Scientific discovery as meta-optimization: a combinatorial optimization case study

2026-06-25

AI Summary

This work formulates scientific discovery as a meta-optimization problem, wherein evaluation criteria are dynamically refined alongside the search for solutions. To this end, the authors propose a Consensus Objective Aggregation approach that leverages large language models to generate diverse candidate objective functions, which are then fused via correlation-weighted voting to yield a stable, self-correcting, and adaptive evaluation metric that evolves with emerging understanding. Integrating large language models, meta-optimization, weighted voting, and a digital MemComputing architecture, the framework is applied to the discovery of 3-SAT solvers, successfully reducing algorithmic complexity from approximately $N^{2.51}$ to $N^{1.33}$ and achieving a speedup of about 67× on the largest tested instances.

Abstract

Scientific discovery is fundamentally an optimization problem, defined by a vast "state space" of theories and experiments, and an evaluation criterion based on quality, novelty, and validity. Large language models (LLMs) have enabled automated exploration of this space, but we argue that simultaneous modification of the evaluation criteria is equally important. Here, we propose formalizing research as meta-optimization, where the optimization objective itself is also being optimized. Our key contribution is "consensus objective aggregation," where LLM-generated objective functions are combined via correlation-weighted voting, yielding a stable, self-correcting evaluation criterion that evolves as understanding deepens. We apply this framework to algorithm discovery for 3-SAT problems based on digital MemComputing machines, reducing the baseline scaling with problem size $N$ from $\sim N^{2.51}$ to $\sim N^{1.33}$ and delivering a $\sim 67\times$ speedup on the largest instances tested. As a problem-agnostic framework, we hope this approach will considerably aid scientific discovery.

Problem

• scientific discovery
• meta-optimization
• evaluation criteria
• objective function
• combinatorial optimization

Innovation

• meta-optimization
• consensus objective aggregation
• large language models
• algorithm discovery
• 3-SAT