Linear algebra libraries and tensor domain-specific languages are able to deliver high performance for modern scientific and machine learning workloads. While there has been recent work in automatically translating legacy software to use these libraries/DSLs using pattern matching and program lifting, this has been largely limited to dense linear algebra.

This paper tackles the more challenging problem of porting legacy sparse linear algebra code to libraries and DSLs. It exploits the power of large language models to predict a sketch of the solution and then uses type-based program synthesis to search the space of possible code to target pa- rameter bindings. We implement this in a tool named SLEB and evaluate it on a large set of benchmarks and real-world datasets, comparing against two state-of-the-art compiler techniques, LiLAC and SpEQ; and GPT 4.o. Overall, we lift 94% of programs compared to 11%, 17%, and 48% for LiLAC, SpEQ, and GPT 4.o respectively. All lifted programs are completely correct compared to the 52% hallucinations of GPT4.o. This delivers a geomean speedup of 2.6x and 7.2x on a CPU and GPU platform, respectively.