Reproduce “The Continuous Tensor Abstraction: Where Indices are Real” on OpenResearch
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About this paper
Jaeyeon Won, Willow Ahrens, Teodoro Fields Collin, Joel S. Emer, Saman Amarasinghe
Researchers from MIT and Georgia Institute of Technology developed the Continuous Tensor Abstraction, enabling tensor operations with real-number indices to unify geometric and numerical computations. This approach achieves code reductions up to 101x and demonstrates competitive performance, including a 9.2x speedup for radius search over baselines and 1.22x for genomic interval operations, by efficiently compiling operations over piecewise-constant domains.
Key insights
- Continuous domains can be effectively managed in a tensor framework by specializing tensors as piecewise-constant, transforming potentially infinite computations into finite operations over disjoint intervals.
- Existing sparse tensor compilation techniques, specifically fibertrees and the Looplets abstraction, can be successfully extended to handle real-valued, interval-based indices for efficient code generation on continuous data.
- Unifying complex geometric reasoning with numerical computations under a single, high-level tensor abstraction dramatically simplifies application development and reduces code complexity for diverse domains.
Summary by alphaXiv.
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