Tootfinder

TFZ: Topology-Preserving Compression of 2D Symmetric and Asymmetric Second-Order Tensor Fields
Nathaniel Gorski, Xin Liang, Hanqi Guo, Bei Wang
https://arxiv.org/abs/2508.09235 …

TFZ: Topology-Preserving Compression of 2D Symmetric and Asymmetric Second-Order Tensor Fields
In this paper, we present a novel compression framework, TFZ, that preserves the topology of 2D symmetric and asymmetric second-order tensor fields defined on flat triangular meshes. A tensor field assigns a tensor - a multi-dimensional array of numbers - to each point in space. Tensor fields, such as the stress and strain tensors, and the Riemann curvature tensor, are essential to both science and engineering. The topology of tensor fields captures the core structure of data, and is useful in …

Oscillations and parity violation in gravitational wave background from extra tensor modes
Jaume Garriga, Mohammad Ali Gorji, Fazlollah Hajkarim, Misao Sasaki
https://arxiv.org/abs/2508.08481

Oscillations and parity violation in gravitational wave background from extra tensor modes
Spectator fields which provide additional tensor degrees of freedom, on top of the standard metric tensor perturbations, can produce significant amounts of gravitational waves (GWs). Employing the effective field theory approach for spin-2 fields, we find a universal prediction that linear mixing between the metric and extra tensor modes inevitably induces oscillatory features in the GW spectrum, reminiscent of the so-called neutrino oscillation. Moreover, parity-violating operators in the spin…

Alternating steepest descent methods for tensor completion with applications to spectromicroscopy
Oliver Townsend, Sergey Dolgov, Silvia Gazzola, Misha Kilmer
https://arxiv.org/abs/2506.10661

Alternating steepest descent methods for tensor completion with applications to spectromicroscopy
In this paper we develop two new Tensor Alternating Steepest Descent algorithms for tensor completion in the low-rank $\star_{M}$-product format, whereby we aim to reconstruct an entire low-rank tensor from a small number of measurements thereof. Both algorithms are rooted in the Alternating Steepest Descent (ASD) method for matrix completion, first proposed in [J. Tanner and K. Wei, Appl. Comput. Harmon. Anal., 40 (2016), pp. 417-429]. In deriving the new methods we target the X-ray spectromic…

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Wenjin Qin, Hailin Wang, Jingyao Hou, Jianjun Wang
https://arxiv.org/abs/2506.09594 https:/…

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale high-order tensor data. To alleviate these issue, assisted by the Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies, this article first devises two fast and accurate randomized algorithms for low-rank tensor approx…

Weak Centrality for Certain Tensor Products of $C^\ast$-algebras
Anmol Paliwal, Ranjana Jain
https://arxiv.org/abs/2508.08838 https://arxiv.org/pdf/2508.08…

Weak Centrality for Certain Tensor Products of $C^\ast$-algebras
In this article, we discuss the weak centrality of the tensor product $A\otimes_αB$ of $C^\ast$-algebras $A$ and $B$ in terms of the weak centrality of $A$ and $B$, where $α$ is either the Haagerup or the Banach space projective tensor product. In the due course, we also identify the largest weakly central ideal of $A\otimes_αB$ in certain cases. Centralilty and quasi-centrality of these tensor products are also discussed.

Tensor perturbations in higher derivative gravity theories in $D$ dimensions
Ercan Kilicarslan
https://arxiv.org/abs/2506.10563 https://

Tensor perturbations in higher derivative gravity theories in $D$ dimensions
We study tensor perturbations of the ghost-free generic non-local gravity theory constructed infinite series of higher derivative terms in $D$ dimensions. The infinite series of higher derivative terms are encoded by form factors, the forms of which can be restricted by requiring that the action remains perturbatively free of ghosts and tachyons around maximally symmetric backgrounds for transverse traceless fluctuations. To demonstrate this, we obtain field equations for AdS plane wave metric …

Diagonal Isometric Form for Tensor Product States in Two Dimensions
Benjamin Sappler, Masataka Kawano, Michael P Zaletel, Frank Pollmann
https://arxiv.org/abs/2507.08080

Diagonal Isometric Form for Tensor Product States in Two Dimensions
Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transvers…

Semi-Tensor-Product Based Convolutional Neural Networks
Daizhan Cheng
https://arxiv.org/abs/2506.10407 https://arxiv.org/pdf/2506.104…

Semi-Tensor-Product Based Convolutional Neural Networks
The semi-tensor product (STP) of vectors is a generalization of conventional inner product of vectors, which allows the factor vectors to of different dimensions. This paper proposes a domain-based convolutional product (CP). Combining domain-based CP with STP of vectors, a new CP is proposed. Since there is no zero or any other padding, it can avoid the junk information caused by padding. Using it, the STP-based convolutional neural network (CNN) is developed. Its application to image and thir…

Tensor train representations of Greeks for Fourier-based pricing of multi-asset options
Rihito Sakurai, Koichi Miyamoto, Tsuyoshi Okubo
https://arxiv.org/abs/2507.08482

Tensor train representations of Greeks for Fourier-based pricing of multi-asset options
Efficient computation of Greeks for multi-asset options remains a key challenge in quantitative finance. While Monte Carlo (MC) simulation is widely used, it suffers from the large sample complexity for high accuracy. We propose a framework to compute Greeks in a single evaluation of a tensor train (TT), which is obtained by compressing the Fourier transform (FT)-based pricing function via TT learning using tensor cross interpolation. Based on this TT representation, we introduce two approaches…

Functional Tensor Regression
Tongyu Li, Fang Yao, Anru R. Zhang
https://arxiv.org/abs/2506.09358 https://arxiv.org/pdf/2506.09358

Functional Tensor Regression
Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression, which incorporates both the tensor and functional aspects of the covariate. To address the high dimensionality and functional continuity of the regression coefficient, we employ a low Tucker rank decomposition along with smooth regularization for the functional m…

Tensor-Structured Bayesian Channel Prediction for Upper Mid-Band XL-MIMO Systems
Hongwei Hou, Yafei Wang, Xinping Yi, Wenjin Wang, Dirk T. M. Slock, Shi Jin
https://arxiv.org/abs/2508.08491

Tensor-Structured Bayesian Channel Prediction for Upper Mid-Band XL-MIMO Systems
The upper mid-band balances coverage and capacity for the future cellular systems and also embraces XL-MIMO systems, offering enhanced spectral and energy efficiency. However, these benefits are significantly degraded under mobility due to channel aging, and further exacerbated by the unique near-field (NF) and spatial non-stationarity (SnS) propagation in such systems. To address this challenge, we propose a novel channel prediction approach that incorporates dedicated channel modeling, probab…

Tensor-network formulation of QCD in the strong-coupling expansion
Thomas Samberger, Jacques Bloch, Robert Lohmayer, Tilo Wettig
https://arxiv.org/abs/2508.09891 https://…

Tensor-network formulation of QCD in the strong-coupling expansion
We present a tensor-network formulation for the strong-coupling expansion of QCD with staggered quarks at non-zero chemical potential, for arbitrary number of dimensions, colors, and flavors. We integrate out the gauge and quark degrees of freedom and rewrite the partition function as the complete trace of a tensor network. This network consists of local tensors that contain a numerical and a Grassmann part. We truncate the initial tensor at a fixed order in the inverse coupling $β$ and comput…

