The Continuous Tensor Abstraction: Where Indices Are Real
Author(s)
Won, Jaeyeon
Ahrens, Willow
Collin, Teodoro Fields
Emer, Joel S.
Amarasinghe, Saman
Date Issued
October 9, 2025
Journal
Proceedings of the ACM on Programming Languages
Publisher
ACM
Citation
Jaeyeon Won, Willow Ahrens, Teodoro Fields Collin, Joel S. Emer, and Saman Amarasinghe. 2025. The Continuous Tensor Abstraction: Where Indices Are Real. Proc. ACM Program. Lang. 9, OOPSLA2, Article 368 (October 2025), 29 pages.
Version
Final published version
Abstract
This paper introduces the continuous tensor abstraction, allowing indices to take real-number values (e.g., A[3.14]). It also presents continuous tensor algebra expressions, such as Cx,y = Ax,y ∗ Bx,y, where indices are defined over a continuous domain. This work expands the traditional tensor model to include continuous tensors. Our implementation supports piecewise-constant tensors, on which infinite domains can be processed in finite time. We also introduce a new tensor format for efficient storage and a code generation technique for automatic kernel generation. For the first time, our abstraction expresses domains like computational geometry and computer graphics in the language of tensor programming. Our approach demonstrates competitive or better performance to hand-optimized kernels in leading libraries across diverse applications. Compared to hand-implemented libraries on a CPU, our compiler-based implementation achieves an average speedup of 9.20× on 2D radius search with ∼60× fewer lines of code (LoC), 1.22× on genomic interval overlapping queries (with ∼18× LoC saving), and 1.69× on trilinear interpolation in Neural Radiance Field (with ∼6× LoC saving).
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1145/3763146
