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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,181 papers · 148 categories

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8 results for “t-product”

Tensor-Tensor Product Toolboxstat.ML

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.

tensor t-product toolbox matrix linear algebra

2018-06-17abs ↗pdf ↗

Stable Tensor Neural Networks for Rapid Deep Learningcs.LG

Stable tensor neural networks improve deep learning speed and accuracy.

problem Designing efficient neural networks for multidimensional data.

method Introducing a tensor neural network framework based on the t-product algebra.

result Stable tensor neural networks offer faster learning and better generalization.

tensor neural networks t-product deep learning multidimensional data generalization

2018-11-15abs ↗pdf ↗

Clustering multi-way data: a novel algebraic approachcs.LG

In this paper, we develop a method for unsupervised clustering of two-way (matrix) data by combining two recent innovations from different fields: the Sparse Subspace Clustering (SSC) algorithm [10], which groups points coming from a union of subspaces into their respective subspaces, and the t-product [18], which was …

2014-12-22abs ↗pdf ↗

Geometric mean for T-positive definite tensors and associated Riemannian geometrymath.NA

The paper defines and studies the geometric mean for tensors and its associated Riemannian geometry.

problem Defining and studying the geometric mean for tensors.

method Generalized geometric mean for tensors using T-product, verified properties, and investigated Riemannian manifold.

result Geometric mean of T-positive definite tensors is a unique solution of algebraic Riccati tensor equations and a midpoint of geodesics.

geometric mean positive definite tensors Riemannian geometry T-product algebraic Riccati equations

2024-03-30abs ↗pdf ↗

Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normstat.ML

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.

Tensor Robust Principal Component Analysis Tensor Nuclear Norm Low-rank and Sparse Components Convex Programming Exact Recovery

2018-04-10abs ↗pdf ↗

Logarithmic Regret in Feature-based Dynamic Pricingcs.LG

Two algorithms achieve optimal logarithmic regret in feature-based dynamic pricing.

problem Optimal pricing for products with features based on online learning.

method Developed EMLP and ONSP algorithms for stochastic and adversarial settings, proving

O(d\log{T})

regret bounds.

result Achieved optimal

O(d\log{T})

regret, improving over existing bounds.

dynamic pricing online learning regret minimization feature-based stochastic

2021-02-20abs ↗pdf ↗

Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descentstat.ML

ScaledGD algorithm estimates low-rank tensors efficiently from corrupted data.

problem Estimating meaningful information from corrupted tensor data.

method Scaled gradient descent (ScaledGD) algorithm with tailored spectral initializations.

result ScaledGD achieves linear convergence at a constant rate independent of condition number.

Tensor estimation Low-rank tensor Corrupted data Gradient descent Spectral initialization

2025-01-03abs ↗pdf ↗

The power of small initialization in noisy low-tubal-rank tensor recoverycs.LG

Small initialization improves tensor recovery from noisy data.

problem Recovering low-tubal-rank tensors from noisy measurements.

method Factorized gradient descent with small initialization.

result Achieves nearly minimax optimal recovery error.

tensor recovery noisy data small initialization over-parameterization minimax optimality

2026-03-03abs ↗pdf ↗