arXiv research

Algorithm identifies bilinear dynamical systems from noisy data.

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

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

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

Study learns linear system dynamics from noisy bilinear data.

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

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

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

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 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…

Via a non degenerate symmetric bilinear form we identify the coadjoint representation with a new representation and so we induce on the orbits a simplectic form. By considering Hamiltonian systems on the orbits we study some features of them and finally find commuting functions under the corresponding Lie-Poisson brack…

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

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear…

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.

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…

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs), and inherit advantages from both types of models. Like many successful RNN archi…

The paper studies geometric structures on SL(n,R) induced by the Killing form.

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.

Automatic emotion recognition (AER) is a challenging task due to the abstract concept and multiple expressions of emotion. Although there is no consensus on a definition, human emotional states usually can be apperceived by auditory and visual systems. Inspired by this cognitive process in human beings, it's natural to…

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…

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.

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

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.

Enhances ASC using time- and frequency-liked CNNs and bilinear pooling.

Advertising and feed ranking are essential to many Internet companies such as Facebook and Sina Weibo. Among many real-world advertising and feed ranking systems, click through rate (CTR) prediction plays a central role. There are many proposed models in this field such as logistic regression, tree based models, factor…

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…

Financial time-series forecasting has long been a challenging problem because of the inherently noisy and stochastic nature of the market. In the High-Frequency Trading (HFT), forecasting for trading purposes is even a more challenging task since an automated inference system is required to be both accurate and fast. I…

This paper presents a construction of fibered links $(K,Σ)$ out of chord diagrams $\sL$. Let $Γ$ be the incidence graph of $\sL$. Under certain conditions on $\sL$ the symmetrized Seifert matrix of $(K,Σ)$ equals the bilinear form of the simply-laced Coxeter system $(W,S)$ associated to $Γ$; and the monodromy of $(K,Σ)…

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.

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…

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.

Geometric models for Lie algebras from simple singularities.

New method improves convergence for smooth games.

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