Propagation features of Lorentz-violating electrodynamics
E. Goulart, J. E. Ottoni, J. C. C. Felipe
https://arxiv.org/abs/2507.08263 https://

Propagation features of Lorentz-violating electrodynamics
This paper explores some propagation features of electrodynamics in a Lorentz-violating scenario, focusing on a specific CPT-even term within the photon sector of the Standard Model Extension (SME). The study derives a covariant dispersion relation for light propagation in the presence of a Lorentz-violating symmetric tensor field \(C_{ab}(x)\), which reveals a modified light cone structure described by a quartic polynomial. The analysis includes a simplified model where the tensor field assume…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Qiaohua Liu, Jiehui Gu
https://arxiv.org/abs/2508.08557 https://arxiv…

Fast adaptive tubal rank-revealing algorithm for t-product based tensor approximation
Color images and video sequences can be modeled as three-way tensors, which admit low tubal-rank approximations via convex surrogate minimization. This optimization problem is efficiently addressed by tensor singular value thresholding (t-SVT). To mitigate the computational burden of tensor singular value decomposition (t-SVD) in each iteration, this paper introduces an adaptive randomized algorithm for tubal rank revelation in data tensors \(\mathcal{A}\). Our method selectively captures the p…

Semi-inclusive deep inelastic scattering off a tensor-polarized spin-1 target
Jing Zhao, Alessandro Bacchetta, Shunzo Kumano, Tianbo Liu, Ya-jin Zhou
https://arxiv.org/abs/2508.06134

Semi-inclusive deep inelastic scattering off a tensor-polarized spin-1 target
We investigate the semi-inclusive deep inelastic scattering off a tensor-polarized spin-1 target, focusing on the production of an unpolarized hadron. The complete differential cross section is expressed in terms of 23 structure functions, which depend on the spin states of the target and the azimuthal modulations of the final-state hadron. Within the transverse momentum dependent (TMD) factorization framework, we derive the hadronic tensor using quark-quark correlators and quark-gluon-quark co…

Kibble-Zurek dynamical scaling hypothesis in the Google analog-digital quantum simulator of the $XX$ model
Yintai Zhang, Francis A. Bayocboc Jr., Jacek Dziarmaga
https://arxiv.org/abs/2506.10771

Kibble-Zurek dynamical scaling hypothesis in the Google analog-digital quantum simulator of the $XX$ model
The state-of-the-art tensor networks are employed to simulate the Hamiltonian ramp in the analog-digital quantum simulation of the quantum phase transition to the quasi-long-range ordered phase of the 2D square-lattice $XX$ model [Nature 638, 79 (2025)]. We focus on the quantum Kibble-Zurek (KZ) mechanism near the quantum critical point. Using the infinite projected entangled pair state (iPEPS), we simulate an infinite lattice and demonstrate the KZ scaling hypothesis for the $XX$ correlations …

Fast and Provable Hankel Tensor Completion for Multi-measurement Spectral Compressed Sensing
Jinsheng Li, Xu Zhang, Shuang Wu, Wei Cui
https://arxiv.org/abs/2507.04847

Fast and Provable Hankel Tensor Completion for Multi-measurement Spectral Compressed Sensing
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a low-rank Hankel tensor completion task, exploiting the spectral sparsity via the low multilinear rankness of the tensor. Furthermore, we design a scaled gradient descent algorithm for Hankel tensor completion (ScalHT), which integrates the low-rank Tucker deco…

Almost-Optimal Local-Search Methods for Sparse Tensor PCA
Max Lovig, Conor Sheehan, Konstantinos Tsirkas, Ilias Zadik
https://arxiv.org/abs/2506.09959 http…

Almost-Optimal Local-Search Methods for Sparse Tensor PCA
Local-search methods are widely employed in statistical applications, yet interestingly, their theoretical foundations remain rather underexplored, compared to other classes of estimators such as low-degree polynomials and spectral methods. Of note, among the few existing results recent studies have revealed a significant "local-computational" gap in the context of a well-studied sparse tensor principal component analysis (PCA), where a broad class of local Markov chain methods exhibits a notab…

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
Pan Yan
https://arxiv.org/abs/2508.09066 https://

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one…

Raptor: Scalable Train-Free Embeddings for 3D Medical Volumes Leveraging Pretrained 2D Foundation Models
Ulzee An, Moonseong Jeong, Simon A. Lee, Aditya Gorla, Yuzhe Yang, Sriram Sankararaman
https://arxiv.org/abs/2507.08254

Raptor: Scalable Train-Free Embeddings for 3D Medical Volumes Leveraging Pretrained 2D Foundation Models
Current challenges in developing foundational models for volumetric imaging data, such as magnetic resonance imaging (MRI), stem from the computational complexity of training state-of-the-art architectures in high dimensions and curating sufficiently large datasets of volumes. To address these challenges, we introduce Raptor (Random Planar Tensor Reduction), a train-free method for generating semantically rich embeddings for volumetric data. Raptor leverages a frozen 2D foundation model, pretra…

Gauges for quadratic gravity: the extended transverse gauge and the energy-momentum tensor of the massive spin-2 field
Matheus F. S. Alves, L. G. Medeiros, Davi C. Rodrigues
https://arxiv.org/abs/2506.10793

Gauges for quadratic gravity: the extended transverse gauge and the energy-momentum tensor of the massive spin-2 field
We study the 4D Einstein-Hilbert action extension based on the square of the curvature tensors. Analyses of gauge and perturbation modes are often done considering the Teyssandier gauge condition. Although this approach can be useful for other higher-order extensions of quadratic gravity, a generalized transverse (or Lorentz) gauge is clear and sufficient for the present case, as explained here. We provide a detailed analysis of the generalized transverse gauge condition, its residual gauge sym…

This https://arxiv.org/abs/2410.02372 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

Revisiting the Canonicalization for Fast and Accurate Crystal Tensor Property Prediction
Predicting the tensor properties of crystalline materials is a fundamental task in materials science. Unlike single-value property prediction, which is inherently invariant, tensor property prediction requires maintaining O(3) group tensor equivariance. Such equivariance constraint often requires specialized architecture designs to achieve effective predictions, inevitably introducing tremendous computational costs. Canonicalization, a classical technique for geometry, has recently been explore…

Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
Si-Jing Du, Garnet Kin-Lic Chan
https://arxiv.org/abs/2506.08329 https://

Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction uses the fTNS algebra to implement a natural fermionic sign structure and is compatible with standard tensor network algorithms, but gains enhanced expressivity through the neural network parametrization. Using the 1D and 2D Fermi-Hubbard models as benchmarks, …

Replaced article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- Fast Tensor Completion via Approximate Richardson Iteration
Mehrdad Ghadiri, Matthew Fahrbach, Yunbum Kook, Ali Jadbabaie

TensorTouch: Calibration of Tactile Sensors for High Resolution Stress Tensor and Deformation for Dexterous Manipulation
Won Kyung Do, Matthew Strong, Aiden Swann, Boshu Lei, Monroe Kennedy III
https://arxiv.org/abs/2506.08291

TensorTouch: Calibration of Tactile Sensors for High Resolution Stress Tensor and Deformation for Dexterous Manipulation
Advanced dexterous manipulation involving multiple simultaneous contacts across different surfaces, like pinching coins from ground or manipulating intertwined objects, remains challenging for robotic systems. Such tasks exceed the capabilities of vision and proprioception alone, requiring high-resolution tactile sensing with calibrated physical metrics. Raw optical tactile sensor images, while information-rich, lack interpretability and cross-sensor transferability, limiting their real-world u…

