Traditional compiler infrastructures often enforce a rapid transition from source code to a low-level representation. While effective for scalar CPU instructions, this approach frequently discards the structural information needed to optimize dense matrix computations efficiently. MLIR (Multi-Level Intermediate Representation) addresses this limitation by enabling operations at varying levels of abstraction to coexist within the same module. This architecture supports progressive lowering, where high-level tensor semantics, such as shape information $[N, C, H, W]$, are preserved and optimized before being converted to hardware-specific instructions.

This unit examines the modular components of the MLIR ecosystem. We focus on the concept of "dialects," which act as logical groupings for operations and types. You will study the linalg dialect for representing structured linear algebra and the affine dialect for memory dependency analysis. The text also details the pattern rewriting infrastructure used to transform the intermediate representation. By the end of the chapter, you will walk through the process of defining a custom dialect and implementing a lowering pass to translate abstract logic into executable targets like LLVM IR.