Sci-Mind: Cognitively-Inspired Adversarial Debate for Autonomous Mathematical Modeling

TL;DR

Sci-Mind is a framework that mimics human scientific discovery by combining experiential memory, adversarial debate, and self-validation to improve autonomous mathematical modeling with language models.

Contribution

It introduces a cognitively-inspired approach integrating memory recall, adversarial dialectic, and self-validation to enhance autonomous modeling capabilities.

Findings

Sci-Mind outperforms existing agents in modeling rigor and code execution.

The framework effectively grounds reasoning in historical solutions.

Experiments show significant improvements on MM-Bench and EngiBench.

Abstract

Real-world mathematical modeling is inherently an experiential and collaborative endeavor. Domain experts rarely solve complex problems from scratch; instead, they draw upon analogies from historical cases and subject their hypotheses to rigorous peer scrutiny. However, autonomous agents powered by Large Language Models predominantly rely on isolated reasoning paradigms, frequently generating plausible but fundamentally flawed models due to a lack of domain grounding and adversarial verification. To address these limitations, we propose Sci-Mind, a novel framework that mirrors the human scientific discovery process. Sci-Mind integrates Experiential Memory Recall to retrieve executable code snippets and modeling paradigm descriptors, grounding abstract reasoning in historical solutions. Subsequently, it employs an Adversarial Cognitive Dialectic where a Theorist optimizing mathematical coherence and a Pragmatist enforcing data feasibility debate through competing objectives to prune elegant but infeasible formulations. A Self-Validating Execution Strategy further ensures blueprint consistency through formal predicates before code generation, achieving fully autonomous execution. Extensive experiments on the MM-Bench and EngiBench demonstrate that Sci-Mind significantly outperforms leading autonomous agents in both modeling rigorousness and code executability.