The landscape of software for tensor computations

Psarras, Christos; Karlsson, Lars; Li, Jiajia; Bientinesi, Paolo

doi:10.48550/arxiv.2103.13756

Cited by 8 publications

(9 citation statements)

References 21 publications

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“…Given a target tensor of size 50 × 200 × 200, K = 50 models to fit, and R i = 5 components in each model, the efficiency for each of the K MTTKRPs in CP-ALS is about 15% (3%) for 1 ( 24) threads (see Figure 1). The efficiency of the fused MTTKRP in CALS will be as observed for R = K i=1 R i = 250, i.e., 60% (30%) for 1 (24) threads. Since the MTTKRP operation dominates the cost, CALS is expected to be ≈ 4× (≈ 10×) faster than CP-ALS for 1 (24) threads.…”

Section: Concurrent Als (Cals)mentioning

confidence: 72%

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Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

Psarras

Karlsson

Bro

et al. 2022

Front. Appl. Math. Stat.

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The Canonical Polyadic (CP) tensor decomposition is frequently used as a model in applications in a variety of different fields. Using jackknife resampling to estimate parameter uncertainties is often desirable but results in an increase of the already high computational cost. Upon observation that the resampled tensors, though different, are nearly identical, we show that it is possible to extend the recently proposed Concurrent ALS (CALS) technique to a jackknife resampling scenario. This extension gives access to the computational efficiency advantage of CALS for the price of a modest increase (typically a few percent) in the number of floating point operations. Numerical experiments on both synthetic and real-world datasets demonstrate that the new workflow based on a CALS extension can be several times faster than a straightforward workflow where the jackknife submodels are processed individually.

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Section: Concurrent Als (Cals)mentioning

confidence: 72%

“…Several projects offer high-performance implementations of CP-ALS, for example, Cyclops [19], PLANC [20], Partensor [21], SPLATT [22], and Genten [23]. For a more comprehensive list of software implementing some variant of CP-ALS, refer to Psarras et al [24].…”

Section: Related Workmentioning

confidence: 99%

Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

Psarras

Karlsson

Bro

et al. 2022

Front. Appl. Math. Stat.

Self Cite

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“…Readers are referred to Ref. [62] where a comprehensive and up-to-date snapshot of software for tensor computations is assembled.…”

Section: Numerical Resultsmentioning

confidence: 99%

Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System

Gu¹,

Zhang²

2022

Preprint

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We apply tensor networks to counting statistics for the stochastic particle transport in an out-of-equilibrium diffusive system. This system is composed of a one-dimensional channel in contact with two particle reservoirs at the ends. Two tensor-network algorithms, namely, Density Matrix Renormalization Group (DMRG) and Time Evolving Block Decimation (TEBD), are respectively implemented. The cumulant generating function for the current is numerically calculated and then compared with the analytical solution. Excellent agreement is found, manifesting the validity of these approaches in such an application. Moreover, the fluctuation theorem for the current is shown to hold.

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“…Such a broad class of successful applications has resulted in a need for efficient software libraries [24] providing necessary primitives for composing tensor network algorithms. Apart from a plethora of basic tensor processing libraries, which are not the focus here, a number of specialized software packages have been developed recently, directly addressing the tensor network algorithms (in these latter software packages a tensor network is the first-class citizen).…”

Section: Introductionmentioning

confidence: 99%

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

Liakh

Nguyen

Claudino

et al. 2022

Front. Appl. Math. Stat.

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We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

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The landscape of software for tensor computations

Cited by 8 publications

References 21 publications

Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

Accelerating Jackknife Resampling for the Canonical Polyadic Decomposition

Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System

ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

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