrix completion with online and batch methods.

Paper explores tradeoff between standard and robust accuracy for latent models.

Paper presents a new method for learning hyperbolic representations using tree structures.

Proposes a neural density estimator that adapts to low-dimensional structures and integrates into generative models.