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The Sparse Abstract Machine

31 Aug 2022arXiv:2208.14610links table onlyarchive 2025-07-28

Olivia Hsu, Maxwell Strange, Ritvik Sharma, Jaeyeon Won, Kunle Olukotun, Joel Emer, Mark Horowitz, Fredrik Kjolstad

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We propose the Sparse Abstract Machine (SAM), an abstract machine model for targeting sparse tensor algebra to reconfigurable and fixed-function spatial dataflow accelerators. SAM defines a streaming dataflow abstraction with sparse primitives that encompass a large space of scheduled tensor algebra expressions. SAM dataflow graphs naturally separate tensor formats from algorithms and are expressive enough to incorporate arbitrary iteration orderings and many hardware-specific optimizations. We also present Custard, a compiler from a high-level language to SAM that demonstrates SAM's usefulness as an intermediate representation. We automatically bind from SAM to a streaming dataflow simulator. We evaluate the generality and extensibility of SAM, explore the performance space of sparse tensor algebra optimizations using SAM, and show SAM's ability to represent dataflow hardware.

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