arXiv research

Estimates for $p$-capacities on symmetric manifolds.

Managing data storage growth is of crucial importance to businesses. Poor practices can lead to large data and financial losses. Access to storage information along with timely action, or capacity forecasting, are essential to avoid these losses. In addition, ensuring high accuracy of capacity forecast estimates along …

Improves online learning algorithms for functional models with capacity assumptions.

Sharp estimates for p-capacity on manifolds with Ricci curvature bounds.

BestChanID identifies the channel with maximal capacity using training sequences.

The paper proposes a probabilistic autoencoder for discovering causal directions between variables.

In this paper we address the following question, given a face representation, how many identities can it resolve? In other words, what is the capacity of the face representation? A scientific basis for estimating the capacity of a given face representation will not only benefit the evaluation and comparison of differen…

This note develops certain sharp inequalities relating the fractional Sobolev capacity of a set to its standard volume and fractional perimeter.

We conduct an axiomatic study of the problem of estimating the strength of a known causal relationship between a pair of variables. We propose that an estimate of causal strength should be based on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause), and study d…

Previously, Cristofaro-Gardiner, Hutchings and Ramos have proved that embedded contact homology (ECH) capacities can recover the volume of a contact 3-manifod in their paper "the asymptotics of ECH capacities" . There were two main steps to proving this theorem: The first step used an estimate for the energy of min-max…

Using a new method we give elementary estimates for the capacity of non-contractible annuli on cylinders and provide examples, where these inequalities are sharp. Here the lower bound depends only on the area of the annulus. In the case of constant curvature this lower bound is obtained with the help of a symmetrizatio…

Proposes unbiased estimators for training mixture of experts models.

We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacitie…

New algorithm for shareable arms with load-dependent rewards in stochastic bandits.

We study the volume of extrinsic balls and the capacity of extrinsic annuli in minimal submanifolds which are properly immersed with controlled radial sectional curvatures into an ambient manifold with a pole. The key results are concerned with the comparison of those volumes and capacities with the corresponding entit…

New bounds for Dirac eigenvalue involving boundary capacity.

Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.

The paper extends IPC framework to stationary physical systems and validates it with a photonic system.

Study shows how activation functions impact the storage capacity of treelike neural networks.

Introduces Rashomon Capacity to measure predictive multiplicity in probabilistic classifiers.

New complete panel dataset for LMICs helps analyze innovation and development.

Algorithm performance in supervised learning is a combination of memorization, generalization, and luck. By estimating how much information an algorithm can memorize from a dataset, we can set a lower bound on the amount of performance due to other factors such as generalization and luck. With this goal in mind, we int…

New study shows how model complexity affects test risk, challenging classical theory.

Study shows how correlations between neural activity affect classification capacity.

Study on existence and properties of continuous solutions to complex Hessian equations.

Paper develops an online learning algorithm for functional data models.

Given a surface in an asymptotically flat 3-manifold with nonnegative scalar curvature, we derive an upper bound for the capacity of the surface in terms of the area of the surface and the Willmore functional of the surface. The capacity of a surface is defined to be the energy of the harmonic function which equals 0 o…

Study optimal treatment assignment policies under strategic agent responses.

Derives new monotone quantities for p-harmonic functions on asymptotically flat 3-manifolds.

A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary logarithm of the number of functions it can compute, as the synaptic weights are vari…

We provide a rigorous mathematical treatment to the crowding issue in data visualization when high dimensional data sets are projected down to low dimensions for visualization. By properly adjusting the capacity of high dimensional balls, our method makes right enough room to prepare for the embedding. A key component …

Estimates on Einstein manifolds improve Brownian motion behavior and curvature limits.

The paper defines capacities for minimal graphs over manifolds and proves the half-space property.

We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle 9pi - theta, for a suitable theta with cos(theta) in Q(sqrt{19}). Relying on some delicate capacity estimates, we also show that the extrem…

The paper sharpens inequalities in hyperbolic spaces.

India's 2020-21 GDP growth forecast is projected at 1.9% due to COVID-19.

In this paper, we introduce the anisotropic Sobolev capacity with fractional order and develop some basic properties for this new object. Applications to the theory of anisotropic fractional Sobolev spaces are provided. In particular, we give geometric characterizations for a nonnegative Radon measure $μ$ that naturall…

In this paper we study asymptotic behavior of $n$-superharmonic functions at isolated singularity using the Wolff potential and $n$-capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of Arsove-Huber and Taliaferro in 2 dimensions. To study $n$-superharmonic functions we use a…

The study uses symplectic capacities to bound the systole on the sphere.

Study optimizes pricing under uncertainty and capacity constraints.

The study calculates the injectivity capacity of ReLU networks using a novel mathematical approach.

Measures neural network complexity using tangent space diversity.

Analyzes factors affecting flow VI performance.

Many post-disaster and -conflict regions do not have sufficient data on their transportation infrastructure assets, hindering both mobility and reconstruction. In particular, as the number of aging and deteriorating bridges increase, it is necessary to quantify their load characteristics in order to inform maintenance …

New bounds on neural network capacity for treelike sign perceptrons using RDT.

Scalable Gaussian process models trained with unbiased stochastic ELBO.

The memory capacity of linear echo state networks is accurately calculated using new numerical methods.

Let $X$ be a compact Kähler manifold and $\om$ a smooth closed form of bidegree $(1,1)$ which is nonnegative and big. We study the classes ${\mathcal E}_χ(X,\om)$ of $\om$-plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight $χ$ has fast growth at infinity, the corresponding functions are …