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Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field…
Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position,…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
Tensor decomposition is a well-known tool for multiway data analysis. This work proposes using stochastic gradients for efficient generalized canonical polyadic (GCP) tensor decomposition of large-scale tensors. GCP tensor decomposition is…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
Comparing tensors and identifying their (dis)similar structures is fundamental in understanding the underlying phenomena for complex data. Tensor decomposition methods help analysts extract tensors' essential characteristics and aid in…
We present a geometric and dynamical approach to the micro-canonical ensemble of classical Hamiltonian systems. We generalize the arguments in \cite{Rugh} and show that the energy-derivative of a micro-canonical average is itself…
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…
Canonical Correlation Analysis (CCA) is a method for feature extraction of two views by finding maximally correlated linear projections of them. Several variants of CCA have been introduced in the literature, in particular, variants based…
Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…
Developing a theory for quantum gravity is one of the big open questions in theoretical high-energy physics. Recently, a tensor model approach has been considered that treats tensors as the generators of commutative non-associative…
Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…
We study concircular tensors in spaces of constant curvature and then apply the results obtained to the problem of the orthogonal separation of the Hamilton-Jacobi equation on these spaces. Any coordinates which separate the geodesic…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
We propose a framework for discrete scientific data compression based on the tensor-train (TT) decomposition. Our approach is tailored to handle unstructured output data from discrete element method (DEM) simulations, demonstrating its…
Hamiltonian formulation of the string with dynamical geometry and two-dimensional gravity with torsion is given. Canonical Hamiltonian equals to the linear combination of first class constraints satisfying closed algebra. It is the…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…