Cost-Efficient LLM Training with Lifetime-Aware Tensor Offloading via GPUDirect Storage
Ziqi Yuan, Haoyang Zhang, Yirui Eric Zhou, Apoorve Mohan, I-Hsin Chung, Seetharami Seelam, Jian Huang
https://arxiv.org/abs/2506.06472

Cost-Efficient LLM Training with Lifetime-Aware Tensor Offloading via GPUDirect Storage
We present the design and implementation of a new lifetime-aware tensor offloading framework for GPU memory expansion using low-cost PCIe-based solid-state drives (SSDs). Our framework, TERAIO, is developed explicitly for large language model (LLM) training with multiple GPUs and multiple SSDs. Its design is driven by our observation that the active tensors take only a small fraction (1.7% on average) of allocated GPU memory in each LLM training iteration, the inactive tensors are usually large…

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates
Nis-Luca van H\"ulst, Pia Siegl, Paul Over, Sergio Bengoechea, Tomohiro Hashizume, Mario Guillaume Cecile, Thomas Rung, Dieter Jaksch
https://arxiv.org/abs/2507.05222

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm …

Symmetry and Thermodynamic Bounds on Cross-Coupling Transport in Chiral Liquid Crystals
Shunsuke Takano, Takuya Nakanishi, Kenta Nakagawa, Toru Asahi
https://arxiv.org/abs/2507.08225

Symmetry and Thermodynamic Bounds on Cross-Coupling Transport in Chiral Liquid Crystals
We reformulate the Leslie effects that describe the dynamic cross-couplings in chiral liquid crystals driven by the transport of heat, electric charge, and mass. The Ericksen--Leslie model is extended in the linear response framework by representing nematic order with the Q-tensor. Subsequently, the thermodynamic uncertainty relation is applied to identify the upper bounds of the Leslie cross-coupling coefficients. We reveal that the cross-coupling coefficients are dependent on the scalar order…

Brushstrokes and Tensor Products: Painting with a Monoidal Category
Khyathi Komalan
https://arxiv.org/abs/2508.05482 https://arxiv.org/pdf/2508.05482

Brushstrokes and Tensor Products: Painting with a Monoidal Category
This article offers an intuitive introduction to monoidal categories through the lens of painting, presenting abstract mathematical concepts with visual and tactile analogies. Aimed at curious undergraduates and non-specialists, it seeks to demystify category theory by showing how ideas like the tensor product, associators, and braidings can be understood as compositional tools on a canvas.

Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition
Shibo Li, Yao Zheng
https://arxiv.org/abs/2506.06919 https://

Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition
As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified framework for high-dimensional tensor stochastic regression based on CANDECOMP/PARAFAC (CP) decomposition, which encompasses vector, matrix, and tensor responses and predictors as special cases. Tensor autoregression naturally arises as a special case within th…

Momentum-space Metric Tensor from Nonadiabatic Evolution of Bloch Electrons
Yafei Ren
https://arxiv.org/abs/2506.06439 https://arxiv.…

Momentum-space Metric Tensor from Nonadiabatic Evolution of Bloch Electrons
We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor -- the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase …

Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using $\mathbb{F}_2$
Keren Zhou, Mario Lezcano, Adam Goucher, Akhmed Rakhmati, Jeff Niu, Justin Lebar, Pawel Szczerbuk, Peter Bell, Phil Tillet, Thomas Raoux, Zahi Moudallal
https://arxiv.org/abs/2505.23819

Linear Layouts: Robust Code Generation of Efficient Tensor Computation Using $\mathbb{F}_2$
Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and hardware resources. The increasing complexity of DL algorithms and hardware demands a generic and systematic approach to handling tensor layouts. In this work, we introduce Linear Layouts, a novel approach that models tensor layouts using linear algebra over $\…

Magnetic Moment vs Angular Momentum: Spin Hall Response in Bismuth
Junji Fujimoto, Yuki Izaki, Yuki Fuseya
https://arxiv.org/abs/2508.07200 https://arxiv.o…

Magnetic Moment vs Angular Momentum: Spin Hall Response in Bismuth
Spin currents can carry either spin angular momentum or its associated magnetic moment, which are no longer strictly proportional in multiband systems. Using a multiband $k \cdot p$ model, we compute the intrinsic spin Hall conductivity tensors of elemental Bi. The magnetic-moment tensor emerges about two orders of magnitude larger and far less anisotropic than the angular-momentum tensor, while quasiparticle damping activates otherwise longitudinal components. The magnetic-moment spin Hall ang…

Diagonalizing large-scale quantum many-body Hamiltonians using variational quantum circuit and tensor network
Peng-Fei Zhou, Shuang Qiao, An-Chun Ji, Shi-Ju Ran
https://arxiv.org/abs/2508.06159

Diagonalizing large-scale quantum many-body Hamiltonians using variational quantum circuit and tensor network
Exact diagonalization (ED) is an essential tool for exploring quantum many-body physics but is fundamentally limited by the exponentially-scaled computational complexity. Here, we propose tensor network variational diagonalization (TNVD), which encodes the full eigenenergy spectrum of a quantum many-body Hamiltonian into a matrix product state, and encodes the eigenstates as the evolutions of product states using variational quantum circuit (VQC). Thereby, TNVD reduces the computational complex…

Probing small-scale primordial power spectra with tensor-scalar induced gravitational waves
Di Wu, Zhi-Chao Li, Peng-Yu Wu, Fei-Yu Chen, Jing-Zhi Zhou
https://arxiv.org/abs/2507.07836

Probing small-scale primordial power spectra with tensor-scalar induced gravitational waves
Large-scale primordial perturbations have been well constrained by current cosmological observations, but the properties of small-scale perturbations remain elusive. This study focuses on second-order tensor-scalar induced gravitational waves (TSIGWs) generated by large-amplitude primordial scalar and tensor perturbations on small scales. We provide the analytical expressions for the kernel functions and the corresponding energy density spectra of second-order TSIGWs. By combining observations …

Lie algebra homology with coefficients tensor products of the adjoint representation in relative polynomial degree 2
Geoffrey Powell
https://arxiv.org/abs/2507.03453

Lie algebra homology with coefficients tensor products of the adjoint representation in relative polynomial degree 2
The homology of free Lie algebras with coefficients in tensor products of the adjoint representation working over Q contains important information on the homological properties of polynomial outer functors on free groups. The latter category was introduced in joint work with Vespa, motivated by the study of higher Hochschild homology of wedges of circles. There is a splitting of this homology by polynomial degree (for polynomiality with respect to the generators of the free Lie algebra) and o…

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_{\alpha}$-tensor
Jueru Liu, Lizhu Sun, Changjiang Bu
https://arxiv.org/abs/2507.02650

