arXiv research

The abstract shows how embeddings inscribe trapezoids or map three points to a line, proving nonexistence of certain maps.

Study on embeddings and their topological properties in R^d.

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

We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group $G$. The invariants are constructed from any right $G$-modules $M$ and any $G$-invariant bilinear function on $M$, and are of bilinear forms. For instance, when $G$ is the mapping class group of the closed surface, $\mathcal{M}_g$, w…

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

Invariant covariant derivatives on homogeneous spaces are characterized.

Study biderivations in complete Leibniz algebras, extending Lie algebra results.

We show that the quantum field theoretical formulation of the $τ$-function theory has a geometrical interpretation within the classical transformation theory of conjugate nets. In particular, we prove that i) the partial charge transformations preserving the neutral sector are Laplace transformations, ii) the basic ver…

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…

New mathematical proposal for TQFTs using TMF-modules.

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…

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…

New algorithm reduces regret in graphical bilinear bandits.

The abstract describes a new manifold structure for NLS type equations.

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…

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.

Sprays on Frechet manifolds connect connections and tangent structures.

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

BAM model learns graph structure from data with robustness across linear and non-linear dependencies.

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 …

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 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…

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

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.

We study a natural map from representations of a free group of rank g in GL(n,C), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat bundles are shown to arise in this way. We give a necessary and sufficient cond…

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…

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.

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

Study learns linear system dynamics from noisy bilinear data.

Recently, there has been emerging interest in constructing reproducing kernel Banach spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling reconstruction, sparse approximation and functional analysis. Existing constructions include the reflexive RKBS via a bilinear form, the semi-inner-p…

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 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.

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

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.

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

The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.

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…

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.

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

Defines coupled embeddability for maps on products of spaces, generating examples and nonexamples.

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…