arXiv research

Solves a discrete logarithmic Minkowski problem for electrostatic p-capacity.

Study capacity constraints in continual learning with a simple model.

Improves online learning algorithms for functional models with capacity assumptions.

Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p \geq 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and uniqueness of the solution are given when $p \geq 1$ and $1<\mathfrak{p}\le 2$. These r…

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between capacities often lead to surprising relations between different aspects of sympl…

BestChanID identifies the channel with maximal capacity using training sequences.

Capacity analysis has been recently introduced as a way to analyze how linear models distribute their modelling capacity across the input space. In this paper, we extend the notion of capacity allocation to the case of neural networks with non-linear layers. We show that under some hypotheses the problem is equivalent …

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

New analysis tightens memory capacity of Hopfield models using spherical codes.

Through using the semidiameter (in connection to: the mean radius and surface radius) of a convex closed hypersurface in $\mathbb R^{n\ge 2}$ as an sharp upper bound of the variational $(1,n)\ni p$-capacity radius, this paper settles a restriction/variant of S.-T. Yau's \cite[Problem 59]{Yau} from the surface area to t…

Study shows how correlations between neural activity affect classification capacity.

Paper applies theorem to find optimal investment boundary in stochastic capacity expansion.

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…

Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.

Paper tackles inventory management with deep learning, improving performance and adherence to constraints.

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…

Recurrent neural networks are powerful models for processing sequential data, but they are generally plagued by vanishing and exploding gradient problems. Unitary recurrent neural networks (uRNNs), which use unitary recurrence matrices, have recently been proposed as a means to avoid these issues. However, in previous …

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

Paper studies optimal investing for retirees with risk constraints.

This paper addresses the so-called conformal capacities in $\mathbb R^n$, $n\ge 3$, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-c…

Maximizes capacity of extensions with fixed boundary data.

Optimizes the conformal capacity of linked curves in $S^3$.

The electric capacity of a conductor in the 3-dimensional Euclidean space $R^3$ is defined as a ratio of a given positive charge on the conductor to the value of potential on the surface. This definition of the capacity is independent of the given charge. The capacity of a set as a mathematical notion was defined firs…

New algorithm bounds regret in mediator feedback bandit problems.

We study a stochastic, continuous time model on a finite horizon for a firm that produces a single good. We model the production capacity as an Ito diffusion controlled by a nondecreasing process representing the cumulative investment. The firm aims to maximize its expected total net profit by choosing the optimal inve…

A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances that can fit in memory - must grow with the data set size. In practice, while one c…

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…

Dropout controls model capacity in deep learning and matrix completion.

Sparse neural encoding can store more memories as targets become sparser.

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…

A note proves the binary perceptron's capacity is less than 0.847.

Capacity-Constrained Online Convex Optimization with Delayed Feedback

An online learning framework optimizes pricing and capacity in service systems.

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

Researchers solve Dirichlet problem for complex Monge-Ampère equation on Hermitian manifolds.

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

Study characterizes hulls and capacities on Riemannian manifolds, proving isoperimetric inequalities.

We study various capacities on compact Kähler manifolds which generalize the Bedford-Taylor Monge-Ampère capacity. We then use these capacities to study the existence and the regularity of solutions of complex Monge-Ampère equations.

New method reduces overfitting in deep neural networks by measuring and regulating hidden unit diversity.

CapOptix uses options theory to price capacity in electricity markets.

GD outperforms ridge regression and SGD in linear regression problems.

This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions suffer from a dimensionality curse, we consider a restricted setting. In partic…

In this article, we propose the notion of the general $p$-affine capacity and prove some basic properties for the general $p$-affine capacity, such as affine invariance and monotonicity. The newly proposed general $p$-affine capacity is compared with several classical geometric quantities, e.g., the volume, the $p$-var…

Study excess capacity in neural networks using Rademacher complexity.

Study optimizes pricing under uncertainty and capacity constraints.

Study rigidity by logarithmic capacity and related functions.

Study derives error decay rates for kernel classification under source and capacity conditions.

Study binary perceptrons' capacity using random duality theory.