The ordering of hypertrees and unicyclic hypergraphs by the traces of $\mathcal{A}_α$-tensor
For a real number $α\in[0,1]$ and a $k$-uniform hypergraph $\mathcal{H}$, $\mathcal{A}_α(\mathcal{H})=α\mathcal{D}(\mathcal{H})+(1-α)\mathcal{A}(\mathcal{H})$ is called the $\mathcal{A}_α$-tensor of $\mathcal{H}$, where $\mathcal{D}(\mathcal{H})$ and $\mathcal{A}(\mathcal{H})$ are the degree tensor and adjacency tensor of $\mathcal{H}$, respectively. The sum of the $d$-th powers of all eigenvalues of $\mathcal{A}_α(\mathcal{H})$ is called the $d$-th order $\mathcal{A}_α$-spectral moment …

Symbolic identification of tensor equations in multidimensional physical fields
Tianyi Chen, Hao Yang, Wenjun Ma, Jun Zhang
https://arxiv.org/abs/2507.01466

Symbolic identification of tensor equations in multidimensional physical fields
Recently, data-driven methods have shown great promise for discovering governing equations from simulation or experimental data. However, most existing approaches are limited to scalar equations, with few capable of identifying tensor relationships. In this work, we propose a general data-driven framework for identifying tensor equations, referred to as Symbolic Identification of Tensor Equations (SITE). The core idea of SITE--representing tensor equations using a host-plasmid structure--is ins…

Holographic Correlators from Thermal Bootstrap
Ilija Buri\'c, Ivan Gusev, Andrei Parnachev
https://arxiv.org/abs/2508.08373 https://arxiv.org/pdf/2508.…

Holographic Correlators from Thermal Bootstrap
Holographic thermal two-point functions can be analyzed using the operator product expansion which contains contributions from both multi-stress-tensor and double-trace operators. The former can be computed by analyzing the bulk equation of motion in a near-boundary expansion, but the latter has remained elusive-in practice, one resorts to solving a partial differential equation with limited accuracy. We show that imposing the Euclidean periodicity condition on the holographic correlator (also …

Modern search demands scalable personalisation. Join Piotr Kobziakowski
at this year's Berlin Buzzwords to discover how Vespa's multi-stage ranking and tensor framework can be used for hybrid queries, multimodal retrieval, and real-time machine learning. Learn how to deploy low-latency, high-relevance search systems at petabyte scale.
Learn more:

Vespa.ai’s Personalized Search: Advanced Ranking & Tensor framework
Today’s applications require search engines to unify text, vectors, and business logic with millisecond latency at petabyte scale. It’s not easy to balance speed, relevance, and personalization for a large user population and a billion scale item base. Vespa.ai, the open-source engine powering Yahoo, Perplexity, Qwant, Vinted, Spotify addresses this through multi-stage ranking with close to data tensor operations and easy to understand custom functions. Vespa’s phased architecture enables…

Tensor powers of representations of (diagram) monoids
David He, Daniel Tubbenhauer
https://arxiv.org/abs/2508.04054 https://arxiv.org/pdf/2508.04054…

Tensor powers of representations of (diagram) monoids
We study tensor powers of representations of finite monoids, focusing on the growth behavior of their composition length and the number of indecomposable summands. Special attention is given to diagram monoids such as the Temperley-Lieb, Motzkin, and Brauer monoids. For these examples, we compute explicit data, including some character tables, and analyze patterns in the decomposition of their tensor powers.

High precision measurement of phi-nucleon cross section using a tensor polarized deuteron target
Mark M. Dalton, Alexandre Deur, Chris D. Keith, Nadia Fomin, Misak Sargsian
https://arxiv.org/abs/2508.06481

High precision measurement of phi-nucleon cross section using a tensor polarized deuteron target
We propose to measure the $ϕ$-nucleon cross section $σ_{ϕN}$ to solve the longstanding puzzle of whether $σ_{ϕN} \simeq 10$ mb, as extracted from photoproduction, or $\sim$30 mb, as obtained from nuclear rescattering. CLAS data demonstrated that even precision data for unpolarized $ϕ$ photoproduction are insufficient to unambiguously extract $σ_{ϕN}$, allowing the possibilities of both $σ_{ϕN}$ values. However, as it often happens, the additional spin degrees of freedom afforded by a …

Prime Factorization Equation from a Tensor Network Perspective
Alejandro Mata Ali, Jorge Mart\'inez Mart\'in, Sergio Mu\~niz Subi\~nas, Miguel Franco Hernando, Javier Sedano, \'Angel Miguel Garc\'ia-Vico
https://arxiv.org/abs/2508.00907

Prime Factorization Equation from a Tensor Network Perspective
This paper presents an exact and explicit equation for prime factorization, along with an algorithm for its computation. The proposed method is based on the MeLoCoToN approach, which addresses combinatorial optimization problems through classical tensor networks. The presented tensor network performs the multiplication of every pair of possible input numbers and selects those whose product is the number to be factorized. Additionally, in order to make the algorithm more efficient, the number an…

Quantics Tensor Train for solving Gross-Pitaevskii equation
Aleix Bou-Comas, Marcin P{\l}odzie\'n, Luca Tagliacozzo, Juan Jos\'e Garc\'ia-Ripoll
https://arxiv.org/abs/2507.03134

Quantics Tensor Train for solving Gross-Pitaevskii equation
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutt…

Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
Adri\'an Andrada, Mar\'ia Laura Barberis, Beatrice Brienza
https://arxiv.org/abs/2508.07889 https://…

Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that the holonomy algebra of the Obata connection is always an abelian subalgebra of $\mathfrak{sl}(n, \mathbb{H})$: to establish this, we prove the $\mathbb{H}$-solvable conjecture for 2-step hypercom…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[2/4]:
- Statistical Coherence Alignment for Large Language Model Representation Learning Through Tensor F...
Gale, Aldington, Thistlewood, Tattershall, Wentworth, Enoasmo

Tensor Renormalization Group Meets Computer Assistance
Nikolay Ebel, Tom Kennedy, Slava Rychkov
https://arxiv.org/abs/2506.03247 https://

Tensor Renormalization Group Meets Computer Assistance
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here we introduce a new renormalization map - the 2x1 map - which coarse-grains the lattice anisotropically by a factor of two in one direction followed by a 90-degree rotation. We develop a novel graphical language that translates the action of the 2x1 map into a system of inequalities on tensor components, with rigorous e…

Statistical Limits for Finite-Rank Tensor Estimation
Riccardo Rossetti, Galen Reeves
https://arxiv.org/abs/2506.06749 https://arxiv.o…

Statistical Limits for Finite-Rank Tensor Estimation
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each observation depends on the interactions among a finite number of unknown parameters. Our main results provide asymptotically exact formulas for the mutual information (equivalently, the free energy) as well as the minimum mean-squared error in the Bayes-optimal sett…

Digital Quantum Simulation of Flat-Band and All-Bands-Flat Dynamics for Tunable Quantum Transport
Mrinal Kanti Giri, Pochung Chen
https://arxiv.org/abs/2508.08734 https://

Digital Quantum Simulation of Flat-Band and All-Bands-Flat Dynamics for Tunable Quantum Transport
We study the dynamics on the flat-band (FB) and all-bands-flat (AFB) lattices using a digital quantum computer. By utilizing an advanced tensor network method to compress the quantum circuit, we overcome the intrinsic limitations of current noisy intermediate-scale quantum (NISQ) computers. This enables high-fidelity simulations of time evolution over extended timescales and various interesting dynamical behaviours are observed in our digital quantum simulation. We start from the quantum simula…

W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
Daniel Drimbe, Stefaan Vaes
https://arxiv.org/abs/2507.04691 https://

