arXiv research

The study characterizes heat flow and concentration on directed graphs with a lower Ricci curvature bound.

New method certifies anti-concentration for various non-Gaussian distributions.

Concentration of infinitely exchangeable sequences with bounded-difference constants

DCL method improves congruency in machine learning tasks.

Study proves uniqueness of Yang-Mills field tangent cones in arbitrary dimensions.

We consider a priori generalization bounds developed in terms of cross-validation estimates and the stability of learners. In particular, we first derive an exponential Efron-Stein type tail inequality for the concentration of a general function of n independent random variables. Next, under some reasonable notion of s…

Paper develops bounds for stochastic approximation with averaging.

In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This surprising classification of positively-curved Riemannian manifolds results from combin…

A new distance metric for vMF distributions simplifies spherical data analysis.

Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven approach for the learning, modeling, and prediction of phase segregation. A direct …

It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the measure of sets separated from sets having half the total measure, as a…

Repelling random walks improve graph-based sampling efficiency.

Proves existence of solutions with concentrated energy in 2+1 spacetime.

Develops neural network for directed hypergraphs for node classification.

Constructs ε-splitting maps for geodesic balls with non-negative Ricci curvature.

The paper solves a specific type of Ambrosetti-Prodi problem with solutions having clustering concentration layers.

Although stochastic gradient descent (SGD) is a driving force behind the recent success of deep learning, our understanding of its dynamics in a high-dimensional parameter space is limited. In recent years, some researchers have used the stochasticity of minibatch gradients, or the signal-to-noise ratio, to better char…

ZDP detects drift in large language models without labels, proving key theorems and metrics.

Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.

New algorithms reduce regret in neural logistic bandits.

TRA detects causal direction from bivariate data using geometric shapes.

ConMeZO speeds up zeroth-order optimization for large language models.

The Langevin Algorithm's stationary distribution is shown to be sub-exponential or sub-Gaussian under certain conditions.

LASER compresses recursive model activations by exploiting their low-dimensional structure.

We study how network structure affects the dynamics of collateral in presence of rehypothecation. We build a simple model wherein banks interact via chains of repo contracts and use their proprietary collateral or re-use the collateral obtained by other banks via reverse repos. In this framework, we show that total col…

We analyze a family of methods for statistical causal inference from sample under the so-called Additive Noise Model. While most work on the subject has concentrated on establishing the soundness of the Additive Noise Model, the statistical consistency of the resulting inference methods has received little attention. W…

High-probability bound for distributed stochastic approximation tracking error.

Study geodesics on a special cylinder with arbitrary wind.

A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the presence of regression symmetric relationships, without the need to impose further…

New method accelerates neural network training by focusing on flat directions.

New method for community detection in sparse directed SBMs with exact recovery guarantees.

The paper tackles learning varying DAG structures based on contextual features.

Unified framework for critical scaling of inverse temperature in self-attention.

Theory for algebraic data on categories via concentration structures.

Study on stochastic approximation with Polyak-Ruppert averaging for linear systems.

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

Proves convergence of gradient Ricci shrinkers with uniform bounds.

Study Finsler metric measure manifolds' concentration properties.

Generative Adversarial Network (GAN) and its variants have recently attracted intensive research interests due to their elegant theoretical foundation and excellent empirical performance as generative models. These tools provide a promising direction in the studies where data availability is limited. One common issue i…

New method improves missing mass concentration bounds.

SGD noise helps select flat minima by concentrating in sharp directions and being proportional to loss value.

New inequality for ternary variables improves on existing measures.

We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $α< 1$, our algorithm takes as input a sample $\{(x_i,y_i)\}_{i \leq n}$ of $n$ linear equations where $αn$ of the equations satisfy $y_i = \l…

The paper shows robustness and generalization are closely connected via data-dependent bounds.

Surfaces in 3-manifolds concentrate at curvature critical points.

Sharp concentration bounds for i.i.d. variables.

We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for $L^1$-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.

New regularization method corrects over-shrinkage in small data regression.