On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,695 papers · 148 categories

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48 results for “Intrinsically low-dimensional data”

Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionalitycs.LG

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

problem Theoretical inefficiency of DDPM in high-dimensional data.

method Investigates how DDPM can exploit intrinsic low dimensionality of data.

result Proves DDPM's iteration complexity scales nearly linearly with intrinsic dimension

k

DDPM denoising diffusion low dimensionality intrinsic dimension KL divergence

2024-10-24abs ↗pdf ↗

The Intrinsic Dimension of Images and Its Impact on Learningcs.CV

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

problem Understanding the intrinsic dimensionality of images for better model performance.

method Applied dimension estimation tools to popular image datasets and used GANs to manipulate intrinsic dimensionality.

result Natural image datasets have very low intrinsic dimensionality, which aids neural networks in learning and generalizing.

intrinsic dimension image datasets deep learning neural networks GANs

2021-04-18abs ↗pdf ↗

Adaptive Approximation and Generalization of Deep Neural Network with Intrinsic Dimensionalitystat.ML

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…

2019-07-04abs ↗pdf ↗

On the intrinsic dimensionality of Covid-19 data: a global perspectivestat.AP

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

problem Understanding the complexity of Covid-19 data across countries.

method Used a Bayesian mixture model (Hidalgo) to estimate intrinsic dimensionality.

result Covid-19 data projects onto two low-dimensional manifolds without significant loss of information.

Covid-19 Intrinsic Dimensionality Global Perspective Stringency Index Bayesian Mixture Model

2022-03-08abs ↗pdf ↗

A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Datacs.LG

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

problem Limited statistical guarantees for WAEs in low-dimensional data.

method Proper network architecture selection and analysis of expected excess risk convergence rates.

result WAEs can learn data distributions efficiently when intrinsic dimension is considered.

Wasserstein Autoencoders Intrinsically low-dimensional data Statistical guarantees Excess risk convergence Network architecture

2024-02-24abs ↗pdf ↗

On Deep Generative Models for Approximation and Estimation of Distributions on Manifoldsstat.ML

Generative models learn complex data from low-dimensional manifolds.

problem Theoretical justification for generative models on manifold structures.

method Prove statistical guarantees of generative networks under Wasserstein-1 loss, considering intrinsic dimensionality.

result Generative networks converge to zero at a fast rate depending on intrinsic dimensionality, not ambient data dimension.

Generative models manifold hypothesis Wasserstein-1 loss statistical guarantees intrinsic dimensionality

2023-02-25abs ↗pdf ↗

Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributionsstat.ML

Diffusion models learn multi-modal distributions with optimal efficiency.

problem Learning high-dimensional distributions with low-dimensional multi-modal structures.

method Score-based diffusion models, focusing on subgaussian distributions within subspaces.

result Diffusion models require

\widetilde{O}(\varepsilon^{-k \vee 2})

samples for 1-Wasserstein

\varepsilon

error, improving over prior guarantees.

diffusion models statistical efficiency multi-modal distributions subgaussian distributions intrinsic dimension

2026-05-28abs ↗pdf ↗

Multi-View Kernel Consensus For Data Analysiscs.LG

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…

2016-06-28abs ↗pdf ↗

Multi-modal contrastive learning adapts to intrinsic dimensions of shared latent variablesstat.ML

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

problem Learning high-dimensional representations from multi-modal data.

method Multi-modal contrastive learning with temperature optimization.

result Contrastive learning adapts to intrinsic dimensions of data, not specified dimensions.

contrastive learning representation learning multi-modal intrinsic dimensions temperature optimization

2025-05-18abs ↗pdf ↗

Verifying the Union of Manifolds Hypothesis for Image Datastat.ML

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

problem The manifold hypothesis fails to capture the structure of image data.

method Empirical verification of the union of manifolds hypothesis on image datasets.

result Image data lies on a disconnected set with varying intrinsic dimensions.

image data manifold hypothesis union of manifolds deep learning intrinsic dimension