W*-correlations of II$_1$ factors and rigidity of tensor products and graph products
A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for tensor products and graph products of II$_1$ factors. As a consequence, we construct the first uncountable family of discrete groups $Γ$ that are not von Neumann equivalent, which means that their group von Neumann algebras $L(Γ)$ are not W*-correlated, and wh…

(2 1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
Kansei Inamura, Sheng-Jie Huang, Apoorv Tiwari, Sakura Schafer-Nameki
https://arxiv.org/abs/2506.09177

(2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In this paper, we provide a systematic lattice model construction for all such gapped phases. Specifically, we consider ``All boson type" fusion 2-category symmetries, all of which are obtainable from 0-form symmetry groups $G$ (possibly with an 't Hooft anomaly) v…

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
Domingo Barrera, Francesco Dell'Accio, Filomena Di Tommaso, Salah Eddargani, Mar\'ia Jos\'e Ib\'a\~nez, Francesco Larosa, Federico Nudo, Juan F. Reinoso
https://arxiv.org/abs/2508.07764

Multinode Shepard Functions and Tensor Product Polynomial Interpolation: Applications to Digital Elevation Models
The paper presents an in-depth exploration of the multinode Shepard interpolant on a regular rectangular grid, demonstrating its efficacy in reconstructing surfaces from DEM data. Additionally, we study the approximation order associated to this interpolant and present a detailed algorithm for reconstructing surfaces. Numerical tests showcase the effectiveness of the proposed algorithm.

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- On a variant of the Grothendieck inequality and estimates on tensor product norms
Rajeev Gupta, Gadadhar Misra, Samya Kumar Ray

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Convexity in tensor triangular geometry
Changhan Zou
https://

Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral
Sami Kaya, Pratik Rath, Kyle Ritchie
https://arxiv.org/abs/2506.10064 ht…

Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral
Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the …

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
Haiyang Yu, Yuchao Lin, Xuan Zhang, Xiaofeng Qian, Shuiwang Ji
https://arxiv.org/abs/2506.09398

Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames
We consider the task of predicting Hamiltonian matrices to accelerate electronic structure calculations, which plays an important role in physics, chemistry, and materials science. Motivated by the inherent relationship between the off-diagonal blocks of the Hamiltonian matrix and the SO(2) local frame, we propose a novel and efficient network, called QHNetV2, that achieves global SO(3) equivariance without the costly SO(3) Clebsch-Gordan tensor products. This is achieved by introducing a set o…

Tidal effects in gravitational and scalar waveforms and fluxes to one post-Newtonian order in massless scalar-tensor theories
Eve Dones, Laura Bernard
https://arxiv.org/abs/2507.07676

Tidal effects in gravitational and scalar waveforms and fluxes to one post-Newtonian order in massless scalar-tensor theories
Within scalar-tensor (ST) theories, neutron stars in binary systems experience tidal deformations caused by both their companion and the scalar field. These deformations are strongly correlated to the star's internal structure and composition. Accurately modeling their imprint on the emitted gravitational waves will be essential for interpreting the high-precision data expected from future detectors and for disentangling potential signatures of modified gravity from those arising due to the pro…

Quantum Circuit Complexity of Matrix-Product Unitaries
Georgios Styliaris, Rahul Trivedi, J. Ignacio Cirac
https://arxiv.org/abs/2508.08160 https://arxiv.o…

Quantum Circuit Complexity of Matrix-Product Unitaries
Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit since the individual tensors describing the MPU are not unitary. In this paper, we show that a large class of MPUs can be implemented with a polynomial-depth quantum circuit. For an $N$-site MPU built from a repeated bulk tensor with open boundary, we explici…

Multiple Axions Save High-Scale Inflation
Dan Kondo, Hitoshi Murayama
https://arxiv.org/abs/2507.07973 https://arxiv.org/pdf/2507.079…

Multiple Axions Save High-Scale Inflation
Many models of dark matter QCD axion requires inflation at a scale $H_{\text{inf}} \lesssim 10^{6}$~GeV and hence does not allow for a detectable tensor mode fluctuation. This is because the domain wall problem forces the Peccei--Quinn symmetry to be broken during the inflation and the axions to be produced by the misalignment mechanism. We point out that theories with multiple axions can evade this constraint and allow for a high-scale inflation with detectable tensor mode. It only requires a …

Primordial Gravitational Waves in Parity-violating Symmetric Teleparallel Gravity
Rongrong Zhai, Chengjie Fu, Xiangyun Fu, Puxun Wu, Hongwei Yu
https://arxiv.org/abs/2508.06984 …

Primordial Gravitational Waves in Parity-violating Symmetric Teleparallel Gravity
In this paper, we investigate the inflationary phenomenology of parity-violating (PV) extensions of symmetric teleparallel gravity by applying this PV gravity theory to axion inflation. The presence of PV terms induces velocity birefringence in the tensor perturbations. During inflation, when the inflaton rapidly traverses the cliff-like region in its potential, the tensor modes at specific scales for one of the two circular polarization states undergo significant amplification due to tachyonic…

An analytic approach to the stress energy tensor in quantum field theory
Alexander Strohmaier
https://arxiv.org/abs/2508.00487 https://arxiv.org/pdf/2508.0…

An analytic approach to the stress energy tensor in quantum field theory
We discuss a framework for quantum fields in curved spacetimes that possess a stress energy tensor as a connection one form on a suitable moduli space of metrics. In generic spacetimes the existence of such a tensor is thought to be a replacement for the existence of symmetries that the Minkowski theory relies on. It is shown that the local time-slice property and the implementability of local isometries is a consequence of the existence of a stress energy tensor that is a local field. We prove…

Compression, simulation, and synthesis of turbulent flows with tensor trains
Stefano Pisoni, Raghavendra Dheeraj Peddinti, Egor Tiunov, Siddhartha E. Guzman, Leandro Aolita
https://arxiv.org/abs/2506.05477

Compression, simulation, and synthesis of turbulent flows with tensor trains
Numerical simulations of turbulent fluids are paramount to real-life applications, from predicting and modeling flows to diagnostic purposes in engineering. However, they are also computationally challenging due to their intrinsically non-linear dynamics, which requires a very high spatial resolution to accurately describe them. A promising idea is to represent flows on a discrete mesh using tensor trains (TTs), featuring a convenient scaling of the number of parameters with the mesh size. Howe…

The thermal backreaction of a scalar field in de Sitter spacetime
Nikos Irges, Antonis Kalogirou, Fotis Koutroulis
https://arxiv.org/abs/2507.08774 https:/…

The thermal backreaction of a scalar field in de Sitter spacetime
We argue that a scalar field in de Sitter spacetime should feel explicit thermal effects associated with its curvature. Starting from the Bunch-Davies vacuum and a scalar field with small mass compared to the de Sitter curvature, we use the thermo-field dynamics formalism in order to expose these thermal effects. We compute the thermal Wightman function connecting two spacetime points and from it, via the point-splitting regularization technique, the renormalized thermal energy-momentum tensor.…

Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics
Qian-Can Chen, I-Kang Liu, Jheng-Wei Li, Chia-Min Chung
https://arxiv.org/abs/2507.04279

Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics
We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics…

A Tight Lower Bound for the Approximation Guarantee of Higher-Order Singular Value Decomposition
Matthew Fahrbach, Mehrdad Ghadiri
https://arxiv.org/abs/2508.06693 https://

