arXiv research

Logarithmic separation profile in hyperbolic groups shows hierarchical structure.

Optimal ReLU networks can memorize any separable set of points with a small number of parameters.

Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.

Optimizes quantile and semi-adversarial regret with novel root-logarithmic regularizers.

We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic programming, we characterize the value function with a backward stochastic differential equ…

AIHT improves online high-dimensional quantile regression by separating support discovery and refinement.

We consider the closeness testing problem for discrete distributions. The goal is to distinguish whether two samples are drawn from the same unspecified distribution, or whether their respective distributions are separated in $L_1$-norm. In this paper, we focus on adapting the rate to the shape of the underlying distri…

This work introduces reward teaching for federated multi-armed bandits to guide clients towards global optimality.

Transformers can learn noisy linear systems with depth and IID data.

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…

New method finds subsets of vertices to minimize interventions in causal discovery.

We examine gradient descent on unregularized logistic regression problems, with homogeneous linear predictors on linearly separable datasets. We show the predictor converges to the direction of the max-margin (hard margin SVM) solution. The result also generalizes to other monotone decreasing loss functions with an inf…

We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under…

A new method for estimating probabilities and risks using Markov processes.

This paper compares Transformers and RNNs in various tasks, showing size differences.

GCNs distinguish graph models based on embeddings, but depth matters.

We introduce jet topics: a framework to identify underlying classes of jets from collider data. Because of a close mathematical relationship between distributions of observables in jets and emergent themes in sets of documents, we can apply recent techniques in "topic modeling" to extract jet topics from data with mini…

Let G be a countable group which acts by isometries on a separable, but not necessarily proper, Gromov hyperbolic space X. We say the action of G is weakly hyperbolic if G contains two independent hyperbolic isometries. We show that a random walk on such G converges to the Gromov boundary almost surely. We apply the co…

Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.

Study shows a universal local obstruction to the Samuelson condition for tangent Lagrangian 2-webs.

Linear memory stores associations up to a logarithmic scale, but listwise retrieval can handle a quadratic scale.

Paper improves DP-ERM for binary linear classification with large-margin subsets.

Algorithm learns means of spherical Gaussian mixtures efficiently in low dimensions.

In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…

We analyze the classical EM algorithm for parameter estimation in the symmetric two-component Gaussian mixtures in $d$ dimensions. We show that, even in the absence of any separation between components, provided that the sample size satisfies $n=Ω(d \log^3 d)$, the randomly initialized EM algorithm converges to an esti…

Study designs experiments to identify causal graph structure with cycles and latent confounders.

We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsyb…

Study rigidity by logarithmic capacity and related functions.

Adaptive model selection for RL with unknown function classes.

Study real logarithms of semi-simple matrices, focusing on differential structure.

Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.

Logarithmic connections on principal bundles over normal varieties are studied.

We present a new method to solve certain $\bar{\partial}$-equations for logarithmic differential forms by using harmonic integral theory for currents on Kahler manifolds. The result can be considered as a $\bar{\partial}$-lemma for logarithmic forms. As applications, we generalize the result of Deligne about closedness…

Local logarithmic Brunn-Minkowski holds for zonoids.

New framework for logarithmically divergent integrals on manifolds with corners.

Directly proves logarithmic systolic growth for all hyperbolic surfaces.

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

Study improves privacy-preserving online prediction from experts with speed-ups.

Investment and consumption strategy optimized under uncertain conditions.

The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.

Extended logarithm for solvable elements in mapping class groups.

KSDAgg combines multiple KSD tests to improve goodness-of-fit testing without splitting data.

In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation bet…

Study of conformal logarithmic Laplacian on sphere, connecting Yamabe problems and Sobolev spaces.

Paper finds necessary condition for logarithmic Minkowski problem in higher dimensions.

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.

Bandit algorithms struggle with consistent performance and robustness.

Analytic surgery and gluing formula for torsion forms in fiber bundles.