2022-07-06abs ↗pdf ↗

Intrinsic Dimension Estimation Using Wasserstein Distancesstat.ML

Estimates intrinsic dimension of data for GANs.

problem Estimating intrinsic dimension of high-dimensional data.

method Uses Wasserstein distances for estimation.

result Provides sample complexity bounds for GANs.

intrinsic dimension Wasserstein distances GANs sample complexity

2021-06-08abs ↗pdf ↗

Asymptotic Learning Curves for Diffusion Models with Random Features Score and Manifold Datacs.LG

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

problem Learning efficiency of diffusion models on manifolds.

method Analyzes denoising score matching with random feature neural networks.

result Sample complexity scales linearly with intrinsic dimension, not ambient dimension.

Diffusion models Score matching Random features Low-dimensional manifolds Intrinsic dimension

2026-03-24abs ↗pdf ↗

Cryo-em images are intrinsically low dimensionalq-bio.QM

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

problem Understanding the geometric structure of cryo-em data.

method Applied manifold learning techniques to CryoSBI representations.

result Cryo-em data inherently populate low-dimensional manifolds.

cryo-em manifold learning latent representations neural networks inference

2025-04-15abs ↗pdf ↗

Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networksstat.ML

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

problem Lack of statistical theories for deep learning on high-dimensional data.

method Exploits low-dimensional geometric structures of real-world data sets using ConvResNets.

result ConvResNets can approximate Besov functions and learn classifiers with optimal excess risk.

Convolutional Residual Networks Besov Functions Binary Classification Low-Dimensional Manifolds Intrinsic Dimension

2021-09-07abs ↗pdf ↗

Understanding Scaling Laws with Statistical and Approximation Theory for Transformer Neural Networks on Intrinsically Low-dimensional Datacs.LG

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

problem Understanding why transformer scaling laws exist for large models trained on low-dimensional data.

method Established statistical estimation and mathematical approximation theories for transformers on low-dimensional manifolds.

result Predicted a power law between generalization error and model and data sizes, with power depending on intrinsic data dimension.

Transformer scaling laws Statistical estimation Mathematical approximation Low-dimensional data Manifold hypothesis

2024-11-11abs ↗pdf ↗

Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspectivestat.ML

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

problem Improving sampling efficiency in low-dimensional data.

method Investigates Rectified Flow's adaptation to low-dimensional support and introduces a stochastic version.

result Shows improved sampling efficiency with

O(k/\varepsilon)

complexity.

Rectified Flow Sampling Efficiency Low-Dimensional Data Stochastic Localization Diffusion

2026-01-21abs ↗pdf ↗

Novelty Search in Representational Space for Sample Efficient Explorationcs.LG

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

problem Efficient exploration in complex environments with sparse rewards.

method Combines model-based and model-free objectives to learn a low-dimensional representation. Uses intrinsic novelty rewards based on nearest neighbor distances in this space.

result Our approach achieves more sample-efficient exploration compared to strong baselines on various tasks.

Novelty Search Representational Space Sample Efficiency Exploration Intrinsic Rewards

2020-09-28abs ↗pdf ↗

From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learningcs.LG

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

problem Improving generalization in deep multi-task learning with high-dimensional models.

method Parametrizing multi-task networks in a low-dimensional space using random expansions and weight compression.

result First non-vacuous generalization bounds for deep multi-task networks are derived.

deep learning multi-task learning generalization intrinsic dimensionality random expansions

2025-01-31abs ↗pdf ↗

Efficient Representation of Low-Dimensional Manifolds using Deep Networkscs.NE

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…

2016-02-15abs ↗pdf ↗

Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustnessstat.ML

Chart autoencoders learn latent features preserving manifold topology and geometry, with robust denoising capabilities.

problem Learning low-dimensional latent features of high-dimensional data sampled near a manifold.

method Chart autoencoders encode data into latent features on charts, preserving manifold topology and geometry.

result Chart autoencoders achieve a squared generalization error of

n^{-\frac{2}{d+2}}\log^4 n

under proper network architectures.

