[Paper Review] TensorNetwork: A Library for Physics and Machine Learning

Chase Roberts, Ashley Milsted+7 more|arXiv (Cornell University)|May 3, 2019

Quantum many-body systemsPhysics and Astronomy25 references70 citations

TL;DR

TensorNetwork is an open source TensorFlow-based library for constructing and contracting tensor networks, enabling applications in physics and machine learning. The paper describes API design, data structures, and use cases.

ABSTRACT

TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other research areas, including machine learning. We demonstrate the use of the API with applications both physics and machine learning, with details appearing in companion papers.

Motivation & Objective

• Motivate the use of tensor networks across physics and machine learning.
• Introduce an API that mirrors graphical tensor network representations.
• Show how TensorNetwork integrates with TensorFlow to leverage GPUs/TPUs.
• Demonstrate basic operations and workflows for common tensor network computations.
• Outline use cases in physics and machine learning and point to companion papers for details.

Proposed method

• Present the graphical notation for tensors and contractions to motivate the API.
• Define core API objects: TensorNetwork, Node, and Edge.
• Describe edge types (standard, trace, dangling) and operations (connect, contract, flatten, contract_between).
• Explain node splitting and outer/inner products with SVD-based decompositions.
• Illustrate memory-saving techniques and optional truncation via max_singular_values or max_truncation_err.
• Reference the integration with TensorFlow and GPU/TPU acceleration.

Experimental results

Research questions

• RQ1 How can tensor networks be efficiently represented and manipulated in a software library?
• RQ2 How does the API map graphical tensor network concepts to computational primitives?
• RQ3 What are the practical benefits of integrating TensorNetwork with TensorFlow for physics and ML workloads?
• RQ4 What memory-saving and approximation strategies are available within the library (e.g., truncation of singular values)?

Key findings

• TensorNetwork provides a programmable, graph-based API to create, connect, contract, and manipulate tensor networks.
• The library supports basic operations such as contracting edges, flattening, and performing node splits with SVD, including options for truncation.
• Edge types and pre-contraction optimizations (like edge flattening) are emphasized to improve memory efficiency.
• The API enables easy implementation of common tensor network architectures such as MPS, TTN, and MERA within TensorFlow.
• Applications span physics and machine learning, with companion papers detailing specific physics and ML use cases and performance benefits on GPUs.