A Matlab toolbox for tensor operations based on t-product.
problem Extending matrix operations to tensors.
method Developed a Matlab toolbox implementing tensor operations based on t-product.
result Implemented several tensor operations including SVD, spectral norm, and nuclear norm.
Combines gating and tensor products for RNNs to improve performance.
problem Improving RNNs' ability to capture long-term dependencies.
method Proposes a novel RNN architecture combining gating mechanism and tensor products.
result Significant performance improvement on word-level and character-level language modeling tasks.
The paper defines and analyzes curvature tensors on super twisted product spaces.
problem Investigating curvature tensors on super twisted product spaces.
method Defined W2-curvature tensor, computed curvature tensors and Ricci tensors, and studied curvature flatness. result Mixed Ricci-flat super twisted product semi-Riemannian manifolds can be expressed as super warped product manifolds.
Graphical notation simplifies tensor operations and decompositions.
problem Complex tensor operations are difficult to understand and represent.
method Introduces graphical notation to represent tensor operations.
result Simplified representation of tensor operations and decompositions.
Paper detects review abuse using tensor decomposition.
problem Detecting review abuse by sellers and reviewers.
method Semi-supervised binary multi-target tensor decomposition.
result The model achieves higher precision and recall.
Killing tensors on reducible spaces are reducible, except for special cases.
problem Characterizing Killing tensors on reducible spaces.
method Analyzing Killing tensors on product manifolds and their lifts.
result Killing tensors on product manifolds are reducible, except for specific cases.
Efficiently compress SPNs using tensor networks.
problem Efficiently compressing Sum-Product Networks (SPNs).
method Mapping SPNs onto tensor networks and employing novel optimization techniques.
result Remarkable parameter compression with negligible loss in accuracy.
Paper solves TRPCA problem for tensor data with new tensor nuclear norm.
problem Exact recovery of tensor low-rank and sparse components.
method Introduces tensor-tensor product and new tensor nuclear norm to solve TRPCA.
result The new tensor nuclear norm guarantees exact recovery of tensor data.
New method improves sales forecasting accuracy using tensor factorization.
problem Improving sales forecasting accuracy in retail businesses.
method Advanced Temporal Latent-factor Approach to Sales forecasting (ATLAS) using tensor factorization.
result Accurate and individualized prediction for sales across multiple stores and products.
Tensor networks improve image classification with less than 1% error.
problem Improving image classification accuracy.
method Adapted tensor network optimization for supervised learning using matrix product states.
result Less than 1% test set classification error on MNIST data.
Two formulas for Chern classes of tensor products of vector bundles are presented.
problem Calculating Chern classes for tensor products of vector bundles.
method Two formulas using matrices and polynomials to compute Chern classes.
result Determinantal formulas for Chern classes of tensor products.
Modeling high-dimensional surfaces for toxicity testing using tensor product basis functions.
problem Characterizing complex high-dimensional surfaces from high-throughput toxicity testing data.
method Developed a novel Bayesian additive adaptive basis tensor product model.
result Model accurately predicts dose-responses for untested chemicals.
Paper studies pseudo-projective tensors on warped products.
problem Characterizing pseudo-projectively flat warped products.
method Analyzes sequential warped products and pseudo-projective tensors.
result Necessary and sufficient conditions for pseudo-projectively flat sequential warped products.
Explores tensor products in hyperdimensional computing.
problem Understanding tensor products in hyperdimensional computing.
method Generalized results from graph embeddings to vector symbolic architectures and hyperdimensional computing.
result Tensor product is the most general and expressive representation with errorless unbinding and detection.
Introduces tensor product for quiver representations and applies to stable bundles and character varieties.
problem Stability and classification of quiver bundles and their subvarieties.
method Definition of tensor product for quiver representations and application to stability and character varieties.
result Tensor products of polystable quiver bundles are polystable and provide insights into character varieties.