chart autoencoders manifold learning denoising generalization error intrinsic dimension

2023-03-17abs ↗pdf ↗

Intrinsic dimension estimation for discrete metricsstat.ML

New algorithm estimates intrinsic dimension of discrete datasets.

problem Inaccuracies in using continuous methods for discrete datasets.

method Introduced an algorithm to infer intrinsic dimension of discrete spaces.

result Demonstrated accuracy on benchmark datasets and found a small intrinsic dimension in a metagenomic dataset.

intrinsic dimension discrete metrics metagenomic species fingerprinting evolutive pressure

2022-07-20abs ↗pdf ↗

Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Modelscs.LG

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

problem Understanding and adapting to low-dimensional structures in image distributions.

method Developed a novel set of analysis tools to characterize algorithmic dynamics.

result First theoretical demonstration that DDPM can adapt to unknown low-dimensional structures.

Score-based diffusion models Low-dimensional structures Image distributions Denoising Diffusion Probabilistic Model (DDPM)Intrinsic dimension

2024-05-23abs ↗pdf ↗

A deep network construction that adapts to intrinsic dimensionality beyond the domainstat.ML

Deep networks can adapt to intrinsic dimensionality beyond domain constraints.

problem Approximating functions on low-dimensional manifolds with high-dimensional data.

method Two-layer compositions with ReLU activation, using dimensionality reducing feature maps.

result Near optimal approximation rates depend on the complexity of the dimensionality reducing map, not the ambient dimension.

deep learning ReLU activation intrinsic dimensionality dimensionality reduction manifold approximation

2020-08-06abs ↗pdf ↗

Learning Diverse and Discriminative Representations via the Principle of Maximal Coding Rate Reductioncs.LG

Maximizes coding rate difference for robust, discriminative features.

problem Learning robust, discriminative features from high-dimensional data.

method Maximal Coding Rate Reduction (MCR^2) principle.

result Significantly more robust to label corruptions in classification.

coding rate discriminative features robustness label corruption intrinsic low-dimensional structures

2020-06-15abs ↗pdf ↗

Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recoverycs.LG

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…

2019-08-05abs ↗pdf ↗

Isometric Autoencoderscs.LG

Isometry regularizer improves autoencoder performance on manifold learning.

problem Bad generalization in autoencoders, especially extrinsic and intrinsic issues.

method Introduces an isometry regularizer that encourages the decoder to be an isometry and the encoder to be its pseudo-inverse.

result Isometry regularizer leads to better generalization and useful low-dimensional data representations.

Autoencoder Manifold Learning Isometry Regularization Dimensionality Reduction

2020-06-16abs ↗pdf ↗

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theoriescs.LG

New theory shows deep networks adapt to data's intrinsic dimensionality even when data isn't on a low-dimensional manifold.

problem Existing theories on deep nonparametric regression assume data lie on a low-dimensional manifold, which is often not the case in real-world applications.

method Introduces effective Minkowski dimension to characterize the intrinsic dimension of data subsets and proves sample complexity depends on this new complexity notation.

result Deep neural networks can adapt to the effective Minkowski dimension of data, circumventing the curse of dimensionality for moderate sample sizes.

deep learning nonparametric regression effective Minkowski dimension curse of dimensionality data manifold

2023-06-26abs ↗pdf ↗

Separation Capacity of Scattering Networks on Low-Dimensional Datasetsstat.ML

Scattering networks maximize separation on low-dimensional data.

problem Maximizing separation capacity on low-dimensional datasets.

method Characterize and bound separation capacity for feature extractors, then apply to scattering networks with specific criteria.

result Design criteria for scattering networks to maximize separation on low-dimensional data.

scattering networks low-dimensional data separation capacity rectifiable sets nonlinearities

2026-07-07abs ↗pdf ↗

Intrinsic Isometric Manifold Learning with Application to Localizationstat.ML

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 …

2018-06-01abs ↗pdf ↗

A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Datastat.ML

Paper improves deep learning convergence rates for low-dimensional data.

