arXiv research

New algorithm reduces regret in graphical bilinear bandits.

Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.

This paper presents a novel unifying framework of bilinear LSTMs that can represent and utilize the nonlinear interaction of the input features present in sequence datasets for achieving superior performance over a linear LSTM and yet not incur more parameters to be learned. To realize this, our unifying framework allo…

Identifies bilinear systems from a single trajectory with optimal sample complexity.

Improved SEG method converges to Nash equilibrium in bilinear games.

In this paper, we propose to employ a bank of modality-dedicated Convolutional Neural Networks (CNNs), fuse, train, and optimize them together for person classification tasks. A modality-dedicated CNN is used for each modality to extract modality-specific features. We demonstrate that, rather than spatial fusion at the…

New algorithm solves complex stopping problems with robust optimization.

New method improves convergence for smooth games.

Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since associations among adjacent scalars are not modeled. In this paper, we propose a n…

Neuc-MDS extends MDS for non-Euclidean data.

Improved convergence rates for saddle-point optimization algorithms.

Optimal Strichartz estimates for Schrödinger on Zoll manifolds.

Develops methods for fair classification under linear disparity constraints.

Two-stage nonconvex algorithm and convex relaxation both achieve optimal accuracy in noisy blind deconvolution.

Generalization of twistor spinors to Kähler manifolds which are called Kählerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of Kählerian twistor spinors. We show that the bilinear form equation reduces to Kählerian conformal Killing-Yano equation under special cond…

Efficient algorithm converges to Nash equilibrium in bilinear problems with bandit feedback.

Algorithm identifies bilinear dynamical systems from noisy data.

In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Bruening-Ma's Cheeger-Mueller type theorem…

Bilinear MLPs offer a new way to interpret deep learning models without complex nonlinearities.

Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…

While classic work in convex-concave min-max optimization relies on average-iterate convergence results, the emergence of nonconvex applications such as training Generative Adversarial Networks has led to renewed interest in last-iterate convergence guarantees. Proving last-iterate convergence is challenging because ma…

The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we must consider every symmetric bilinear form on a Riemannian manifold as a one-form with values in the cotangent bundle of this manifold. In thi…

We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient method (OG) and consensus optimization (CO), which enjoy linear convergence in cas…

New framework allows reinforcement learning with polynomial sample complexity.

New methods solve saddle point problems without line search.

New methods solve min-max problems on manifolds using Riemannian Hamiltonians.

Paper reduces sample complexity for bilinear systems identification to nearly constant.

Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed, and most of them assume that all views share a same coefficient matrix. However, the underlying information of multi-view data are not fully exploited under this assumption, since the coefficie…

This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hin…

Enhances knot invariants using bilinear forms on vector spaces.

Constructs a bilinear form from a quasimorphism on symplectic manifold groups.

We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates of the primal and dual solutions to update. The linear convergence of our method…

A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.

Study learns linear system dynamics from noisy bilinear data.

We use the Jones-Wenzl idempotents to construct a basis of Temperley-Lieb algebra TL_n. This allows a short calculation for a Gram determinant of Lickorish's bilinear form on the Temperley-Lieb algebra.

This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all giv…

Unified bounds for sketched bilinear forms in machine learning and statistics.

BiN normalizes financial time-series for better forecasting.

Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.

Study dynamics of alternating minimization for bilinear regression under large system limits.

The extragradient method accelerates convergence in complex game dynamics.

In this paper the notion of an M-th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a classification of all first order invariant bilinear differential pairings on homogeneo…

New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.

Many DNN-enabled vision applications constantly operate under severe energy constraints such as unmanned aerial vehicles, Augmented Reality headsets, and smartphones. Designing DNNs that can meet a stringent energy budget is becoming increasingly important. This paper proposes ECC, a framework that compresses DNNs to m…

We are interested in approximation of a multivariate function $f(x_1,\dots,x_d)$ by linear combinations of products $u^1(x_1)\cdots u^d(x_d)$ of univariate functions $u^i(x_i)$, $i=1,\dots,d$. In the case $d=2$ it is a classical problem of bilinear approximation. In the case of approximation in the $L_2$ space the bili…

We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a corollary, we construct bilinear forms on the twisted Alexander modules of links.