Data-Driven Dynamic Algorithm Dispatch with Large Language Models

Rushil Shah; Emmanuel Lujan; Rabab Alomairy; Alan Edelman

cs.AIAug 21, 2026

Data-Driven Dynamic Algorithm Dispatch with Large Language Models

Authors: Rushil Shah, Emmanuel Lujan, Rabab Alomairy, Alan Edelman

Organizations: Computer Science & Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA.

Abstract

We introduce a large language model (LLM)-driven approach for generating dynamic algorithmic dispatch heuristics in high-performance linear algebra. By combining prompt engineering with LLaMA 3 and a curated performance database, the model learns to synthesize selection heuristics that exploit structural patterns to identify fast algorithmic choices. A case study on LU factorization demonstrates the model's ability to replicate expert-designed strategies. This work, developed as part of the DARPA-MIT SmartSolve project, highlights the promise of LLMs for algorithmic discovery and the development of more adaptive, fast linear algebra software.

Figures & tables

Fig. 1: Overview of our LLM-driven approach for generating dynamic algorithm dispatch heuristics in linear algebra.

Fig. 2: Time and accuracy trade-offs of LU performance on a $2^{12}$ x $2^{12}$ Poisson matrix, used to guide LLM-generated dispatch heuristics.

Algorithm Selection

Algorithm selection predicts which solver, model, or strategy will work best for a given instance, context, or computational budget.

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Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.

Abstract

Algorithm Selection

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