The paper explores conditions for non-abelian tensor products to be linear.
problem Conditions for non-abelian tensor products to be linear.
method Formulated sufficient conditions and used these to prove linearity for specific groups.
result Proved linearity of tensor squares of some groups and the Peiffer square of linear groups.
Properties of pairs of product conjugate connections are stated with a special view towards the integrability of the given almost product structure. We define the analogous in product geometry of the structural and the virtual tensors from the Hermitian geometry and express the product conjugate connections in terms of…
Some invariant tensors in two Naveira classes of Riemannian product manifolds are considered. These tensors are related with natural connections, i.e. linear connections preserving the Riemannian metric and the product structure.
This research shows how quadratic models can recover tensors with fewer samples than traditional methods.
problem Predicting missing entries in tensors with limited observations.
method Examined non-convex methods for learning quadratic models and their sample complexity.
result All local minima of the mean squared error objective are global minima, recovering the original tensor with linear samples.
Combines RNNs and tensor products for sequential data, outperforming state-of-the-art.
problem Improving symbolic interpretation and systematic generalization in natural language reasoning.
method End-to-end training of a recurrent neural network architecture with tensor product representations.
result Significantly outperforms state-of-the-art models in natural language reasoning tasks.
Defines tensor products for A-infinity structures using diagonals.
problem No specific problem stated; focuses on new definitions.
method Uses diagonals of associahedra and multiplihedra to define tensor products.
result Defines tensor products for various A-infinity structures.
A new method for higher-order co-occurrences in hypergraphs.
problem Computing higher-order co-occurrences in hypergraphs.
method Face-splitting product or transpose Khatri-Rao product for higher order tuple co-occurrences.
result Demonstrates the utility of the higher order co-occurrence tensor in NLP and hypergraph models.
The study extends Jacobi-orthogonality to indefinite scalar product spaces.
problem Generalizing Jacobi-orthogonality to indefinite scalar product spaces.
method Comparing principles, investigating tensor relations, proving properties.
result Every quasi-Clifford tensor is Jacobi-orthogonal; certain tensors are Jacobi-dual or Osserman.
The paper studies curvature properties of warped product manifolds.
problem Curvature conditions of pseudosymmetry type for warped product manifolds.
method Formulates curvature conditions using metrics, tensors, and curvature properties.
result Curvature conditions for specific warped products are proportional to a tensor Q(g,C).
Defines semi-symmetric metric connection on super warped products.
problem Computing curvature and Ricci tensors on super warped products.
method Introduced semi-symmetric metric connection and conditions for Einstein spaces.
result Conditions for super warped product spaces to be Einstein with semi-symmetric metric connection.
The paper explores tensor product kernels and their characteristic properties.
problem Understanding when HSIC characterizes independence and MMD with tensor product kernel discriminates probability distributions.
method Study of various notions of characteristic property of tensor product kernels.
result The paper answers questions about the characteristic and universal properties of tensor product kernels.
The paper characterizes warped product manifolds under pseudosymmetric conditions.
problem Characterizing warped product manifolds under pseudosymmetric conditions.
method Examining the pseudosymmetric type condition \( R \cdot R = L_1 Q(g,R) + L_2 Q(S,R) \) and evaluating the characterization theorem.
result Necessary and sufficient conditions for various pseudosymmetric types in warped product manifolds.
Tensor networks improve unsupervised learning performance.
problem Improving unsupervised machine learning models.
method Autoregressive Matrix Product States (AMPS) combining quantum and machine learning.
result AMPS significantly outperforms existing tensor network models and neural networks.
The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
Paper introduces tensor product of quandles for knot classification.
problem Classifying knot invariants of surface-links with 1-handles.
method Introduces tensor product of quandles and applies to surface-links.
result Tensor product of knot quandles/classical quandles can classify surface-link invariants.
