The Syntax and Semantics of einsum
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Abstract (arXiv)
In 2011, einsum was introduced to NumPy as a practical and convenient notation for tensor expressions in machine learning, quantum circuit simulation, and other fields. It has since been implemented in additional Python frameworks such as PyTorch and TensorFlow, as well as in other programming languages such as Julia. Despite its practical success, the einsum notation still lacks a solid theoretical basis, and is not unified across the different frameworks, limiting opportunities for formal reasoning and systematic optimization. In this work, we discuss the terminology of tensor expressions and provide a formal definition of the einsum language. Based on this definition, we formalize and prove important equivalence rules for tensor expressions and highlight their relevance in practical applications.
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References · 5
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
- 2016TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systemscited by 664
- 2018Tensor Comprehensions: Framework-Agnostic High-Performance Machine Learning Abstractionscited by 85
- 2020A Tensor Network based Decision Diagram for Representation of Quantum Circuitscited by 1
- 2023How to enumerate trees from a context-free grammarcited by 1
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