Are Language Models Up to Sequential Optimization Problems? From Evaluation to a Hegelian-Inspired Enhancement

TL;DR

This paper evaluates Large Language Models on Sequential Optimization Problems, introduces a dynamic generation framework for testing, and applies Hegelian Dialectics to enhance their reasoning without retraining.

Contribution

It presents WorldGen for generating complex SOPs and introduces ACE, a Hegelian-inspired method to improve LLM reasoning performance without retraining.

Findings

LLMs perform well on simple SOPs but struggle with complexity.

Hegelian Dialectics can significantly enhance LLM reasoning in SOPs.

Performance improvements occur without additional training or fine-tuning.

Abstract

Large Language Models (LLMs) have demonstrated impressive capabilities across numerous fields, presenting an opportunity to revolutionize optimization problem-solving, a crucial, ubiquitous, and complex domain. This paper explores the proficiency of LLMs in handling Sequential Optimization Problems (SOPs). We introduce WorldGen, a dynamic framework for generating unseen SOPs with controllable complexities, to evaluate LLM performance. Our initial observations reveal that while LLMs perform well on simple SOPs, their performance significantly degrades with increased complexity. Motivated by this, we revisit philosophical hypotheses on reasoning to enhance LLM performance. Inspired by the influential framework of Hegelian Dialectics, we propose ACE, demonstrating how the performance of LLMs in SOP contexts can be significantly improved without any retraining or further fine-tuning.