arXiv research

Proposes a new CNN approach for multimodal biometric identification.

The paper studies harmonic symmetric bilinear forms on Riemannian manifolds and proves properties of the Bourguignon Laplacian.

The study finds points on surfaces where a tensor is conformal to a metric.

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

Hyperplane hashing aims at rapidly searching nearest points to a hyperplane, and has shown practical impact in scaling up active learning with SVMs. Unfortunately, the existing randomized methods need long hash codes to achieve reasonable search accuracy and thus suffer from reduced search speed and large memory overhe…

We extend the complex-valued analytic torsion, introduced by Burghelea and Haller on closed manifolds, to compact Riemannian bordisms. We do so by considering a flat complex vector bundle over a compact Riemannian manifold, endowed with a fiberwise nondegenerate symmetric bilinear form. The Riemmanian metric and the bi…

This article is an attempt to generalize Riemann's bilinear relations on compact Riemann surface of genus at least 2, which may lead to new structures in the theory of hyperbolic Riemann surfaces. No significant result is obtained, the article serves to bring the readers' attention to the observation made by [Bol-1949]…

A new framework improves LSTM performance without adding more parameters.

New algorithm reduces regret in graphical bilinear bandits.

The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.

Defines metric bundles for manifold geometries, unifying various types of metrics.

Compact bilinear pooling approximates covariance features for faster training.

We establish in this note some Cauchy-Schwarz-type inequalities on compact Kähler manifolds, which generalize the classical Khovanskii-Teissier inequalities to higher-dimensional cases. Our proof is to make full use of the mixed Hodge-Riemann bilinear relations due to Dinh and Nguy$\hat{\text{e}}$n. A proportionality p…

New method deforms function algebras on manifolds using spectral decomposition.

This note improves on universal portfolios by using bilinear strategies.

Every smooth vector field is a combination of gradient fields.

Simply connected indefinite homogeneous spaces are compact and have specific Lie algebra structures.

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.

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

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

The paper explores geometric decompositions for Ricci tensors and their applications.

Harmonic 3-forms defined on compact homogeneous spaces are studied and conditions for their harmonicity are provided.

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

Enhances knot invariants using bilinear forms on vector spaces.

For a principal $\rmSU(n)$-bundle over a compact manifold of dimension $2,3,4$, we determine the orbit types of the action of the gauge group on the space of connections modulo pointed local gauge transformations. We find that they are given by Howe subgroups of $\rmSU(n)$ for which a certain characteristic equation is…

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

A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form $ω$, for which the bilinear form $ω(I\cdot,\cdot)$ is positive definite. In this work we prove $dd^c$-lemma for 1- and (1,1)-forms for compact Hermitian symplectic manifolds of dimension 3. This shows that Albanese map for such manifol…

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.

Introduces and studies generalized B-opers with bilinear forms.

Gradient methods converge better for alternating updates in bilinear zero-sum games.

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

Study learns linear system dynamics from noisy bilinear data.

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

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.

Novel hybrid bilinear model improves epilepsy diagnosis accuracy.

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…

Characterizes alternating links in thickened surfaces using Gordon-Litherland pairing.

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…

Improved SEG method converges to Nash equilibrium in bilinear games.

Proposes a bilinear form to efficiently represent high-order temporal action information.

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…