Named Tensor Notation

Published: 13 Jan 2023, Last Modified: 28 Feb 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: We propose a notation for tensors with named axes, which relieves the author, reader, and future implementers of machine learning models from the burden of keeping track of the order of axes and the purpose of each. The notation makes it easy to lift operations on low-order tensors to higher order ones, for example, from images to minibatches of images, or from an attention mechanism to multiple attention heads. After a brief overview and formal definition of the notation, we illustrate it through several examples from modern machine learning, from building blocks like attention and convolution to full models like Transformers and LeNet. We then discuss differential calculus in our notation and compare with some alternative notations. Our proposals build on ideas from many previous papers and software libraries. We hope that this document will encourage more authors to use named tensors, resulting in clearer papers and more precise implementations.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: - Deanonymized and added CTAN link. - Fixed typos in Section 3.1. - Fixed layer normalization in Appendix A.1. - Changed date to 1/2023.
Assigned Action Editor: ~Danny_Tarlow1
Submission Number: 409