arXiv research

Abstract: Generalizes Riemann's bilinear relations for surfaces of genus ≥ 2.

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

New inequalities generalize Li's theorem on mixed Hodge structures.

We compute the Chen-Ruan orbifold cohomology ring of the Batyrev mirror orbifold of a smooth quintic hypersurface in 4-dimensional projective space. We identify the obstruction bundle for this example by using the Riemann bilinear relations for periods. We outline a general method of computing the Chen-Ruan ring for Ca…

We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a hermitian manifold, where the B-field 2-form is imaginary and proportional to the canonical form associat…

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…

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 extend the main result in the previous paper of Zhang and the author relating the Milnor-Turaev torsion with the complex valued analytic torsion to the equivariant case.

Optimal Strichartz estimates for Schrödinger on Zoll manifolds.

A new loss function penalizes different types of errors in deep learning models.

Improved KG completion on large datasets using entity-relation pair occurrences.

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…

A new framework improves LSTM performance without adding more parameters.

Based on the Lie theoretical methods of algebraic Fourier transformation, we classify in the case of generic values of inducing parameters the scalar singular vectors corresponding to the diagonal branching rules for scalar generalized Verma modules in the case of orthogonal Lie algebra and its conformal parabolic suba…

New algorithm reduces regret in graphical bilinear bandits.

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

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

This note improves on universal portfolios by using bilinear strategies.

We obtain bounds on the least dimension of an affine space that can contain an $n$-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points. This problem is closely related to the generalized vector field problem, non-singular bilinear maps, and the immersion problem for re…

Deep Fusion improves audio-video emotion recognition accuracy.

Algorithm identifies bilinear dynamical systems from noisy data.

In this paper we present a unified framework for modeling multi-relational representations, scoring, and learning, and conduct an empirical study of several recent multi-relational embedding models under the framework. We investigate the different choices of relation operators based on linear and bilinear transformatio…

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 ideal of relations in the (small) quantum cohomology ring of the generalized flag manifold $G/B$ has been determined by B. Kim. We are going to point out a limited number of properties that, if they are satisfied by an $R[q_1,...,q_l]$-bilinear product $\circ$ on $H^*(G/B)\otimes R[q_1,...,q_l$, then the ring $(H^*…

Invariants from bilinear forms help classify Lefschetz fibrations.

Proposes a new CNN approach for multimodal biometric identification.

New metrics defined on SPD matrices link to divergences and curvature.

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

Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map Π: \wedge^2 W \to V. If the skew symmetric vector valued bilinear form Πis nondegenerate then (M,Q) i…

The second fundamental form of Riemannian geometry is generalised to the case of a manifold with a linear connection and an integrable distribution. This bilinear form is generally not symmetric and its skew part is the torsion. The form itself is closely related to the shape map of the connection. The codimension one …

Study Lie algebras of indefinite spaces with finite volume.

Enhances knot invariants using bilinear forms on vector spaces.

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

Develops a bialgebra theory for post-Lie algebras using geometric interpretations and bilinear forms.

Introduces and studies generalized B-opers with bilinear forms.

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.

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

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

We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…

Study learns linear system dynamics from noisy bilinear data.

New algorithm solves complex stopping problems with robust optimization.

ABIPNN improves neural network performance by processing vectors in each neuron.

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.

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