arXiv research

Paper analyzes sample complexity for offline RL with deep ReLU networks.

Wavelet-based online learning adapts to noisy Besov spaces with high probability.

New spatiotemporal Besov process improves CT image reconstruction and other inverse problems.

Adaptive algorithm minimizes online prediction errors for irregular data.

Extends Onsager's conjecture to Besov spaces on manifolds with boundary.

Bayesian nonparametric LABS model adapts to function smoothness in Besov spaces.

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this work, we present a framework of operator inference to extract the governing dynamic…

Kolmogorov-Arnold Networks improve deep learning adaptivity and can approximate Besov functions optimally.

This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.

Deep learning has shown high performances in various types of tasks from visual recognition to natural language processing, which indicates superior flexibility and adaptivity of deep learning. To understand this phenomenon theoretically, we develop a new approximation and estimation error analysis of deep learning wit…

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

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

Study analyzes deep learning's performance on variable exponent Besov space, highlighting adaptivity benefits.

Study minimax rates for density estimation under Huber contamination and Besov IPM losses.

Paper proves higher-order flow matching preserves optimality in generative modeling.

The study connects lamination and orbit closures in hyperbolic manifolds.

Bayesian neural network achieves nearly optimal performance in Besov space.

The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…

A new method predicts non-Markovian closure terms for complex systems.

Deep ReLU networks approximate functions in Sobolev and Besov spaces efficiently.

Bayesian KANs achieve near-minimax posterior contraction rates in anisotropic Besov spaces.

Characterizes when differential forms have weak exterior derivatives based on limiting behavior of integration over simplices.

Deep ReLU networks can efficiently approximate Sobolev and Besov functions.

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

Study stationary measures and orbit closures for non-abelian actions on surfaces.

In this paper we propose a function space approach to Representation Learning and the analysis of the representation layers in deep learning architectures. We show how to compute a weak-type Besov smoothness index that quantifies the geometry of the clustering in the feature space. This approach was already applied suc…

Study on distributed nonparametric function estimation with optimal rate and cost of adaptation.

Researchers develop methods to learn neuron dynamics from colored noise.

Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-depen…

Deep ReLU networks can approximate and learn smooth functions efficiently.

Deep learning models can adaptively estimate functions with varying smoothness using regularization.

Intelligence emerges from stabilizing invariant cycles in memory.

New surfaces with special geodesic and horocycle behaviors discovered.

Combines ML and KB modeling for large chaotic systems.

Study on stochastic covariant derivatives in curved space-time.

MARL improves LBM stability and accuracy across scales.

We show that all GL(2, R)-equivariant point markings over orbit closures of primitive genus two translation surfaces arise from marking pairs of points exchanged by the hyperelliptic involution, Weierstrass points, or the golden points in the golden eigenform locus. As corollaries, we classify the holomorphically varyi…

In this paper, we consider various tensorial estimates in geometric Besov-type norms on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to do this with only very weak control on these geometries. Several of these estimates were established in previous works by S. Klainerman and I. Rodn…

Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces called strata that are related to the moduli space of Riemann surfaces. There is a …

Diffusion models achieve nearly optimal distribution estimation in various spaces.

Kernel analog forecasting studied for multiscale systems.

The paper studies harmonic map heat flow stability and decay rates.

No trapped surfaces can form under low-regularity bounds in certain spacetimes.

We study the problem of estimating a nonparametric probability density under a large family of losses called Besov IPMs, which include, for example, $\mathcal{L}^p$ distances, total variation distance, and generalizations of both Wasserstein and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide b…

Algorithm converts plat to standard closure of braids in 3D and related spaces.

This work introduces a new probabilistic process for regularization in machine learning.

The paper studies knitted surfaces and surface-links, showing their isotopy and closure properties.

The restricted class of quasicircles sometimes called the "Weil-Petersson-class" has been a subject of interest in the last decade. In this paper we establish a Sokhotski-Plemelj jump formula for WP-class quasicircles, for boundary data in a certain conformally invariant Besov space. We show that this Besov space is pr…