Automated Algorithm Selection Discovery via LLMs

Explore automated algorithm selection for matrix factorizations using large language models in this 11-minute conference talk from JuliaCon Global 2025. Learn about the SmartSolve project, funded by DARPA-DIAL, which develops a toolbox that systematically benchmarks performance and accuracy of diverse algorithms across various computational architectures. Discover how the project leverages matrix pattern databases to generate heuristics that adaptively select optimal solutions for different inputs, with some matrix patterns achieving over 50X speedup compared to default selections in major linear algebra libraries. Examine the structured discovery process that measures performance metrics including casting time, computation time, and accuracy across diverse matrix patterns and data structures such as dense, sparse, and banded matrices. Understand how automated Pareto analysis identifies the most efficient and accurate algorithms while illustrating performance variations across different patterns. Investigate preliminary experiments with Llama 3 that demonstrate LLM capabilities in classifying and recommending optimal algorithms and data structures for LU and QR decompositions. Analyze the potential for LLM-driven classification to deliver greater speedups and accelerate heuristic generation for dynamic algorithm selection, moving beyond traditional static approaches. Consider the research impact of integrating artificial intelligence models with heuristic-driven strategies to optimize computational linear algebra performance, and explore how enhancements in SmartSolve.jl could benefit the Julia linear algebra ecosystem including widely adopted packages like LinearSolve.jl and LinearAlgebra.jl.