Tensor Estimation
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Related Articles from SNS
Free Energy Universality in Tensor Estimation via Generic Chaining
arXiv:2605.30636v1 Announce Type: cross Abstract: We study high-dimensional inference problems with tensor-structured data and establish conditions under which their free energy can be approximated by that of a Gaussian comparison model. Our framework applies to models with independent observations and mismatch between the data-generating distribution and the statistical model. The results extend prior work beyond matrix settings and accommodate scaling regimes where the model parameters...
Deconstructing the Composite Channel for Beyond Diagonal RIS: Channel Estimation and Beamforming Design
arXiv:2606.01564v1 Announce Type: cross Abstract: As beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) gain increasing attention in high-frequency wireless communications, accurate and scalable channel-estimation methods become essential. This paper develops a parametric channel-estimation and beamforming framework that deconstructs the composite BD-RIS channel into its generating directional factors, revealing the tensor structure induced jointly by propagation geometry and...
Closed-Form Pose Estimation of Endoluminal Medical Devices via Gradiometer-Based Electromagnetic Localization System
arXiv:2606.01946v1 Announce Type: new Abstract: Embedded magnetic tracking holds highly attractive prospects for remote navigation of endoluminal medical devices. However, existing six-degree-of-freedom pose recovery approaches often require pre-calibrated workspace field maps or iterative nonlinear optimization. This letter presents a Gradiometer-Based Electromagnetic Localization System (GELS), a closed-form tracking framework that uses a compact magnetometer array as an embedded...
Low-rank Distributional Matrix Completion
arXiv:2606.04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar. In this setting, only a subset of matrix entries is observed, and even for observed entries, the underlying distributions are not directly accessible; instead, we observe finitely many samples drawn from them. To represent distributional entries, we employ kernel mean embeddings...
Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states
arXiv:2605.00998v2 Announce Type: replace Abstract: Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this Perspective, we discuss how TTNS methods enable accurate, full-dimensional computations of thousands of eigenstates for molecular systems ranging from quartic-force-field benchmarks to molecules with...
Pauli propagation enables fast classical simulation of strongly correlated quantum systems
Announce Type: replace-cross Abstract: Ground state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here we present a variational double bracket flow (vDBF) algorithm that leverages Pauli Propagation, a technique originally developed for classical simulation of quantum...
Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis
Announce Type: cross Abstract: Matrix completion has been extensively studied for real-valued data, but existing methods are often limited in handling categorical variables. We propose LCMC, a double-loop optimization framework for categorical matrix completion via latent factorization based on a binary tensor representation. In this setting, each categorical entry is encoded as a one-hot vector along a third tensor mode, thereby preserving its discrete, non-ordinal nature.
ND-TNN: Tensor-Neural-Network Approximation for High-Dimensional Nonlocal Diffusion Models
arXiv:2606.08685v1 Announce Type: new Abstract: We study a numerical method, built on the tensor neural network (TNN) architecture introduced in \cite{wang2022tensor}, for solving nonlocal diffusion models in high-dimensional spaces. The tensor-product structure of the TNN ansatz, combined with the separability of the Gaussian kernel, reduces the high-dimensional integrals in the nonlocal energy to products of low-dimensional integrals, which are evaluated by Gauss--Legendre quadrature;...
Vectorized Online POMDP Planning
arXiv:2510.27191v5 Announce Type: replace Abstract: Planning under partial observability is an essential capability of autonomous robots. The Partially Observable Markov Decision Process (POMDP) provides a powerful framework for planning under partial observability problems, capturing the stochastic effects of actions and the limited information available through noisy observations. POMDP solving could benefit tremendously from massive parallelization on today's hardware, but parallelizing...
Symmetric-Tensor Distributional Mixed Method for Fourth-Order Elliptic Singular Perturbation Problem
new Abstract: A symmetric-tensor distributional mixed method for a fourth-order elliptic singular perturbation problem is developed in this paper. The moment variable is approximated by normal-normal continuous symmetric tensor elements, while the scalar variable is represented by an $H^1$-nonconforming virtual element space coupled with a polynomial multiplier on interior subsimplices of codimension two. Optimal parameter-uniform error estimates are derived, independent of the presence of...