JAXMg: A multi-GPU linear solver in JAX

Abstract: Solving large dense linear systems and eigenvalue problems is a core requirement in many areas of scientific computing, but scaling these operations beyond a single GPU remains challenging within modern programming frameworks. While highly optimized multi-GPU solver libraries exist, they are typically difficult to integrate into composable, just-in-time (JIT) compiled Python workflows. JAXMg provides multi-GPU dense linear algebra for JAX, enabling Cholesky-based linear solves and symmetric eigendecompositions for matrices that exceed single-GPU memory limits. By interfacing JAX with NVIDIA's cuSOLVERMg through an XLA Foreign Function Interface, JAXMg exposes distributed GPU solvers as JIT-compatible JAX primitives. This design allows scalable linear algebra to be embedded directly within JAX programs, preserving composability with JAX transformations and enabling multi-GPU execution in end-to-end scientific workflows.