Decomposes Riemannian and Lorentzian manifolds for computing holonomy groups.
problem Computing the connected holonomy group of manifolds.
method Finding parallel symmetric bilinear forms and applying linear algebra.
result Computes the connected holonomy group of Riemannian and Lorentzian manifolds.
Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.
problem Link prediction in incomplete knowledge graphs.
method Factorized bilinear pooling model with Tucker decomposition constraints.
result Efficient and parameter-efficient model with low-rank approximation.
We are interested in approximation of a multivariate function f ( x 1 , … , x d ) f(x_1,\dots,x_d) f ( x 1 , … , x d ) by linear combinations of products u 1 ( x 1 ) ⋯ u d ( x d ) u^1(x_1)\cdots u^d(x_d) u 1 ( x 1 ) ⋯ u d ( x d ) of univariate functions u i ( x i ) u^i(x_i) u i ( x i ) , i = 1 , … , d i=1,\dots,d i = 1 , … , d . In the case d = 2 d=2 d = 2 it is a classical problem of bilinear approximation. In the case of approximation in the L 2 L_2 L 2 space the bili…
A new algorithm solves bilinear saddle-point problems efficiently.
problem Solving bilinear saddle-point problems in optimization.
method Doubly stochastic primal-dual coordinate method.
result The method converges linearly and has lower complexity than existing methods.
The paper explores geometric decompositions for Ricci tensors and their applications.
problem Understanding Ricci tensors on compact Riemannian manifolds.
method Utilizes Berger-Ebin and York L 2 L^2 L 2 -orthogonal decompositions. result New insights into Ricci almost solitons and harmonic maps.
New method deforms function algebras on manifolds using spectral decomposition.
problem Deforming function algebras on compact Riemannian manifolds.
method Introducing a bilinear product on the finite spectral core of smooth functions using unimodular phases.
result The product extends to a Sobolev algebra and admits iteration under certain conditions.
This paper introduces a new method for dialog state tracking.
problem Accurately estimating dialog state from noisy observations.
method Bilinear algebraic decomposition model with collective matrix factorization.
result The proposed tracker performs well compared to state-of-the-art trackers.
PSRNNs combine RNN and PSR insights for system filtering and prediction.
problem Modeling dynamical systems efficiently and accurately.
method Combines insights from RNNs and PSRs using bilinear transfer functions and tensor decomposition.
result PSRNNs outperform other models in filtering and prediction tasks across multiple datasets.
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…
Extended current algebra on S^3 with new bilinear form and 2-cocycle.
problem Investigate the current algebra on S^3 of complex Lie algebras.
method Defined a new quaternion-valued 2-cocycle and symmetric invariant bilinear form.
result Extended affine Kac-Moody algebra to Lie algebra of smooth mappings.
In this paper, we want to discuss the topology of the non-singular hypersurface Y n Y^{n} Y n with complex dimension n n n in a projective toric manifold X n + 1 X^{n+1} X n + 1 . When n n n is odd, our main results are a decomposition of Y n ≅ Y ′ ♯ s ( S n × S n ) Y^{n}\cong Y'\sharp \ s(S^n \times S^n) Y n ≅ Y ′ ♯ s ( S n × S n ) as a connected sum of s s s copies of S n × S n S^n \times S^n S n × S n with a dif…
Study tackles distribution shift in combinatorial settings using matrix completion techniques.
problem Tackling distribution shift in combinatorial settings with rigorous statistical guarantees.
method Develops novel algorithms and theoretical results for extrapolating to test distributions not covered in training.
result Achieves bilinear combinatorial extrapolation under gradual spectral decay in high-dimensional data.
The paper generalizes Hodge theory to semisimple local systems and proves a geometric Decomposition theorem.
problem Generalizing Hodge theory to semisimple local systems.
method Establishing a canonical isomorphism and proving a global invariant cycle theorem.
result A new geometric proof of the Decomposition theorem for semisimple local systems.
