Related papers: Low-rank Tree Tensor Network Operators for Long-Ra…

Starting from the matrix elements of the nucleon-nucleon interaction in momentum space we present a method to derive an operator representation with a minimal set of operators that is required to provide an optimal description of the…

Tensors with finite correlation afford very compact tensor network representations. A novel tensor network-based decomposition of real-time path integral simulations involving Feynman-Vernon influence functional is introduced. In this…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

In optimization, one of the well-known classical algorithms is power iterations. Simply stated, the algorithm recovers the dominant eigenvector of some diagonalizable matrix. Since numerous optimization problems can be formulated as an…

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, long-horizon…

Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…

It is well known that tensor network regression models operate on an exponentially large feature space, but questions remain as to how effectively they are able to utilize this space. Using a polynomial featurization, we propose the…

Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator and the harmonic oscillator. Experimental results show the…

The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…

Multiway data often naturally occurs in a tensorial format which can be approximately represented by a low-rank tensor decomposition. This is useful because complexity can be significantly reduced and the treatment of large-scale data sets…

We present a fast multiscale approach for the network minimum logarithmic arrangement problem. This type of arrangement plays an important role in a network compression and fast node/link access operations. The algorithm is of linear…

Multiple network alignment is the problem of identifying similar and related regions in a given set of networks. While there are a large number of effective techniques for pairwise problems with two networks that scale in terms of edges,…

Deep neural networks (DNNs) have achieved outstanding performance in a wide range of applications, e.g., image classification, natural language processing, etc. Despite the good performance, the huge number of parameters in DNNs brings…

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially…

We recently introduced a method to approximate functions of Hermitian Matrix Product Operators or Tensor Trains that are of the form $\mathsf{Tr} f(A)$. Functions of this type occur in several applications, most notably in quantum physics.…

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…

The performance of tensor network methods has seen constant improvements over the last few years. We add to this effort by introducing a new algorithm that efficiently applies tree tensor network operators to tree tensor network states…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…

The fermionic many-body problem in the strong correlation regime is notoriously difficult to tackle. In a previous work (Phys. Rev. B 101, 045109 (2020)), we have proposed to extend the single-reference coupled-cluster (SRCC) method to the…

Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…