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.
Develops methods for fair classification under linear disparity constraints.
problem Disparate impacts of machine learning algorithms on protected groups.
method Bayes-optimal fair classification methods via pre-, in-, and post-processing.
result Explicit forms of Bayes-optimal fair classifiers under linear disparity measures.
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…
Efficient algorithms for large-scale multiclass classification with linear classifiers.
problem Training ℓ 1 \ell_1 ℓ 1 -regularized linear classifiers with high dimensionality and many classes. method Combines quasi-bilinear objective, stochastic mirror descent, and non-uniform sampling.
result Proposes a sublinear algorithm for multiclass hinge loss.
A new loss function penalizes different types of errors in deep learning models.
problem Different types of errors in deep learning models are not equally harmful.
method Introducing the log bilinear loss to differentiate error penalties.
result The log bilinear loss method better contains error within the correct super-class.
It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the classification of two-symmetric Lorentzian manifolds is explained; conformally …
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.
Predicts group membership using latent variables and a tensor product model.
problem Predicting whether instances share a certain semantic property.
method Proposes a novel probability model with latent view-specific and view-shared random variables, learning data-independent parameters with bilinear classifiers.
result Significantly outperforms state-of-the-art methods on visual recognition tasks.
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.
Researchers classify invariant operators on weighted densities.
problem Classifying invariant differential operators on weighted densities.
method Investigated the a f f ( n ∣ 1 ) \mathfrak{aff}(n|1) aff ( n ∣1 ) -module structure and invariant binary differential operators. result Computed the first a f f ( n ∣ 1 ) − \mathfrak{aff}(n|1)- aff ( n ∣1 ) − relative differential cohomology. 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.
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.
Enhances ASC using time- and frequency-liked CNNs and bilinear pooling.
problem Improving acoustic scene classification accuracy.
method Harmonic and percussive source separation, two-stream CNN architecture, bilinear pooling.
result Improved accuracy on DCASE 2019 sub task 1a dataset.
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.
Let F λ {\cal F}_λ F λ be the space of tensor densities on R n {\bf R}^n R n of degree λ λ λ (or, equivalently, of conformal densities of degree − λ n -λn − λn ) considered as a module over the Lie algebra s o ( p + 1 , q + 1 ) so(p+1,q+1) so ( p + 1 , q + 1 ) . We classify s o ( p + 1 , q + 1 ) so(p+1,q+1) so ( p + 1 , q + 1 ) -invariant bilinear differential operators from F λ ⊗ F μ {\cal F}_λ\otimes{\cal F}_μ F λ ⊗ F μ to~ F ν {\cal F}_ν F ν . The…
We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characte…
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.
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.
Two algorithms approximate CMI for feature selection, improving classifier model development.
problem Estimating MI for feature subsets is hard and combinatorial.
method Truncated Power Method (TPower) and Low Rank Bilinear Approximation (LowRank).
result Approximations to NP-hard CMI feature selection are very effective.
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.
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.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
Proposes a bilinear form to efficiently represent high-order temporal action information.
problem Efficiently capturing subtle and precise actions in long videos.
method Low-rank frontal tensors and bilinear form for extracting high-order information.
result Bilinear form outperforms state-of-the-art methods on temporal action segmentation.
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.