A Tight Lower Bound for the Approximation Guarantee of Higher-Order Singular Value Decomposition
We prove that the classic approximation guarantee for the higher-order singular value decomposition (HOSVD) is tight by constructing a tensor for which HOSVD achieves an approximation ratio of $N/(1+\varepsilon)$, for any $\varepsilon > 0$. This matches the upper bound of De Lathauwer et al. (2000a) and shows that the approximation ratio of HOSVD cannot be improved. Using a more advanced construction, we also prove that the approximation guarantees for the ST-HOSVD algorithm of Vannieuwenhoven …

Applications of Weak Metric Structures to Non-Symmetrical Gravitational Theory
Milan Zlatanovi\'c, Vladimir Rovenski
https://arxiv.org/abs/2508.08021 https://

Applications of Weak Metric Structures to Non-Symmetrical Gravitational Theory
Linear connections satisfying the Einstein metricity condition are important in the study of generalized Riemannian manifolds $(M,G=g+F)$, where the symmetric part $g$ of $G$ is a non-degenerate $(0,2)$-tensor, and $F$ is the skew-symmetric part. Such structures naturally arise in spacetime models in theoretical physics, where $F$ can be defined as an almost complex or almost contact metric (a.c.m.) structure. In the paper, we first study more general models, where $F$ has constant rank and is …

An Image Noise Level Estimation Based on Tensor T-Product
Hanxin Liu, Yisheng Song
https://arxiv.org/abs/2507.20515 https://arxiv.org/pdf/2507.20515…

An Image Noise Level Estimation Based on Tensor T-Product
Currently, the noise level of color images is estimated by many algorithms through separate selection of each page of the third-order tensor using sliding blocks of size ${M_1} \times {M_1}$. The data structure of the tensor is disrupted by this method, leading to errors in the estimation results. In order not to disrupt the data structure of the tensor, we directly select the tensor using a sliding block of size ${M_1} \times {M_1} \times 3$ and then re-arrange it. The newly obtained tensor is…

Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization
Teng Xue, Amirreza Razmjoo, Yan Zhang, Sylvain Calinon
https://arxiv.org/abs/2507.04949

Unifying Robot Optimization: Monte Carlo Tree Search with Tensor Factorization
Many robotic tasks, such as inverse kinematics, motion planning, and optimal control, can be formulated as optimization problems. Solving these problems involves addressing nonlinear kinematics, complex contact dynamics, and long-horizon planning, each posing distinct challenges for state-of-the-art optimization methods. To efficiently solve a wide range of tasks across varying scenarios, researchers either develop specialized algorithms for the task to achieve, or switch between different fram…

Hybrid quantum tensor networks for aeroelastic applications
M. Lautaro Hickmann (Institute for AI Safety and Security, German Aerospace Center), Pedro Alves (Institute for AI Safety and Security, German Aerospace Center), David Quero (Institute of Aeroelasticity, German Aerospace Center), Friedhelm Schwenker (Institute of Neural Information Processing, University of Ulm, Ulm, Germany), Hans-Martin Rieser (Institute for AI Safety and Security, German Aerospace Center)

Hybrid quantum tensor networks for aeroelastic applications
We investigate the application of hybrid quantum tensor networks to aeroelastic problems, harnessing the power of Quantum Machine Learning (QML). By combining tensor networks with variational quantum circuits, we demonstrate the potential of QML to tackle complex time series classification and regression tasks. Our results showcase the ability of hybrid quantum tensor networks to achieve high accuracy in binary classification. Furthermore, we observe promising performance in regressing discrete…

On quantum creation of a toroidal universe
Alan H. Guth, Alexander Vilenkin
https://arxiv.org/abs/2508.08747 https://arxiv.org/pdf/2508.08747

On quantum creation of a toroidal universe
We consider the quantum creation of a universe with flat spatial sections and the topology of a 3-torus, taking into account the effect of Casimir energy. We show that the corresponding instantons are singular. Since these instantons describe universes originating in a state of infinite energy, we argue that they cannot be interpreted as quantum creation from `nothing'. If quantum corrections to the energy-momentum tensor are neglected, the spacetime of the toroidal universe reduces to de Sitte…

Normed representations of weight quivers
Yu-Zhe Liu
https://arxiv.org/abs/2507.06962 https://arxiv.org/pdf/2507.06962

Normed representations of weight quivers
Let $A$ and $B$ be two tensor rings given by weight quivers. We introduce norms for tensor rings and $(A,B)$-bimodules, and define an important category $\mathscr{A}^p_ς$ in this paper. We show that $\mathscr{A}^p_ς$ has an initial object such that Daniell integration, Bochner integration, Lebesgue integration, Stone--Weierstrass Approximation Theorem, power series expansion, and Fourier series expansion are morphisms in $\mathscr{A}^p_ς$ start with this initial object.

Inflationary Models with Gauss-Bonnet Coupling in Light of ACT Observations
Yigan Zhu, Qing Gao, Yungui Gong, Zhu Yi
https://arxiv.org/abs/2508.09707 https://

Inflationary Models with Gauss-Bonnet Coupling in Light of ACT Observations
Recent analyses combining Atacama Cosmology Telescope (ACT) data with other cosmological datasets report a higher scalar spectral index $n_s$, creating tension with a wide range of inflationary models. Since a Gauss-Bonnet term with a coupling function $ξ(ϕ) = 3λ/[4V(ϕ)]$ leaves $n_s$ nearly unchanged (up to a field rescaling) while reducing the tensor-to-scalar ratio $r$ by a factor $(1-λ)$, so choosing $(1-λ)$ sufficiently small effectively removes $r$ as a limiting observable, making i…

Correlation functions of von Neumann entropy
Mathew W. Bub, Allic Sivaramakrishnan
https://arxiv.org/abs/2506.10917 https://arxiv.org…

Correlation functions of von Neumann entropy
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which are special cases of these correlators. Then we specialize to two spacelike-separated spherical subregions in conformal field theories. We present direct computations of the vacuum two-point function that confirm its equivalence to the stress-tensor conformal …

Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions
Atsushi Ueda, Sander De Meyer, Adwait Naravane, Victor Vanthilt, Frank Verstraete
https://arxiv.org/abs/2508.05406

Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions
We propose a new tensor network renormalization group (TNR) scheme based on global optimization and introduce a new method for constructing the finite-temperature density matrix of two-dimensional quantum systems. Combining these two into a new algorithm called thermal tensor network renormalization (TTNR), we obtain highly accurate conformal field theory (CFT) data at thermal transition points. This provides a new and efficient route for numerically identifying phase transitions, offering an a…

A Tensor Train Approach for Deterministic Arithmetic Operations on Discrete Representations of Probability Distributions
Gerhard Kirsten, Bilgesu Bilgin, Janith Petangoda, Phillip Stanley-Marbell
https://arxiv.org/abs/2508.06303

A Tensor Train Approach for Deterministic Arithmetic Operations on Discrete Representations of Probability Distributions
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers from the curse of dimensionality, as memory and computational costs grow exponentially with dimension. Monte Carlo methods require thousands to billions of samples, incurring high computational costs and producing inconsistent results due to stochasticity. We p…

Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space
Junichi Takahashi, Shousuke Ohmori
https://arxiv.org/abs/2508.06923 https…

