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.

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

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

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

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

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

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

Shallow diffusion models learn hidden low-dimensional structures effectively.

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 …

Study symplectic structures on low dimensional 2-step nilmanifolds.

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

New embeddings capture local structure in complex networks.

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

Generates low-dimensional node vectors for graphs with privacy while preserving structural preferences.

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

A new framework detects anomalies in structured data.

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…

Improved likelihood estimation for singular distributions using deep models.

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

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

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

MoEs can efficiently model complex tasks with low-dimensionality and sparsity.

Diffusion models adapt to low-dimensional structures for nonparametric density estimation.

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

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…

Mercat preserves angles to create accurate low-dimensional embeddings.

LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.

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…

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

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

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…

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

We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the kernel space. The kernel space contains a set of meta states which are desired …

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

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

Study metric learning from limited preference comparisons, showing how low-dimensional structure can still reveal metric information.

Extends dimension reduction to data-driven settings without gradients.

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

In this paper we propose Structuring AutoEncoders (SAE). SAEs are neural networks which learn a low dimensional representation of data which are additionally enriched with a desired structure in this low dimensional space. While traditional Autoencoders have proven to structure data naturally they fail to discover sema…

Diffusion models learn multi-modal distributions with optimal efficiency.

Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distri…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space that spans the conditional means, it is possible to consistently recover the struc…

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…

We propose to model the acoustic space of deep neural network (DNN) class-conditional posterior probabilities as a union of low-dimensional subspaces. To that end, the training posteriors are used for dictionary learning and sparse coding. Sparse representation of the test posteriors using this dictionary enables proje…

This paper improves diffusion models for low-dimensional data.