New method tackles blind demixing from noisy bilinear measurements.
problem Blind demixing of source signals from noisy bilinear measurements.
method Provably nonconvex demixing via Wirtinger flow, similar to vanilla gradient descent.
result Aggressive step size and computational optimality guarantees without regularization.
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.
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.
This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.
problem Finding pure equilibria in machine learning problems is computationally hard.
method Entropic regularization, simultaneous gradient ascent-descent, and particle discretization in the Wasserstein metric.
result Global convergence towards the global equilibrium in mixed equilibria problems.
Proposes neural similarity for CNNs to enhance flexibility and performance.
problem Limited flexibility of inner product-based convolution in CNNs.
method Introduces neural similarity as a learnable parametric similarity measure, and proposes NSL for adaptive learning from data.
result Dynamic neural similarity improves flexibility and performance in visual recognition and few-shot learning.
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.
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.
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. 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.
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.
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.
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.
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.
Zero-shot audio classification using class label embeddings.
problem Classifying audio without labeled data.
method Bilinear model with audio feature embeddings and class label embeddings.
result Achieved accuracy up to 39.7% for natural audio categories.
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.
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…
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.
problem Controlling bilinear systems with noisy data.
method Proposes an end-to-end algorithm using statistical learning theory and robust controller design.
result Derived finite sample identification error bounds and structurally suitable for control.
We introduce invariants of Hurwitz equivalence classes with respect to arbitrary group G G G . The invariants are constructed from any right G G G -modules M M M and any G G G -invariant bilinear function on M M M , and are of bilinear forms. For instance, when G G G is the mapping class group of the closed surface, M g \mathcal{M}_g M g , w…
The study proves symplectic quandles cannot have good involutions.
problem Existence of good involutions in symplectic quandles.
method Investigation of necessary and sufficient conditions for good involutions.
result Nonexistence of good involutions in symplectic quandles.
New algorithm tackles bilinear bandit problem with low-rank structure.
problem Finding the optimal action in a bilinear bandit problem with low-rank reward matrix.
method Two-stage algorithm: subspace exploration followed by linear bandit refinement.
result Regret bound of ESTR is O ~ ( ( d 1 + d 2 ) 3 / 2 r T ) \widetilde{\mathcal{O}}((d_1+d_2)^{3/2} \sqrt{r T}) O (( d 1 + d 2 ) 3/2 r T ) . The paper defines Z-graded hom-Lie superalgebras and explores their properties.
problem Understanding the structure and properties of Z-graded hom-Lie superalgebras.
method Definition and exploration of Z-graded hom-Lie superalgebras, invariant bilinear forms, and simplicity conditions.
result Maximal and minimal Z-graded hom-Lie superalgebras for local hom-Lie superalgebras are identified, and conditions for simplicity are checked.
Proposes RBLDA for multivariate time series data classification.
problem Classifying multivariate time series data.
method Regularized Bilinear Discriminant Analysis (RBLDA) for multivariate time series data.
result RBLDA achieves the best overall recognition performance on real MTS data sets.
Study natural operators transforming tensor fields, proving all bilinear ones are of order one.
problem Understanding natural differential operators on tensor fields.
method Proved all bilinear operators are of order one, then classified operators in specific cases.
result Full classification of natural differential operators on tensor fields.
New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
Rectifiability shown for sub-Riemannian manifolds with Carnot tangent structure.
problem Understanding rectifiability in sub-Riemannian manifolds with specific tangent properties.
method Analyzing nilpotentization and embedding properties of sub-Riemannian manifolds into Carnot groups.
result Sub-Riemannian manifolds are countably rectifiable under certain conditions.
The study finds points on surfaces where a tensor is conformal to a metric.
problem Existence of conformal points on surfaces.
method Analyzes symmetric bilinear two-tensor fields and Riemannian metrics.
result Provides conditions for the existence of conformal points.