Rigged Hilbert Space Formulation of Quantum Thermo Field Dynamics and Mapping to Rigged Liouville Space
The rigged Hilbert space, a triplet extension of the Hilbert space, provides a mathematically rigorous foundation for quantum mechanics by extending the Hilbert space to accommodate generalized eigenstates. In this paper, we construct a triplet structure for the thermal space arising in Thermo Field Dynamics with the aid of the tensor product formulation of rigged Hilbert spaces, a formalism that reformulates thermal averages as pure-state expectation values in a doubled Hilbert space. We then …

This https://arxiv.org/abs/2505.09714 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Overcoming the entanglement barrier with sampled tensor networks
The rapid growth of entanglement under unitary time evolution is the primary bottleneck for modern tensor-network techniques--such as Matrix Product States (MPS)--when computing time-dependent expectation values. This {entanglement barrier} restricts classical simulations and, conversely, underpins the quantum advantage anticipated from future devices. Here we show that, for one-dimensional Hamiltonian dynamics, the spatio-temporal tensor network encoding the evolved wave function amplitudes ca…

This https://arxiv.org/abs/2505.06990 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some critical Riemannian metrics and Thorpe-type conditions
Let \((M, g)\) be a compact, closed Riemannian manifold of dimension \(n\), and let \(k\) be an integer such that \(2 \leq 2k \leq n\). Denote by \(R^k\) the \(k\)-th Thorpe tensor, defined as the \(k\)-fold exterior product of the Riemann curvature tensor \(R\). We consider the geometric functionals $ H_{2k}(g) := \int_M \operatorname{tr}(R^k) \, \mathrm{dvol}_g$ and $ G_{2k}(g) :=\int_M \|R^k\|^2 \, \mathrm{dvol}_g,$ where \(\operatorname{tr}(R^k)\) denotes the full contraction (tra…

An Efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series
Yuxi Cai, Lan Li, Yize Wang, Guodong Li
https://arxiv.org/abs/2506.01658

An Efficient and Interpretable Autoregressive Model for High-Dimensional Tensor-Valued Time Series
In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor order. Conversely, canonical polyadic (CP) decomposition maintains efficiency but lacks a precise statistical interpretation. To attain both interpretability and powerful dimension reduction, this paper proposes a novel approach under the supervised factor mode…

Replaced article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Support theories for non-Noetherian tensor triangulated categories
Changhan Zou

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
A. Tawfik (Egyptian Ctr. Theor. Phys., Cairo,Future U. in Egypt), S. G. Elgendi (Islamic U. in Madinah), M. Hanafy (Benha U.)
https://arxiv.org/abs/2506.08254

Vacuum Homogeneous and Nonhomogeneous Metrics with Conventional and Quantized Metric Tensor: Singular or Nonsingular Solution
To investigate whether the Universe underwent a singularity or maintained a nonsingular state, we carry out analytical and numerical analyses of the evolution of the Raychaudhuri equations in vacuum, alongside homogeneous and nonhomogeneous cosmic backgrounds. The results obtained from the Schwarzschild, Friedmann--Lemaitre--Robertson--Walker (FLRW), and Einstein--Gilbert--Straus (EGS) metrics are systematically compared. Analyzing the results from both, conventional and quantized metric tensor…

On the computation of tensor functions under tensor-tensor multiplications with linear maps
Jeong-Hoon Ju, Susana Lopez-Moreno
https://arxiv.org/abs/2506.18713

On the computation of tensor functions under tensor-tensor multiplications with linear maps
In this paper we study the computation of both algebraic and non-algebraic tensor functions under the tensor-tensor multiplication with linear maps. In the case of algebraic tensor functions, we prove that the asymptotic exponent of both the tensor-tensor multiplication and the tensor polynomial evaluation problem under this multiplication is the same as that of the matrix multiplication, unless the linear map is injective. As for non-algebraic functions, we define the tensor geometric mean and…

Superactivation of Bell nonlocality in pure anyonic states
Cheng-Qian Xu, Wenhao Ye, Li You
https://arxiv.org/abs/2506.08919 https://…

Superactivation of Bell nonlocality in pure anyonic states
Standard quantum information theory is founded on the assumption that multi-party state space possesses a tensor product structure. Anyons, as quasiparticles in two-dimensional systems, exhibit unique entanglement properties that differ from the conventional quantum systems, resulting from the absence of a tensor product structure in their state spaces. This motivates us to investigate the relationship between Bell nonlocality and entanglement in anyonic states. Specifically, we find that certa…

Photon polarization tensor in presence of constant and arbitrary electric field
Luis A. Hern\'andez, Juan D. Mart\'inez-S\'anchez, R. Zamora
https://arxiv.org/abs/2508.03133

Photon polarization tensor in presence of constant and arbitrary electric field
We compute the photon polarization tensor at one-loop order in the presence of a constant and uniform electric field. Our calculation is carried out for arbitrary field strength using the Schwinger proper-time formalism, and we explicitly derive an expression for the polarization tensor without approximations. We also present a complementary derivation within the strong field approximation. Our main contribution lies in expressing the polarization tensor in terms of a physically motivated tenso…

The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory
Guojun Huang, Kai Zhou
https://arxiv.org/abs/2507.05303 https:…

The Neural Networks with Tensor Weights and the Corresponding Fermionic Quantum Field Theory
In this paper, we establish a theoretical connection between complex-valued neural networks (CVNNs) and fermionic quantum field theory (QFT), bridging a fundamental gap in the emerging framework of neural network quantum field theory (NN-QFT). While prior NN-QFT works have linked real-valued architectures to bosonic fields, we demonstrate that CVNNs equipped with tensor-valued weights intrinsically generate fermionic quantum fields. By promoting hidden-to-output weights to Clifford algebra-valu…

GW170817 Viable Einstein-Gauss-Bonnet Inflation Compatible with the Atacama Cosmology Telescope Data
S. D. Odintsov, V. K. Oikonomou
https://arxiv.org/abs/2506.08193

GW170817 Viable Einstein-Gauss-Bonnet Inflation Compatible with the Atacama Cosmology Telescope Data
In this work we investigate several Einstein-Gauss-Bonnet models that are compatible with the GW170817 event, the Atacama Cosmology Telescope data and the BICEP/Keck updated Planck constraints on the tensor-to-scalar ratio. We consider two distinct classes of Einstein-Gauss-Bonnet theories, which are equally successful for GW170817-compatible model building and we examine their viability against the Atacama Cosmology Telescope data and the updated Planck constraints on the tensor-to-scalar rati…

sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation
Renjie Xu, Chong Wu, Maolin Che, Zhuoheng Ran, Yimin Wei, Hong Yan
https://arxiv.org/abs/2506.08670

sparseGeoHOPCA: A Geometric Solution to Sparse Higher-Order PCA Without Covariance Estimation
We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and reformulating the resulting subproblems as structured binary linear optimization problems, our method transforms the original nonconvex sparse objective into a tractable geometric form. This eliminates the need for explicit covariance estimation and iterative …

Preheating and gravitational waves in large-field hilltop inflation
Diganta Das, Shreyas Revankar
https://arxiv.org/abs/2508.07442 https://arxiv.org/pdf/25…

Preheating and gravitational waves in large-field hilltop inflation
The combined Planck, BICEP/Keck Array and BAO measurements of the scalar spectral index and the tensor-to-scalar ratio from the cosmic microwave background observations severely constrain or completely rule out several models of inflationary potentials. On the other hand, the data seems to favor concave potentials over convex ones. In this paper, we study preheating and gravitational waves after inflation in a large-field, regularized hilltop potential where inflation takes place in the concave…

