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Retrieval-Augmented Generation (RAG) has significantly enhanced Large Language Models' ability to access external knowledge, yet current graph-based RAG approaches face two critical limitations in managing hierarchical information: they…
The CANDECOMP/PARAFAC (CP) tensor decomposition is a popular dimensionality-reduction method for multiway data. Dimensionality reduction is often sought after since many high-dimensional tensors have low intrinsic rank relative to the…
Recent advances in fine-grained representation learning leverage local-to-global (emergent) relationships for achieving state-of-the-art results. The relational representations relied upon by such methods, however, are abstract. We aim to…
In the framework of tensor spaces, we consider orthogonalization kernels to generate an orthogonal basis of a tensor subspace from a set of linearly independent tensors. In particular, we experimentally study the loss of orthogonality of…
Large sparse linear systems of equations are ubiquitous in science and engineering, such as those arising from discretizations of partial differential equations. Algebraic multigrid (AMG) methods are one of the most common methods of…
We introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates…
We describe a low cost alternative to the standard variational DMRG (density matrix renormalization group) algorithm that is analogous to the combination of selected configuration interaction plus perturbation theory (SCI+PT). We denote the…
In this study, the higher-order tensor renormalization group (HOTRG) method is applied to a lattice glass model that has local constraints on the occupation number of neighboring particles represented by many-body interactions. This model…
Fluorescence microscopy images usually show severe anisotropy in axial versus lateral resolution. This hampers downstream processing, i.e. the automatic extraction of quantitative biological data. While deconvolution methods and other…
Tensor ring (TR) decomposition has been widely applied as an effective approach in a variety of applications to discover the hidden low-rank patterns in multidimensional data. A well-known method for TR decomposition is the alternating…
We introduce the order-separated Grassmann higher-order tensor renormalization group (OS-GHOTRG) method for QCD with staggered quarks in the strong-coupling expansion. The method allows us to determine the expansion coefficients of the…
Despite the recent success of deep learning models in numerous applications, their widespread use on mobile devices is seriously impeded by storage and computational requirements. In this paper, we propose a novel network compression method…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate…
Ab-initio calculations of real-time evolution for lattice gauge theory have very interesting potential applications but present challenging computational aspects. We show that tensor renormalization group methods developed in the context of…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…
Adder neural network (AdderNet) is a new kind of deep model that replaces the original massive multiplications in convolutions by additions while preserving the high performance. Since the hardware complexity of additions is much lower than…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
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…