Reading AI Model Compilation in MLIR Through the Lens of Formal Theories
The paper explores the intersection of AI model compilation in MLIR with formal programming language theories, aiming to build a principled framework for understanding compilation flows. It demonstrates how concepts from lambda calculus and type theory can provide a unified view of compilation passes, and discusses benefits for correctness, optimization, and interoperability of AI compilers.
Background
- MLIR (Multi-Level Intermediate Representation) is an open-source compiler framework created by Google to make it easier to build and optimize machine learning models. It supports multiple levels of abstraction so AI frameworks can gradually lower their computations down to hardware.
- This paper connects MLIR's compilation passes to formal / mathematical computation theories — specifically abstract data types, term rewriting, and lambda calculus — to give a rigorous explanation of what the compiler is doing at each stage.
- The authors aim to demystify MLIR by showing that its apparently complex lowering and optimization steps correspond to well-understood theoretical operations (e.g., converting high-level tensor ops into loops or linear algebra kernels follows patterns that can be expressed as term-rewriting systems).
- Why it matters: As AI models grow, compilation efficiency and correctness become critical. Understanding MLIR through formal theories can help researchers design better compilers and prove that optimizations preserve correctness — without having to reframe the entire toolchain from scratch.