Deep learning software demands reliability and performance. We present DLVM, a design and implementation of a compiler infrastructure with a linear algebra intermediate representation, algorithmic differentiation by adjoint code generation, domain-specific optimizations and a code generator targeting GPU via LLVM. Designed as a modern compiler framework inspired by LLVM, DLVM is more modular and more generic than existing deep learning compiler frameworks, and supports tensor DSLs with high expressivity. With our prototypical staged DSL embedded in Swift, we argue that the DLVM system enables a form of modular, safe and performant frameworks for deep learning.