A new framework improves LSTM performance without adding more parameters.
problem Improving LSTM performance without increasing model complexity.
method A unifying framework of bilinear LSTMs that balances hidden state vector size and weight matrix approximation quality.
result Bilinear LSTMs achieve superior performance compared to linear LSTMs without additional parameters.
The paper characterizes harmonic maps and studies their properties on Riemannian manifolds.
problem Characterizing and analyzing harmonic maps between Riemannian manifolds.
method Analytic and geometric methods, including L2-orthogonal decomposition and energy density analysis.
result A criterion for harmonic submersions and diffeomorphisms, and new results linking harmonic symmetric bilinear forms and metrics.
New algorithm reduces regret in graphical bilinear bandits.
problem Optimizing decisions in a network of agents playing bilinear games.
method Optimism in the face of uncertainty principle applied to combinatorial NP-hard problem.
result Upper bound of i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) on α α α -regret demonstrated. The study generalizes twistor spinors to Kähler manifolds and finds bilinear form equations.
problem Generalizing twistor spinors to Kähler manifolds.
method Finding differential equations and reducing them to conformal Killing-Yano equations.
result Bilinear forms of Kählerian twistor spinors reduce to Kählerian conformal Killing-Yano equations under certain conditions.
The paper studies harmonic symmetric bilinear forms on Riemannian manifolds and proves properties of the Bourguignon Laplacian.
problem Analyzing harmonic symmetric bilinear forms on Riemannian manifolds.
method Developed the theory of harmonic symmetric bilinear forms and proved properties of the Bourguignon Laplacian.
result The kernel of the Bourguignon Laplacian is a finite-dimensional vector space of harmonic symmetric bilinear forms on a compact Riemannian manifold.
This note improves on universal portfolios by using bilinear strategies.
problem Improving on the best constant-rebalanced portfolio.
method Generalizing the best bilinear trading strategy using performance-weighted averaging.
result A universal bilinear portfolio that asymptotically dominates the original universal portfolio.
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
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.
problem Lack of mechanistic understanding in how MLPs compute.
method Introduced bilinear MLPs without element-wise nonlinearities, analyzed their weights using tensor and eigendecomposition.
result Bilinear MLPs provide interpretable weight structures and enable adversarial attacks and overfitting analysis.
Identifies bilinear systems from a single trajectory with optimal sample complexity.
problem Learning bilinear systems from a single trajectory of states and inputs.
method Uses a mild marginal mean-square stability assumption and martingale small-ball condition.
result Sample complexity and statistical error rates are optimal.
Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.
problem Finding flat coordinates for non-symmetric bilinear forms.
method Provides explicit necessary and sufficient conditions for a tensor field of type (0,2) to be flat.
result Explicit conditions for a tensor field to have constant entries in local coordinates.
Study isometries of Clifford algebras, focusing on Lie algebra structure.
problem Understanding isometries of Clifford algebras and their Lie algebra structure.
method Construct Lie algebra L G r , s LG_{r,s} L G r , s , compute bracket relations, determine Lie algebra in specific cases. result Detailed Lie algebra structure of L G r , s LG_{r,s} L G r , s for F = R F = R F = R . Invariants from bilinear forms help classify Lefschetz fibrations.
problem Classifying Lefschetz fibrations over the 2-sphere.
method Construct invariants from right G-modules and bilinear functions.
result Found infinitely many Lefschetz fibrations homeomorphic but not mutually isomorphic.
Study Lie algebras with specific bilinear forms, finding exceptions.
problem Characterizing Lie algebras with symmetric, invariant, and nondegenerate bilinear forms.
method Analyzing structural properties and exceptions of Lie algebras.
result Rare exceptions to the properties of Lie algebras with these bilinear forms.
The massless supermultiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its maximal compact subgroup Spin(9). In an earlier paper, a dynamical Kaluza-Klein origin of this observation is proposed with internal space th…
Proposes a new CNN approach for multimodal biometric identification.
problem Improving biometric identification accuracy across multiple modalities.
method Uses a bank of modality-specific CNNs, fuses their outputs, and optimizes the system.
result Significantly outperforms unimodal systems and demonstrates reduction in parameters.
