arXiv research

New dual approach for hedging Bermudan options efficiently.

DCCNNs reduce computational overhead and ambiguity in convolutional neural networks.

Partial convexification improves tractability of low-rank spectral optimization problems.

The paper extends a neural model to estimate uncertainty in multi-interaction trajectory reconstruction.

The paper tackles fairness in forecasting and learning linear dynamical systems.

Signal estimation problems with smoothness and sparsity priors can be naturally modeled as quadratic optimization with $\ell_0$-"norm" constraints. Since such problems are non-convex and hard-to-solve, the standard approach is, instead, to tackle their convex surrogates based on $\ell_1$-norm relaxations. In this paper…

New algorithm improves dataset distillation with 108% improvement on ImageNet.

Proposes a method to solve deep neural networks' local minimum problem.

New transforms improve signal classification and data analysis.

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms and functions. Iteratively, propagating from node to node along edge, we prove tha…

We introduce normalized nonnegative models (NNM) for explorative data analysis. NNMs are partial convexifications of models from probability theory. We demonstrate their value at the example of item recommendation. We show that NNM-based recommender systems satisfy three criteria that all recommender systems should ide…

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, t…

The omnipresence of deep learning architectures such as deep convolutional neural networks (CNN)s is fueled by the synergistic combination of ever-increasing labeled datasets and specialized hardware. Despite the indisputable success, the reliance on huge amounts of labeled data and specialized hardware can be a limiti…

BP fails to find sparsest solution for structured matrices.

Given a $C^1$ planes distribution $P_T$ on all ${\mathbb R}^m$ we consider {\em horizontal $α$-harmonic maps}, $α\ge 1/2$, with respect to such a distribution. These are maps $u\in H^α({\mathbb R}^k,{\mathbb R}^m)$ satisfying $P_T\nabla u=\nabla u$ and $P_T(u)(-Δ)^αu=0$ in ${\mathcal D}'({\mathbb R}^k).$ If the distrib…

Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper…

New bounds show complexity of adversarial decision making.

This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz $\varphi$-radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz $\varphi$-radial addition of two star bodies, we derive a f…

Dual spherical conchoidal motion has been defined by Yapar. In this work, we define this motion on a dual hyperbolic unit sphere in the dual Lorentzian space with dual signature, and the results carried to the Lorentzian lines space by means of the Study s mapping. We also obtain the study maps of the orbits drawn on t…

Study of curves in dual space with constant curvature and torsion.

The paper classifies curves in dual affine and Lorentz-Minkowski planes with constant curvature.

In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …

Geodesic currents on hyperbolic surfaces have dual spaces that are metric trees.

The paper explores dual learning, a technique that improves machine translation and image transformation.

New construction of self-dual black holes using quadrics.

Dehn surgery on a knot determines a dual knot in the surgered manifold, the core of the filling torus. We consider duals of knots in $S^3$ that have a lens space surgery. Each dual supports a contact structure. We show that if a universally tight contact structure is supported, then the dual is in the same homology cla…

New formula for dual knots using involutions.

Notions of self-dual and anti self-dual almost quaternionic structures are introduced. The complete classification of self-dual and anti self-dual generalized Kaehler manifolds is obtained.

Construct dual F-manifolds for regular F-manifolds.

Dual martingales improve primal optimal stopping problem efficiency.

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …

We introduce the dual isoperimetrix which solves the isoperimetric problem in the dual Brunn-Minkowski theory. We then show how the dual isoperimetrix is related to the isoperimetrix from the Brunn-Minkowski theory.

This paper solves the dual Minkowski problem for q-torsional rigidity.

Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.

The aim of this paper is to develop a general framework for training neural networks (NNs) in a distributed environment, where training data is partitioned over a set of agents that communicate with each other through a sparse, possibly time-varying, connectivity pattern. In such distributed scenario, the training prob…

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

Develops torsion dual connections for statistical manifolds.

In this paper, we study Mannheim surface offsets in dual space. By the aid of the E. Study Mapping, we consider ruled surfaces as dual unit spherical curves and define the Mannheim offsets of the ruled surfaces by means of dual geodesic trihedron (dual Darboux frame). We obtain the relationships between the invariants …

Researchers prove uniqueness and continuity of solution to L_p dual Minkowski problem.

Dual representations for robust risk measures and uncertainty sets.

Solves a generalized dual Minkowski problem for specific values of q.

Let $\{P_1, P_2, P_3, P_4\}$ be a quadruplet of points in $S^3$ . We define a ``dual'' quadruplet of it in a conformal geometric way. We show that the dual of a dual quadruplet coincides with the original one. We also show that the cross ratio of the dual quadruplet is equal to the complex conjugate of that of the orig…

Classifies self-dual almost-Kähler 4-manifolds, proving uniqueness up to rescaling.

In this paper, we define dual geodesic trihedron(dual Darboux frame) of a spacelike ruled surface. Then, we study Mannheim offsets of spacelike ruled surfaces in dual Lorentzian space by considering the E. Study Mapping. We represent spacelike ruled surfaces by dual Lorentzian unit spherical curves and define Mannheim …

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging primal-dual algorithm for minimizing a composite convex function. We also derive a stoch…

We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of …

Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.

Many supervised learning tasks are emerged in dual forms, e.g., English-to-French translation vs. French-to-English translation, speech recognition vs. text to speech, and image classification vs. image generation. Two dual tasks have intrinsic connections with each other due to the probabilistic correlation between th…