Lattice Gauge Theory via LLVM-Level Automatic Differentiation

TL;DR

This paper introduces a method to automatically generate HMC forces in lattice gauge theory by applying reverse-mode automatic differentiation at the LLVM level, enabling efficient, portable force computation from existing action code.

Contribution

It presents a novel LLVM-based automatic differentiation approach that simplifies and optimizes the generation of HMC forces directly from lattice action code, applicable across CPU and GPU.

Findings

Automatic differentiation produces forces with performance comparable to hand-written code.

The method supports both gauge and Wilson fermion actions.

It enables a single-source, compiler-optimized workflow for force generation.

Abstract

We enable the automatic construction of Hybrid Monte Carlo (HMC) forces in lattice gauge theory by performing reverse-mode automatic differentiation at the level of optimized LLVM intermediate representation, making the approach applicable to any language that lowers lattice action code to LLVM. In practice, this means that once the action evaluation routine is implemented, the corresponding HMC force can be generated automatically from the same code path, without deriving or maintaining a separate force routine. The method preserves conventional imperative, in-place implementations and enables a single-source workflow in which forces are generated directly from the action code while inheriting compiler optimizations. We perform end-to-end reverse-mode differentiation of both gauge and Wilson fermion actions. For the Wilson fermion case, we find that the force generated by automatic differentiation achieves performance comparable to a conventional hand-written fermion force implementation. The same differentiation pipeline targets both CPU and GPU backends, providing a practical route to performance-portable force construction for compositional lattice actions.