arXiv research

New method estimates intrinsic dimensionality using angles, not distances.

This paper addresses the following questions pertaining to the intrinsic dimensionality of any given image representation: (i) estimate its intrinsic dimensionality, (ii) develop a deep neural network based non-linear mapping, dubbed DeepMDS, that transforms the ambient representation to the minimal intrinsic space, an…

In this study, we prove that an intrinsic low dimensionality of covariates is the main factor that determines the performance of deep neural networks (DNNs). DNNs generally provide outstanding empirical performance. Hence, numerous studies have actively investigated the theoretical properties of DNNs to understand thei…

Estimates intrinsic dimension of data for GANs.

Bayesian neural networks achieve optimal posterior contraction rates in Besov spaces with intrinsic dimensionality.

Efficient method estimates intrinsic dimension for big data.

Deep multi-task learning benefits from low intrinsic dimensionality, leading to better generalization.

Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.

New algorithm estimates intrinsic dimension of discrete datasets.

Deep networks can adapt to intrinsic dimensionality beyond domain constraints.

LIDL estimates local intrinsic dimension in high dimensions.

In this expository paper we present short simple proofs of Conway-Gordon-Sachs' theorem on intrinsic linking in three-dimensional space, as well as van Kampen-Flores' and Ummel's theorems on intrinsic intersections. The latter are related to nonrealizability of certain hypergraphs in four-dimensional space. The proofs …

Most exact methods for k-nearest neighbour search suffer from the curse of dimensionality; that is, their query times exhibit exponential dependence on either the ambient or the intrinsic dimensionality. Dynamic Continuous Indexing (DCI) offers a promising way of circumventing the curse and successfully reduces the dep…

Diffusion models learn multi-modal distributions with optimal efficiency.

Study shows stable graphs in Heisenberg group are essentially planes.

eDCF estimates intrinsic dimension using local connectivity.

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

Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points being located close to low-dimensional varieties or fine-grained lumping. We test a…

GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.

In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the intrinsic dimensionality of the input dataset is high and the manifold where th…

Investigates projections onto explicit subspaces and their variance effects.

Rdimtools simplifies DR and IDE for high-dimensional data analysis.

In previous work, we introduced eta invariants for even dimensional manifolds. It plays the same role as the eta invariant of Atiyah-Patodi-Singer, which is for odd dimensional manifolds. It is associated to $K^1$ representatives on even dimensional manifolds, and is defined on a finite cylinder, rather than on the man…

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

New local ID estimators based on data separability.

The paper characterizes biconservative surfaces in hyperbolic 4-space.

W2S FT often outperforms weak teachers due to low intrinsic dimensionality.

We prove that, in the first Heisenberg group $\mathbb{H}$, an entire locally Lipschitz intrinsic graph admitting vanishing first variation of its sub-Riemannian area and non-negative second variation must be an intrinsic plane, i.e., a coset of a two dimensional subgroup of $\mathbb{H}$. Moreover two examples are given…

A new reward learning module improves imitation learning in high-dimensional environments.

We present an intrinsic formulation of the kinematic problem of two $n-$dimensional manifolds rolling one on another without twisting or slipping. We determine the configuration space of the system, which is an $\frac{n(n+3)}2-$dimensional manifold. The conditions of no-twisting and no-slipping are decoded by means of …

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible to construct an intrinsic and isometric data representation, which respects an …

Contrastive learning adapts to data intrinsic dimensions, learning low-dimensional representations.

Python package for estimating intrinsic dimensionality of datasets.

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

Study intrinsic volume forms on complex hypersurfaces.

The paper refutes the manifold hypothesis for image data and proposes the union of manifolds hypothesis.

We discuss the construction of Sp(2)Sp(1)-structures whose fundamental form is closed. In particular, we find 10 new examples of 8-dimensional nilmanifolds that admit an invariant closed 4-form with stabiliser Sp(2)Sp(1). Our constructions entail the notion of SO(4)-structures on 7-manifolds. We present a thorough inve…

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

New proof shows diffusion models implicitly estimate intrinsic dimensionality.

We study the intrinsic geometry of a one-dimensional complex space provided with a Kaehler metric in the sense of Grauert. We show that if K is an upper bound for the Gaussian curvature on the regular locus, then the intrinsic metric has curvature at most K in the sense of Alexandrov.

Researchers confirm integral formulas for $G_2$-structures in detail.

Conformal Autoencoders infer intrinsic dimensionality and impose invariance.

The paper studies harmonic graphs in the Heisenberg group and their properties.

The success of modern Artificial Intelligence (AI) technologies depends critically on the ability to learn non-linear functional dependencies from large, high dimensional data sets. Despite recent high-profile successes, empirical evidence indicates that the high predictive performance is often paired with low robustne…

Deep networks can approximate high-dimensional distributions from low-dimensional ones.

This paper analyzes deep federated learning for low-dimensional data, revealing intrinsic dimensionality's role in convergence rates.

CCP clusters correlated features and projects them to 1D for efficient dimensionality reduction.

Shallow nonlinear networks can separate classes linearly with polynomially scaling width.