Paper reduces sample complexity for bilinear systems identification to nearly constant.
problem Identifying discrete-time bilinear systems under bounded disturbances.
method Uses trajectory-dependent regressors and polynomial mean-square state growth analysis.
result Proves sample complexity of O ~ ( 1 / ε ) \widetilde{\mathcal O}(1/ε) O ( 1/ ε ) for estimation error ε ε ε . Enhances knot invariants using bilinear forms on vector spaces.
problem Improving classical and virtual knot invariants.
method Uses bilinear forms on vector spaces indexed by pairs of elements of a finite quandle.
result New enhanced invariants of knots and links.
Constructs a bilinear form from a quasimorphism on symplectic manifold groups.
problem Understanding symplectic group properties through quasimorphisms and bilinear forms.
method Develops machinery to construct a real-valued bilinear form from a quasimorphism on the commutator subgroup of symplectic group.
result The constructed bilinear form b \mathfrak{b} b controls extendability of quasimorphisms and triviality of characteristic classes. Diagrammatic method calculates knot pairings in 3-sphere.
problem Computing knot pairings in 3-sphere.
method Diagrammatic computation of bilinear forms.
result Constructs bilinear forms on twisted Alexander modules.
Introduces and studies generalized B-opers with bilinear forms.
problem Understanding higher rank opers with bilinear forms.
method Studies the structure of generalized B-opers using jet bundles and geometric structures on Riemann surfaces.
result Structure of generalized B-opers is studied and related to jet bundles and geometric structures.
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.
problem Understanding the dynamics of gradient algorithms for bilinear zero-sum games.
method Systematic analysis of popular gradient updates for simultaneous and alternating versions of bilinear zero-sum games.
result Alternating updates converge better than simultaneous ones, with optimal parameter setup and rates.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
Study learns linear system dynamics from noisy bilinear data.
problem Learning linear dynamics from bilinear observations with process and measurement noise.
method Regression with Kronecker product design, data-dependent and independent error bounds.
result Upper bounds on statistical error rates and sample complexity for learning dynamics matrices.
ABIPNN improves neural network performance by processing vectors in each neuron.
problem Traditional neural networks fail to model associations among adjacent scalars.
method ABIPNN uses arbitrary bilinear products to process vector-valued neurons.
result ABIPNN outperforms conventional neural networks in multispectral image denoising and singing voice separation.
Abstract: Generalizes Riemann's bilinear relations for surfaces of genus ≥ 2.
problem No new significant results, but highlights a known observation.
method Generalization of Riemann's bilinear relations.
result No significant new results obtained.
Graph-Dictionary model for sparse multivariate signal representation.
problem Capturing complex relational information in multivariate signals.
method Graph dictionaries and bilinear primal-dual splitting algorithm.
result Graph-dictionary model outperforms baselines in signal reconstruction and classification.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
problem Optimal control from bilinear observations in linear systems is challenging.
method Analytical and numerical methods to study the non-convex cost-to-go and non-affine optimal controllers.
result The Separation Principle does not hold for bilinear observations, leading to 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.
problem Uniform bounds on sketched bilinear forms for modern analyses.
method Generic chaining and new techniques for handling suprema over pairs of sets.
result Improved convergence bounds for sketched Federated Learning and bandit algorithms.
BiN normalizes financial time-series for better forecasting.
problem Non-stationarity and multimodality in financial time-series data.
method Bilinear Normalization (BiN) incorporated into TABL networks.
result BiN-TABL outperforms other normalization methods in financial forecasting.
Study dynamics of alternating minimization for bilinear regression under large system limits.
problem Understanding the time evolution of alternating minimization for bilinear regression.
method Replica method applied to a multi-temperature glassy system.
result Dynamics of alternating minimization can be described by a two-dimensional discrete stochastic process.
Novel hybrid bilinear model improves epilepsy diagnosis accuracy.
problem Improving accuracy in epilepsy diagnosis and treatment.
method Hybrid bilinear deep learning network using sEEG and audiovisual monitoring.
result Obtained F1-scores of 97.4% and 97.2% on two seizure datasets.