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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8 results for “Dimension-Uniform”

Dimension-Uniform Discretization Analysis of Preconditioned Annealed Langevin Dynamics for Multimodal Gaussian Mixturesstat.ML

Paper analyzes Langevin dynamics for multimodal Gaussian mixtures, controlling errors across dimensions.

problem Challenges in obtaining stable diffusion-based samplers in high- and infinite-dimensional settings.

method Study of preconditioned Annealed Langevin Dynamics (ALD) for Gaussian mixtures, focusing on Euler-Maruyama (EM) and exponential-integrator schemes.

result Proves dimension-uniform KL bounds for the exponential-integrator scheme, allowing arbitrarily small divergence with dimension.

Langevin Dynamics Annealed Langevin Dynamics Gaussian Mixtures Dimension-Uniform KL Divergence

2026-05-15abs ↗pdf ↗

An Improved Uniform Convergence Bound with Fat-Shattering Dimensioncs.LG

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

problem Gap between upper and lower bounds on sample complexity for fat-shattering dimension.

method Provided an improved uniform convergence bound.

result Closed the gap between existing upper and lower bounds on sample complexity.

fat-shattering dimension uniform convergence sample complexity improved bound

2023-07-13abs ↗pdf ↗

Dimension-Free Multimodal Sampling via Preconditioned Annealed Langevin Dynamicsmath.NA

Paper analyzes Annealed Langevin Dynamics for multimodal sampling stability.

problem Ensuring stability of Annealed Langevin Dynamics across dimensions.

method Uniform-in-dimension analysis of ALD for Gaussian-mixture targets.

result ALD achieves prescribed accuracy in KL divergence with spectral conditions.

Annealed Langevin Dynamics Multimodal Sampling Stability Gaussian-mixture KL Divergence

2026-02-01abs ↗pdf ↗

Convergence of Scalar Curvature of Long Time Kähler-Ricci Flow on Kähler Manifoldmath.DG

Kähler-Ricci flow on Kähler manifolds converges to negative Kodaira dimension

problem Convergence of scalar curvature in Kähler-Ricci flow

method Uniform

μ

-entropy or uniform Sobolev inequality

result Scalar curvature converges to negative Kodaira dimension

Kähler-Ricci flow scalar curvature Kodaira dimension uniform entropy uniform Sobolev inequality

2026-06-16abs ↗pdf ↗

Higher-order Ricci estimates along immortal Kähler-Ricci flowsmath.DG

The paper provides estimates for higher-order Ricci curvature along Kähler-Ricci flows.

problem Estimating higher-order curvature along Kähler-Ricci flows on compact Kähler manifolds.

method Proving uniform bounds for Ricci curvature and scalar curvature in various orders and norms.

result A geometric obstruction causes a specific third-order derivative of Ricci curvature to blow up at rate

e^{t/2}

Kähler-Ricci flows curvature estimates higher-order derivatives Kodaira dimension uniform bounds

2026-03-25abs ↗pdf ↗

Generation through the lens of learning theorycs.LG

Generative models characterized through learning theory.

problem Characterizing generative models using learning theory.

method Formalized Gold, Angluin, and Kleinberg's results; introduced uniform and non-uniform generation; characterized closure dimension.

result Incompatibility between generatability and predictability for certain hypothesis classes.

learning theory generative models closure dimension uniform generation non-uniform generation

2024-10-17abs ↗pdf ↗

Surprises in Proper Positive-Only Learningstat.ML

New insights into learning from only positive examples.

problem Characterizing proper learning from positive-only samples.

method Introducing a new combinatorial condition for proper positive-only learning.

result Proper positive-only learning is characterized by finite VC dimension and uniform exterior separability.

PAC learning positive-only samples VC dimension uniform exterior separability proper learning

2026-06-26abs ↗pdf ↗

Deep ReLU Network Expression Rates for Option Prices in high-dimensional, exponential Lévy modelsmath.NA

Deep neural networks approximate option prices in high-dimensional Lévy models efficiently.

problem Approximating option prices in high-dimensional financial models with jumps.

method Use of deep ReLU neural networks to approximate option prices in multivariate Lévy processes with polynomial growth in network size and dimension.

result Established sufficient conditions for polynomial growth in network size and dimension to approximate option prices with error ε.

deep learning financial modeling option pricing high-dimensional Lévy processes

2021-01-28abs ↗pdf ↗