arXiv research

Optimizes cover parameter in Mapper algorithm for better visualization.

This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an additional non-convex global optimization problem, which can be time-consuming and hard t…

The paper tightens bounds on covering numbers for deep ReLU networks.

In this note we provide natural optimal geometric conditions for a Riemannian manifold suitably covered by two open metric balls to be homeomorphic to a sphere. This can be viewed as a geometric analogue of Brown's theorem in topology stating that a closed manifold covered by two topological balls is a sphere.

New $L_1$-Coverage objective simplifies exploration in reinforcement learning.

Random covers of hyperbolic surfaces have a spectral gap with polynomial rate.

In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $ε$-covering number of $\C([a, b]^d, B)$, in the $L_p$-metric, $1 \le p < \infty$, in terms of the relevant constants, where $d \geq 1$, $a < b \in \mathb…

Combines TSP and SC to solve real-world vaccine distribution.

New bounds on cover degrees for Teichmüller distance between hyperbolic surfaces.

Paper introduces information-constrained optimal transport, generalizing Talagrand's inequality.

New bounds for private learning of high-dimensional Gaussian distributions.

Study bounds Urysohn width of manifolds under surgeries.

Partial Wasserstein Covering aims to identify missing patterns in datasets.

This paper proposes a new method for learning covers of geometric datasets to improve topological inference and visualization.

Study shows offline RL with partial coverage and weak function classes is possible.

We study T. Cover's rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $\$1$ deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A r…

We consider Aubry-Mather theory for a subclass of class A spacetimes, i.e. compact vicious spacetimes with globally hyperbolic Abelian cover. In this subclass, called class A_1, we obtain improved results on timelike maximizers and Lipschitz continuity of the time separation of the Abelian cover on the i.g. optimal sub…

We investigate the filling area conjecture, optimal systolic inequalities, and the related problem of the nonvanishing of certain linking numbers in 3-manifolds.

Minimal constructions of meanders and hyperelliptic pillowcase covers help in understanding ratio-optimizing pseudo-Anosovs.

Cover's celebrated theorem states that the long run yield of a properly chosen "universal" portfolio is as good as the long run yield of the best retrospectively chosen constant rebalanced portfolio. The "universality" pertains to the fact that this result is model-free, i.e., not dependent on an underlying stochastic …

Optimal SGD rates achieved with shuffling, covering non-convex and convex cases.

The study extends convergence theorems for Ricci-limit spaces with bounded curvature.

Within a financial model with linear price impact, we study the problem of hedging a covered European option under gamma constraint. Using stochastic target and partial differential equation smoothing techniques, we prove that the super-replication price is the viscosity solution of a fully non-linear parabolic equatio…

In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm, which jointly maximizes the acquisition function and select points from a whole batch in a holistic way. Theoretically, we derive regret bounds for both the noise-free…

Optimizes Lipschitz estimates for partitions of unity and characterizes spaces with Assouad-Nagata dimension.

Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow neural networks. Our framework is general and covers weight-sharing (convolutional ne…

We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of …

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization can cover Euclidean spaces with large dimensionality, with the optimal dependence…

We give examples of closed hyperbolic 3-manifolds with first Betti number 2 and 3 for which no sequence of finite abelian covering spaces increases the first Betti number. For 3-manifolds $M$ with first Betti number 2 we give a characterization in terms of some generalized self-linking numbers of $M$, for there to exis…

We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.

With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral surfaces with non-positive curvature. We show that in the case of such surfaces discr…

Optimizes shortfall risk using gradient-based methods.

The study proves optimal spectral gaps for hyperbolic surfaces.

We accelerate PMD algorithms for reinforcement learning using functional methods.

Explains optimal functional inequalities, focusing on Sobolev and fractional Sobolev.

We study the rate of growth of normalized Hodge numbers along a tower of abelian covers of a smooth projective variety with semismall Albanese map. These bounds are in some cases optimal. Moreover, we compute the $L^2$-Betti numbers of irregular varieties that satisfy the weak generic Nakano vanishing theorem e.g., var…

Two algorithms for interpreting and boosting tree-based models using rule covering.

Study covers of surfaces, showing types and properties.

Paper estimates area covered by a line-sweep sensor in robotics.

Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.

Adaptive step-size improves optimization in complex geometries.

We analyze a new Markov chain model for better sampling and optimization.

A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of l…

The paper studies moduli spaces of non-smooth metric structures with non-negative Ricci curvature.

Survey on optimizing topological descriptors for machine learning.

After showing that a covering space of surface bundles over $S^1$ factors as a `covering of fibers' followed by a `power covering', we prove that, for torus bundles, power coverings do not lower Heegaard genus, and that fiber coverings lower the genus only in special cases.

This is a review of explicit computations of Connes distance in noncommutative geometry, covering finite dimensional spectral triples, almost-commutative geometries, and spectral triples on the algebra of compact operators. Several applications to physics are covered, like the metric interpretation of the Higgs field, …

Introduces self-regularization for analyzing learning algorithms.