Related papers: Accelerating two-dimensional tensor network contra…

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

$\rm{SO}(3)$-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate…

Despite the decomposition of convolutional kernels for lightweight CNNs being well studied, existing works that rely on tensor network diagrams or hyperdimensional abstraction lack geometry intuition. This work devises a new perspective by…

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…

Google's Tensor Processing Units (TPUs) are integrated circuits specifically built to accelerate and scale up machine learning workloads. They can perform fast distributed matrix multiplications and therefore be repurposed for other…

Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…

An increasing share of captured images and videos are transmitted for storage and remote analysis by computer vision algorithms, rather than to be viewed by humans. Contrary to traditional standard codecs with engineered tools, neural…

The alternating least squares algorithm for CP and Tucker decomposition is dominated in cost by the tensor contractions necessary to set up the quadratic optimization subproblems. We introduce a novel family of algorithms that uses…

Lossy compression introduces complex compression artifacts, particularly blocking artifacts, ringing effects and blurring. Existing algorithms either focus on removing blocking artifacts and produce blurred output, or restore sharpened…

The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies non-perturbatively across a…

We optimize matrix-product state-based algorithms for simulating quantum circuits with finite fidelity, specifically the time-evolving block decimation (TEBD) and the density-matrix renormalization group (DMRG) algorithms, by exploiting the…

Projected Entangled Pair States (PEPS) are recognized as a potent tool for exploring two-dimensional quantum many-body systems. However, a significant challenge emerges when applying conventional PEPS methodologies to systems with periodic…

We propose and evaluate new techniques for compressing and speeding up dense matrix multiplications as found in the fully connected and recurrent layers of neural networks for embedded large vocabulary continuous speech recognition (LVCSR).…

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…

We present applications of the renormalization algorithm with graph enhancement (RAGE). This analysis extends the algorithms and applications given for approaches based on matrix product states introduced in [Phys. Rev. A 79, 022317 (2009)]…

We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…

In the machine learning fields, Recurrent Neural Network (RNN) has become a popular architecture for sequential data modeling. However, behind the impressive performance, RNNs require a large number of parameters for both training and…

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…

The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…