From Tensor Algebras to Hyperbolic Kac-Moody Algebras
Axel Kleinschmidt, Hannes Malcha, Hermann Nicolai
https://arxiv.org/abs/2508.03815 https://arxiv.org/…

From Tensor Algebras to Hyperbolic Kac-Moody Algebras
We propose a novel approach to study hyperbolic Kac-Moody algebras, and more specifically, the Feingold-Frenkel algebra $\mathfrak{F}$, which is based on considering the tensor algebra of level-one states before descending to the Lie algebra by converting tensor products into multiple commutators. This method enables us to exploit the presence of mutually commuting coset Virasoro algebras, whose number grows without bound with increasing affine level. We present the complete decomposition of th…

Calculating the Projective Norm of higher-order tensors using a gradient descent algorithm
Aaditya Rudra, Maria Anastasia Jivulescu
https://arxiv.org/abs/2508.07933 https://

Calculating the Projective Norm of higher-order tensors using a gradient descent algorithm
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in computing due to the complexity of the exponentially growing parameter space for higher-order tensors. We develop a novel gradient descent algorithm to estimate the projective norm of higher-order tensors. The algorithm guarantees convergence to a minimum nuclear r…

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
Wei-guo Ma, Yun-Hao Shi, Kai Xu, Heng Fan
https://arxiv.org/abs/2508.07610 https://

Tomography-assisted noisy quantum circuit simulator using matrix product density operators
In recent years, efficient quantum circuit simulations incorporating ideal noise assumptions have relied on tensor network simulators, particularly leveraging the matrix product density operator (MPDO) framework. However, experiments on real noisy intermediate-scale quantum (NISQ) devices often involve complex noise profiles, encompassing uncontrollable elements and instrument-specific effects such as crosstalk. To address these challenges, we employ quantum process tomography (QPT) techniques …

Norming Sets for Tensor and Polynomial Sketching
Yifan Zhang, Joe Kileel
https://arxiv.org/abs/2506.05174 https://arxiv.org/pdf/2506.…

Norming Sets for Tensor and Polynomial Sketching
This paper develops the sketching (i.e., randomized dimension reduction) theory for real algebraic varieties and images of polynomial maps, including, e.g., the set of low rank tensors and tensor networks. Through the lens of norming sets, we provide a framework for controlling the sketching dimension for \textit{any} sketch operator used to embed said sets, including sub-Gaussian, fast Johnson-Lindenstrauss, and tensor structured sketch operators. Leveraging norming set theory, we propose a ne…

Lower dimensional black holes in nonlinear electrodynamics: causal structure and scalar perturbations
Rodrigo Dal Bosco Fontana
https://arxiv.org/abs/2506.09303

Lower dimensional black holes in nonlinear electrodynamics: causal structure and scalar perturbations
We study the charged black hole solutions of a 2+1 nonlinear electrodynamical theory with cosmological constant. Considered as a one-parameter group of theories (the exponent of the squared Maxwell tensor) the causal structure of all possible black holes is scrutinized. We analyze the singularity character that each theory delivers together with their horizons and the plausible limitations in the black hole charges. The investigation demonstrates a rich structure of three different groups of th…

Tensor network algorithm to solve polaron impurity problems
Ruofan Chen, Lei Gu, Chu Guo
https://arxiv.org/abs/2507.05580 https://arx…

Tensor network algorithm to solve polaron impurity problems
The polaron problem is a very old problem in condensed matter physics that dates back to the thirties, but still remain largely unsolved today, especially when electron-electron interaction is taken into consideration. The presence of both electron-electron and electron-phonon interactions in the problem invalidates most existing numerical methods, either computationally too expensive or simply intractable. The continuous time quantum Monte Carlo (CTQMC) methods could tackle this problem, but a…

Angular $k$-uniformity and the Hyperinvariance of Holographic Codes
Wanli Cheng
https://arxiv.org/abs/2506.06577 https://arxiv.org/pd…

Angular $k$-uniformity and the Hyperinvariance of Holographic Codes
Holographic quantum error-correcting codes, often realized through tensor network architectures, have emerged as compelling toy models for exploring bulk-boundary duality in AdS-CFT. By encoding bulk information into highly entangled boundary degrees of freedom, they capture key features of holography such as subregion duality, operator reconstruction, and complementary recovery. Among them, hyperinvariant tensor networks-characterized by the inclusion of edge tensors and the enforcement of mul…

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
Heiko Gimperlein, Ruma R. Maity
https://arxiv.org/abs/2506.04880

Numerical analysis for constrained and unconstrained Q-tensor energies for liquid crystals
This paper introduces a comprehensive finite element approximation framework for three-dimensional Landau-de Gennes $Q$-tensor energies for nematic liquid crystals, with a particular focus on the anisotropy of the elastic energy and the Ball-Majumdar singular potential. This potential imposes essential physical constraints on the eigenvalues of the $Q$-tensor, ensuring realistic modeling. We address the approximation of regular solutions to nonlinear elliptic partial differential equations with…

Truncating loopy tensor networks by zero-mode gauge fixing
Ihor Sokolov, Yintai Zhang, Jacek Dziarmaga
https://arxiv.org/abs/2508.00338 https://arxiv.org/p…

Truncating loopy tensor networks by zero-mode gauge fixing
Loopy tensor networks have internal correlations that often make their compression inefficient. We show that even local bond optimization can make better use of the insight it has locally into relevant loop correlations. By cutting the bond, we define a set of states whose linear dependence can be used to truncate the bond dimension. The linear dependence is eliminated with zero modes of the states' metric tensor. The method is illustrated by a series of examples for the infinite pair entangled…

Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation
Sanaa Khobizy
https://arxiv.org/abs/2506.22292 ht…

Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of such networks into two components: a low-rank signal tensor that captures the essential network structure and a zero-mean noise tensor that accounts for random variations. Building on recent advancements in tensor decomposition and random tensor theory, we intr…

Higher-Order Newton-Cartan Gravity
Biel Cardona, Luca Romano
https://arxiv.org/abs/2507.05489 https://arxiv.org/pdf/2507.05489…

Higher-Order Newton-Cartan Gravity
We study the non-relativistic Newton-Cartan limit of higher-order gravity theories in arbitrary dimensions. We first study it at the level of the action by introducing an additional 1-form gauge field and coupling it appropriately to the gravity sector. We extend this procedure to any theory whose Lagrangian is a function of the Ricci scalar, quadratic Ricci tensor and quadratic Riemann tensor. We also study the limit of the equations of motion for two models, Einstein-Gauss-Bonnet gravity and …

Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
Simon Cichy, Paul K. Faehrmann, Lennart Bittel, Jens Eisert, Hakop Pashayan
https://arxiv.org/abs/2508.05745 …

Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
Classical simulations of noisy quantum circuits is instrumental to our understanding of the behavior of real world quantum systems and the identification of regimes where one expects quantum advantage. In this work, we present a highly parallelizable tensor-network-based classical algorithm -- equipped with rigorous accuracy guarantees -- for simulating $n$-qubit quantum circuits with arbitrary single-qubit noise. Our algorithm represents the state of a noisy quantum system by a particular ense…