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.

168,742 papers · 148 categories

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48 results for “low intrinsic dimension”

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 ↗

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 ↗

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 ↗

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 ↗

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 ↗

Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimensioncs.LG

The paper proposes a least squares method for binary compressive sampling with low intrinsic dimension signals.

problem Recovering signals from binary measurements with noise and sign flips.

method Least squares decoder for signals with low generative intrinsic dimension.

result The least squares decoder achieves a sharp estimation error of

O(\sqrt{\frac{k\log (Ln)}{m}})

under certain conditions.

binary compressive sampling least squares low intrinsic dimension signal recovery ReLU network

2021-11-29abs ↗pdf ↗

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 ↗

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 ↗

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 ↗

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 ↗

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 ↗

k-NN Regression Adapts to Local Intrinsic Dimensionstat.ML

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that k-NN regression is also adaptive to intrinsic dimension. …

2011-10-19abs ↗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 ↗

A data-driven approach for multiscale elliptic PDEs with random coefficients based on intrinsic dimension reductionmath.NA

We propose a data-driven approach to solve multiscale elliptic PDEs with random coefficients based on the intrinsic low dimension structure of the underlying elliptic differential operators. Our method consists of offline and online stages. At the offline stage, a low dimension space and its basis are extracted from th…

2019-07-01abs ↗pdf ↗

LDLE: Low Distortion Local Eigenmapsmath.SP

LDLE embeds manifolds in lower dimensions with low distortion.

problem Embedding manifolds in lower dimensions with low distortion.

method Constructs local views using global eigenvectors of the graph Laplacian, registers them using Procrustes analysis, and tears manifolds apart for intrinsic dimension embedding.

result LDLE preserves distances up to a constant scale with low distortion.

manifold learning local eigenmaps Procrustes analysis intrinsic dimension closed manifolds

2021-01-26abs ↗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 ↗

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 ↗

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 ↗

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 ↗

A fundamental differential system of 3-dimensional Riemannian geometrymath.DG

We briefly recall a fundamental exterior differential system introduced by the author and then apply it to the case of three dimensions. Here we find new global tensors and intrinsic invariants of oriented Riemaniann 3-manifolds. The system leads to a remarkable Weingarten type equation for surfaces on hyperbolic 3-spa…

2015-04-17abs ↗pdf ↗

Non-Parametric Inference Adaptive to Intrinsic Dimensioncs.LG

We consider non-parametric estimation and inference of conditional moment models in high dimensions. We show that even when the dimension $D$ of the conditioning variable is larger than the sample size $n$ , estimation and inference is feasible as long as the distribution of the conditioning variable has small intrinsic…

2019-01-11abs ↗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 ↗

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 ↗

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 ↗

Low-Rank Plus Sparse Matrix Transfer Learning under Growing Representations and Ambient Dimensionscs.LG

The paper tackles transfer learning for growing matrix representations, improving estimation accuracy.

problem Structured matrix estimation under growing ambient dimensions and latent representations.

method Proposes a general transfer framework decomposing target parameters into embedded source components, low-rank innovations, and sparse edits. Develops an anchored alternating projection estimator.

result Establishes deterministic error bounds that separate target noise, representation growth, and source estimation error, yielding improved rates.

transfer learning matrix estimation low-rank sparse growing dimensions

2026-01-29abs ↗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 ↗

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 ↗

Linearly Separable Features in Shallow Nonlinear Networks: Width Scales Polynomially with Intrinsic Data Dimensioncs.LG

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

problem Understanding the linear separability of deep networks' features.

method Modeling inputs as a union of low-dimensional subspaces and using random weights and quadratic activations.

result Shallow nonlinear networks can achieve linear separation with polynomially scaling width.

deep learning nonlinear networks linear separability shallow networks intrinsic dimensionality

2025-01-04abs ↗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 ↗

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 ↗

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 ↗

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 ↗

Topological Singularity Detection at Multiple Scalescs.LG

Detects singularities in complex data to improve machine learning models.

problem Real-world data often contains non-manifold structures (singularities) that can mislead machine learning models.