problem Sub-optimal rates in deep learning due to unrealistic assumptions on intrinsic dimension.

method Introduced an entropic notion of intrinsic dimension for exponential families and demonstrated improved convergence rates.

result Test error scales as

\tilde{\mathcal{O}}\left(n^{-\frac{2β}{2β+ \bar{d}_{2β}(λ)}}\right)

, improving on best-known rates.

deep learning intrinsic dimension exponential families supervised learning Minkowski dimension

2024-12-13abs ↗pdf ↗

Dataset Distillation Efficiently Encodes Low-Dimensional Representations from Gradient-Based Learning of Non-Linear Taskscs.LG

Paper analyzes dataset distillation for efficient encoding of task-relevant information.

problem Efficiently encoding task-relevant information from gradient-based learning of non-linear tasks.

method Theoretical analysis of dataset distillation applied to two-layer neural networks with gradient-based training.

result Low-dimensional structure of the problem is efficiently encoded into distilled data, reproducing a model with high generalization ability.

dataset distillation gradient-based learning non-linear tasks neural networks intrinsic dimensionality

2026-03-16abs ↗pdf ↗

Estimating the effective dimension of large biological datasets using Fisher separability analysiscs.LG

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…

2019-01-18abs ↗pdf ↗

Adaptivity and Convergence of Probability Flow ODEs in Diffusion Generative Modelsstat.ML

The paper improves the probability flow ODE sampler for faster sampling of natural images.

problem Improving the convergence rate of the probability flow ODE sampler.

method Adapting the probability flow ODE sampler to exploit intrinsic low-dimensional structures in natural image data.

result Achieves a dimension-free convergence rate of

O(k/T)

in total variation distance, improving upon existing results.

probability flow ODE score-based generative models diffusion models convergence theory natural images

2025-01-31abs ↗pdf ↗

Linearly-Recurrent Autoencoder Networks for Learning Dynamicsmath.DS

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…

2017-12-04abs ↗pdf ↗

On Convolutions, Intrinsic Dimension, and Diffusion Modelscs.LG

New proof shows diffusion models implicitly estimate intrinsic dimensionality.

problem Estimating intrinsic dimensionality of data from diffusion models.

method Formal proof of FLIPD under realistic assumptions.

result FLIPD's correctness proven under realistic conditions.

intrinsic dimension diffusion models convolutions intrinsic dimensionality log marginal densities

2025-06-25abs ↗pdf ↗

Which Spatial Partition Trees are Adaptive to Intrinsic Dimension?stat.ML

Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination of theory and experiments, for a broader class of trees that includes k-d trees…

2012-05-09abs ↗pdf ↗

A Statistical Analysis of Deep Federated Learning for Intrinsically Low-dimensional Datastat.ML

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

problem Insufficient investigation of generalization error in heterogeneous federated learning, especially for low-dimensional data.

method Statistical analysis of deep federated regression in a two-stage sampling model.

result Intrinsic dimensionality, characterized by entropic dimension, determines convergence rates for deep learners.

federated learning deep learning generalization error intrinsic dimension two-stage sampling

2024-10-28abs ↗pdf ↗

Generalization Properties of Score-matching Diffusion Models for Intrinsically Low-dimensional Datastat.ML

New diffusion models learn distributions from samples with improved error bounds.

problem Statistical guarantees for score-based diffusion models on low-dimensional data.

method Derive finite-sample error bounds for Wasserstein-

p

distance.

result Error bounds scale as

n^{-1 / d^\ast_{p,q}(μ)}

for diffusion models.

score-matching diffusion models Wasserstein distance low-dimensional data statistical guarantees

2026-03-04abs ↗pdf ↗

Grassmann Stein Variational Gradient Descentstat.ML

A new method for SVGD reduces variance in high dimensions.

problem High-dimensional variance in SVGD.

method Grassmann Stein Variational Gradient Descent (GSVGD) projects onto arbitrary subspaces and uses coupled Grassmann-valued diffusion.

result GSVGD explores high-dimensional problems with intrinsic low-dimensional structure efficiently.