Bayesian hierarchical tensor factorization model for international trade flows
problem Sparse semi-continuous tensor data modeling
method Bayesian hierarchical tensor factorization with Poisson and Gamma models
result Identifies multiway dependence in trade flows
New model uses PEPS for image classification, outperforming tree-like networks.
problem Efficiently modeling and classifying 2D data like images.
method Feature map followed by PEPS contraction with trainable parameters.
result Significantly superior to tree-like networks on MNIST and Fashion-MNIST.
Paper introduces MPS for efficient tensor compression and classification.
problem Efficiently compressing and classifying higher-order tensors.
method Matrix Product State (MPS) using successive SVD.
result MPS achieves better classification performance with lower computation cost.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
AMP algorithm for matrix tensor product model provides recovery conditions.
problem Generalization of standard spiked matrix models with multiple pairwise observations.
method Approximate message passing with optimal weighing and combining of estimates.
result Asymptotically exact performance description and necessary/sufficient recovery conditions.
Study of group orderability using tensor and exterior squares.
problem Circular orderability of groups and torsion elements.
method Analysis of tensor and exterior squares of groups.
result Circularly orderable groups have left-orderable tensor and exterior squares under certain conditions.
Algorithm completes symmetric tensors from few entries, learns product mixtures.
problem Learning product mixtures over the hypercube from incomplete data.
method Tensor completion algorithm applied to matrix completion for adversarially missing entries.
result Recover distributions with many centers in polynomial/quasi-polynomial time.
Paper proposes a new method for exact recovery in robust tensor principal component analysis.
problem Exact recovery of low-rank and sparse components in tensors.
method Proposes a new method based on tensor-tensor product and t-SVD to solve a convex optimization problem.
result Exact recovery achieved in a deterministic fashion without randomness assumptions.
Geometrically, tensors of fixed rank form a minimal submanifold.
problem Understanding the geometric properties of tensors of fixed rank.
method Geometric analysis of tensors in Euclidean space.
result Real tensors of fixed multilinear rank form a minimal submanifold.
A new feature coding method for invariant features using tensor products.
problem Learning invariant features for transformations represented by orthogonal matrices.
method Group-invariant feature vector using tensor-product representations of basic representations.
result Group-invariant feature vector contains sufficient discriminative information for linear classifiers.
A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.
problem Efficiently computing high-dimensional tensor products for polynomial kernels.
method Complex-to-Real (CtR) modification of sketches using complex random projections.
result Achieves state-of-the-art performance in accuracy and speed.
We prove explicit formulas for Chern classes of tensor products of vector bundles, with coefficients given by certain universal polynomials in the ranks of the two bundles.
Study on properties of tangential hypersurfaces in product-like manifolds.
problem Investigating properties of tangential hypersurfaces in product-like manifolds.
method Analyzing basic properties and computing curvature tensor relations.
result Computed relations involving the Riemannian curvature tensor of tangential hypersurfaces.
Tensor networks improve anomaly detection at LHC for new physics.
problem Identifying new phenomena in proton collision events at LHC.
method Tensor network-based anomaly detection using Matrix Product State with an isometric feature map.
result Tensor networks outperform established quantum methods in identifying new phenomena.
The class of the Riemannian almost product manifolds with nonintegrable structure is considered. Some identities for curvature tensor as certain invariant tensors and quantities are obtained.
MCCA extracts shared structure from multiple tensor datasets.
problem Extracting shared structure from multiple tensor datasets.
method Multilinear common component analysis (MCCA) using Kronecker products of mode-wise covariance matrices.
result MCCA constructs a common basis that retains information from multiple tensor datasets.
A new MPS model for both classification and generation.
problem Efficiently representing and manipulating complex, high-dimensional data.
method Inspired by Matrix Product States (MPS) used in quantum computing, applies them in a classical machine learning setting.
result Dual functionality in a supervised learning framework enhances traditional training and generates more realistic samples.
Holomorphic tensors on algebraic cones are invariant under certain group actions.
problem Holomorphic tensors on products of algebraic cones
method Using algebraic structures and embeddings
result Holomorphic tensors are invariant under group actions