method Develops a topological framework to quantify local intrinsic dimension and Euclidicity score for multiple scales.

result Identifies singularities and captures local geometric complexity in image data.

topology singularities machine learning intrinsic dimension Euclidicity

2022-09-30abs ↗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 ↗

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 ↗

ADARL: Adaptive Low-Rank Structures for Robust Policy Learning under Uncertaintycs.LG

AdaRL improves robust RL by adaptively adjusting policy complexity.

problem Handling epistemic uncertainty in environment dynamics.

method Bi-level optimization framework with adaptive rank adjustment.

result AdaRL outperforms existing methods on MuJoCo benchmarks.

Robust RL Adaptive Rank Wasserstein Ball MuJoCo Policy Optimization

2025-10-13abs ↗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 ↗

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 ↗

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 ↗

The K-Nearest Neighbour UCB algorithm for multi-armed bandits with covariatescs.LG

In this paper we propose and explore the k-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates. We focus on a setting where the covariates are supported on a metric space of low intrinsic dimension, such as a manifold embedded within a high dimensional ambient feature space. The algorithm is concept…

2018-03-01abs ↗pdf ↗

Pairwise Ranking with Gaussian Kernelsstat.ML

Develops new oracle inequalities for Gaussian ranking estimators.

problem Lack of rigorous theoretical support for Gaussian ranking estimators.

method Novel oracle inequalities for regularized pairwise ranking.

result Derives fast learning rates under general dimension assumptions.

Gaussian ranking oracle inequalities pairwise ranking learning rates intrinsic dimension

2023-04-06abs ↗pdf ↗

GeLoRA: Geometric Adaptive Ranks For Efficient LoRA Fine-tuningcs.LG

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

problem Efficient fine-tuning of large language models with limited computational resources.

method GeLoRA computes intrinsic dimensionality to adaptively select LoRA ranks, balancing expressivity and efficiency.

result GeLoRA consistently outperforms recent baselines within the same parameter budget on multiple tasks.

LoRA fine-tuning intrinsic dimensionality adaptive ranks computational efficiency

2024-12-12abs ↗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 ↗

Spectral embedding and the latent geometry of multipartite networksstat.ME

This paper improves spectral embedding for multipartite networks, revealing latent subspaces and providing consistent node representations.

problem Improving spectral embedding for multipartite networks to better represent node types.

method Developed a follow-on step to spectral embedding that recovers node representations in their intrinsic rather than ambient dimension, proving consistency under a specific model.

result Node representations in multipartite networks lie near type-specific subspaces, and the proposed method recovers these representations consistently.

spectral embedding multipartite networks latent geometry node representations consistent recovery

2022-02-08abs ↗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 ↗

Gradient Descent Robustly Learns the Intrinsic Dimension of Data in Training Convolutional Neural Networksstat.ML

CNNs trained by gradient descent can learn intrinsic image rank robustly to background noises.

problem Understanding the intrinsic dimension of data in over-parameterized CNNs.

method Theoretical analysis and experiments on synthetic and real datasets.

result CNNs trained by gradient descent can learn the intrinsic dimension of clean images robustly to background noises.

CNNs gradient descent intrinsic dimension over-parameterized networks background noises

2025-04-11abs ↗pdf ↗

Spurious Valleys in Two-layer Neural Network Optimization Landscapesmath.OC

Neural networks provide a rich class of high-dimensional, non-convex optimization problems. Despite their non-convexity, gradient-descent methods often successfully optimize these models. This has motivated a recent spur in research attempting to characterize properties of their loss surface that may explain such succe…

2018-02-18abs ↗pdf ↗

Fast Spectrum Estimation of Some Kernel Matricesstat.ML

New framework estimates eigenvalues of kernel matrices without full matrix construction.

problem Estimating eigenvalues of large kernel matrices efficiently.

method Eigenvalue quantile estimation framework for kernel matrices with quick decay.

result Validates framework with empirical evidence and proves interlacing theorem.

eigenvalue estimation kernel matrices quantile estimation low-rank approximation intrinsic dimension

2024-11-01abs ↗pdf ↗