Stein variational gradient descent high-dimensional inference variance reduction Grassmann space intrinsic low-dimensionality

2022-02-07abs ↗pdf ↗

Bigeometric Organization of Deep Netsstat.ML

In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of the features being irrelevant to modeling functions of interest. Our algorithm begins by defining coarse neighborhoods of the points and defin…

2015-07-01abs ↗pdf ↗

On the Statistical Properties of Generative Adversarial Models for Low Intrinsic Data Dimensionstat.ML

The paper improves GANs' theoretical guarantees for low-dimensional data.

problem Theoretical guarantees for GANs' statistical accuracy remain pessimistic.

method Analytical derivation of statistical guarantees on estimated densities.

result Theoretical rates of convergence for GANs and BiGANs are derived.

Generative Adversarial Networks Intrinsic Dimension Wasserstein-1 Distance Statistical Guarantees Theoretical Analysis

2024-01-28abs ↗pdf ↗

Stochastic Linear Bandits with Partially Observed Actionscs.LG

TOFU-POV tackles partially observed linear bandits, achieving sublinear regret with low-dimensional action vectors.

problem Stochastic linear bandits with partially observed actions in settings like recommendation and healthcare.

method TOFU-POV estimates latent action subspace, imputes missing actions, and runs OFUL in low-dimensional coordinates.

result TOFU-POV achieves

\sqrt{T}

regret scaling with intrinsic subspace dimension, improving upon natural baselines.

stochastic linear bandits partial observability low intrinsic dimension sublinear regret recommendation systems

2026-07-09abs ↗pdf ↗

Polynomial Matrix Completion for Missing Data Imputation and Transductive Learningcs.LG

This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix are generated by polynomials acting on a low-dimensional intrinsic variable, and …

2019-12-15abs ↗pdf ↗

Reflected diffusion models adapt to low-dimensional datamath.ST

The paper analyzes reflected diffusion models on hypercube data.

problem Challenges in modeling bounded domains with low-dimensional data.

method Employed an infinite series expansion of transition densities to bound the score function and its approximation.

result Established convergence rates for generative algorithm adapting to intrinsic dimensionality.

reflected diffusion models bounded domains low-dimensional data intrinsic dimension Wasserstein distance

2026-03-25abs ↗pdf ↗

Extendable and invertible manifold learning with geometry regularized autoencodersstat.ML

A new method integrates autoencoders with geometry regularization for manifold learning.

problem Extracting simplified low-dimensional representations that capture intrinsic geometry in data.

method Integrates autoencoders with a geometric regularization term based on diffusion potential distances.

result The method preserves intrinsic structure, enables out-of-sample extension, and faithful reconstruction.

manifold learning autoencoders geometry regularization intrinsic geometry invertible

2020-07-14abs ↗pdf ↗

On the capacity of deep generative networks for approximating distributionscs.LG

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

problem Approximating high-dimensional distributions from low-dimensional ones.

method Proved neural networks can transform low-dimensional distributions to high-dimensional ones with arbitrary closeness measured by Wasserstein distances and maximum mean discrepancy.

result Upper bounds of the approximation error are obtained in terms of the width and depth of neural network.

deep generative networks distribution approximation Wasserstein distances maximum mean discrepancy f-divergences

2021-01-29abs ↗pdf ↗

Discrepancies are Virtue: Weak-to-Strong Generalization through Lens of Intrinsic Dimensioncs.LG

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

problem Understanding why weak-to-strong finetuning outperforms weak models.

method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.

result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.

weak-to-strong finetuning ridgeless regression intrinsic dimensionality variance reduction sample complexity

2025-02-07abs ↗pdf ↗

Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approachstat.ML

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

problem Learning low-dimensional nonlinear structures from high-dimensional noisy data.

method Adaptive bandwidth spectral embedding using integral operators.

result Convergence to noiseless embeddings and eigenfunctions of integral operators.

kernel spectral embedding integral operators manifold learning noisy data downstream purposes

2022-02-28abs ↗pdf ↗