Related papers: Branch-and-Bound Tensor Networks for Exact Ground-…
A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…
This article introduces the Tensor Network B-spline model for the regularized identification of nonlinear systems using a nonlinear autoregressive exogenous (NARX) approach. Tensor network theory is used to alleviate the curse of…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
We have developed TTNOpt, a software package that utilizes tree tensor networks (TTNs) for quantum spin systems and high-dimensional data analysis. TTNOpt provides efficient and powerful TTN computations by locally optimizing the network…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
The exact contraction of a generic two-dimensional (2D) tensor network state (TNS) is known to be exponentially hard, making simulation of 2D systems difficult. The recently introduced class of isometric TNS (isoTNS) represents a subset of…
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultra-fast numerical solutions of high-dimensional Partial…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…
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…
Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…
Tensor network (TN) states, including entanglement renormalization (ER), can encompass a wider variety of entangled states. When the entanglement structure of the quantum state of interest is non-uniform in real space, accurately…
An augmented tree tensor network (aTTN) is a tensor network ansatz constructed by applying a layer of unitary disentanglers to a tree tensor network. The disentanglers absorb a part of the system's entanglement. This makes aTTNs suitable…
Binary Neural Network (BNN) converts full-precision weights and activations into their extreme 1-bit counterparts, making it particularly suitable for deployment on lightweight mobile devices. While binary neural networks are typically…
The so-called block-term decomposition (BTD) tensor model has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of \emph{blocks} of rank higher than one, a…
Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on…
Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…