arXiv research

Defines constraint tensor for null hypersurfaces, providing explicit geometry.

Improved machine learning with reduced tensor rank constraints and dropout.

One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …

In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in $L^2$.

Paper predicts multiple types of miRNA-disease associations using tensor decomposition.

Paper improves MVSC using tensor low-rank modeling.

Develops TOFU for tensor bandits with low-rank structure.

Paper proposes an algorithm for PARAFAC2-based CMTF models with various constraints.

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abeli…

New algorithm learns interpretable CP-basis from streaming tensor data under Markovian constraints.

New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.

Introduces nondecreasing rank for matrices and tensors, developing methods and applications.

Equations link metrics with tensors, revealing curvature constraints.

Flexible framework for CMTF with ADMM for various constraints and couplings.

Tensor networks help learn complex physical laws from data.

Tensor factorization has been demonstrated as an efficient approach for computational phenotyping, where massive electronic health records (EHRs) are converted to concise and meaningful clinical concepts. While distributing the tensor factorization tasks to local sites can avoid direct data sharing, it still requires t…

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, i…

In this paper, we prove a far-from-CMC result similar to the ones obtained by Holst, Nagy, Tsogtgerel and Maxwell for the conformal Einstein-scalar field constraint equations on compact Riemannian manifolds with positive (modified) Yamabe invariant.

In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in [15, 16, 24], namely existence when the so called TT-tensor $σ$ is small and the Yamabe invariant of the manifold is positive. The method we…

Enhances tensor regression for interpretability and performance.

Exact partitioning of high-order planted models achieved through convex optimization.

The paper defines constraints for commuting endomorphisms in generalized tangent bundles.

New method uses scalar-based models to approximate spherical tensors efficiently.

CP degeneracy affects tensor regression solutions, especially in high dimensions.

GLSKF improves tensor completion by capturing both global and local variations.

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlik…

The paper tackles tensor factorization and completion from noisy data.

Tensor regression networks achieve high compression rate of neural networks while having slight impact on performances. They do so by imposing low tensor rank structure on the weight matrices of fully connected layers. In recent years, tensor regression networks have been investigated from the perspective of their comp…

Paper uses algebraic signatures to identify probabilistic structures in empirical data.

Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single…

Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large scale PTTF analysis, and a parallel solution is critical to accommodate the tre…

New algorithm solves $\ell_0$-norm constrained multilinear logistic regression for tensor data.

New method parameterizes solutions to linearized vacuum constraints on Einstein manifolds.

In this article, we give nonexistence and nonuniqueness results for the vacuum Einstein conformal constraint equations in the far-from-CMC case and also show that in some cases the equations of the conformal method for positive Yamabe metrics and with TT-tensor $σ$ = 0 have a non-trivial solution, and thus answer a que…

Let $( \bar g, \bar k)$ be a solution to the maximal constraint equations of general relativity on the unit ball $B_1$ of $\mathbb{R}^3$. We prove that if $(\bar g,\bar k)$ is sufficiently close to the initial data for Minkowski space, then there exists an asymptotically flat solution $(g,k)$ on $\mathbb{R}^3$ that ext…

The goal of tensor completion is to fill in missing entries of a partially known tensor (possibly including some noise) under a low-rank constraint. This may be formulated as a least-squares problem. The set of tensors of a given multilinear rank is known to admit a Riemannian manifold structure, thus methods of Rieman…

Establishes a connection between Kähler metrics and vector bundle sections.

We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.

Extends RRR to capture nonlinear interactions in multi-response regression.

PARAFAC2 has demonstrated success in modeling irregular tensors, where the tensor dimensions vary across one of the modes. An example scenario is modeling treatments across a set of patients with the varying number of medical encounters over time. Despite recent improvements on unconstrained PARAFAC2, its model factors…

TQFT invariants are either easy or hard to compute, depending on the TQFT type.

Learning an encoding of feature vectors in terms of an over-complete dictionary or a information geometric (Fisher vectors) construct is wide-spread in statistical signal processing and computer vision. In content based information retrieval using deep-learning classifiers, such encodings are learnt on the flattened la…

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching P…

In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather ch…

Study the rank of Nijenhuis tensor on parallelizable almost complex manifolds.

Study characterizes conformal boundaries of de Sitter spacetimes.

SWoTTeD discovers hidden temporal patterns in EHR data.

SimTensor is a multi-platform, open-source software for generating artificial tensor data (either with CP/PARAFAC or Tucker structure) for reproducible research on tensor factorization algorithms. SimTensor is a stand-alone application based on MATALB. It provides a wide range of facilities for generating tensor data w…