Verified Tensor-Program Optimization Via High-level Scheduling Rewrites

Amanda Liu, Gilbert Bernstein, Adam Chlipala, Jonathan Ragan-Kelley. Verified Tensor-Program Optimization Via High-level Scheduling Rewrites. Proceedings of the 49th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'22). January 2022. Conditionally accepted.

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We present a lightweight Coq framework for optimizing tensor kernels written in a pure, functional array language. Optimizations rely on user scheduling using series of verified, semantics-preserving rewrites. Unusually for compilation targeting imperative code with arrays and nested loops, all rewrites are source-to-source within a purely functional language. Our language comprises a set of core constructs for expressing high-level computation detail and a set of what we call reshape operators, which can be derived from core constructs but trigger low-level decisions about storage patterns and ordering. We demonstrate that not only is this system capable of deriving the optimizations of existing state-of-the-art languages like Halide and generating comparably performant code, it is also able to schedule a family of useful program transformations beyond what is reachable in Halide.