Related papers: Cons-training Tensor Networks: Embedding and Optim…

Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…

In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal…

This work discusses tensor network embeddings, which are random matrices ($S$) with tensor network structure. These embeddings have been used to perform dimensionality reduction of tensor network structured inputs $x$ and accelerate…

In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…

Convolutional neural networks have achieved a great success in the recent years. Although, the way to maximize the performance of the convolutional neural networks still in the beginning. Furthermore, the optimization of the size and the…

Correlator product states (CPS) are a powerful and very broad class of states for quantum lattice systems whose amplitudes can be sampled exactly and efficiently. They work by gluing together states of overlapping clusters of sites on the…

The recently introduced locally orderless tensor network (LoTeNet) for supervised image classification uses matrix product state (MPS) operations on grids of transformed image patches. The resulting patch representations are combined back…

Sum-product networks (SPNs) represent an emerging class of neural networks with clear probabilistic semantics and superior inference speed over graphical models. This work reveals a strikingly intimate connection between SPNs and tensor…

While post-training model compression can greatly reduce the inference cost of a deep neural network, uncompressed training still consumes a huge amount of hardware resources, run-time and energy. It is highly desirable to directly train a…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

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…

Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…

Multilayer perceptrons (MLP), or fully connected artificial neural networks, are known for performing vector-matrix multiplications using learnable weight matrices; however, their practical application in many machine learning tasks,…

We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…

We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

This paper shows how to optimize sparse tensor algebraic expressions by introducing temporary tensors, called workspaces, into the resulting loop nests. We develop a new intermediate language for tensor operations called concrete index…

We present a novel approach to enhance the performance of sampling-based Model Predictive Control (MPC) in constrained optimization by leveraging products of experts. Our methodology divides the main problem into two components: one focused…

A new unbiased Monte Carlo technique called Tensor Network Monte Carlo (TNMC) is introduced based on sampling all possible renormalizations (or course-grainings) of tensor networks, in this case matrix-product states. Tensor networks are a…

Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parameter decomposers for recognition tasks. Typical TN models, such as Matrix Product States (MPS), have not yet achieved successful…