arXiv research

This note improves on universal portfolios by using bilinear strategies.

A new framework improves LSTM performance without adding more parameters.

New algorithm reduces regret in graphical bilinear bandits.

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…

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

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.

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

Enhances knot invariants using bilinear forms on vector spaces.

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

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.

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.

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.

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…

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.

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.

End-to-end algorithm for controlling bilinear systems with probabilistic noise.

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…

The study proves symplectic quandles cannot have good involutions.

The paper defines Z-graded hom-Lie superalgebras and explores their properties.

Study natural operators transforming tensor fields, proving all bilinear ones are of order one.

New method improves convergence for smooth games.

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.

Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised and supervised classification. Although dimension reduction in the area of clus…

A new method clusters multi-view data by sharing a common trace-norm of coefficient matrices.

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

Consider a smooth manifold with a smooth metric which changes bilinear type from Riemann to Lorentz on a hypersurface $Σ$ with radical tangent to $Σ$. Two natural bilinear symmetric forms appear there, and we use it to analyze the geometry of $Σ$. We show the way in which these forms control the smooth extensibility ov…

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear form. As a consequence, we prove the Burghelea-Haller conjecture which gives an an…

Neuc-MDS extends MDS for non-Euclidean data.

Wide neural networks become linear, but adding bottlenecks makes them bilinear or multilinear.

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…