SIGMA: Search-Augmented On-Demand Knowledge Integration for Agentic Mathematical Reasoning

TL;DR

SIGMA is a multi-agent framework that improves mathematical reasoning by integrating on-demand knowledge retrieval and synthesis, leading to better accuracy and efficiency on challenging benchmarks.

Contribution

It introduces a novel multi-agent system with specialized reasoning and search agents, coordinated by a moderator, for enhanced knowledge integration in mathematical reasoning.

Findings

Outperforms existing models on MATH500, AIME, and GPQA benchmarks.

Achieves a 7.4% absolute performance improvement over baselines.

Demonstrates scalable, context-sensitive reasoning with improved accuracy and efficiency.

Abstract

Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking. However, current retrieval-augmented models often rely on a single perspective, follow inflexible search strategies, and struggle to effectively combine information from multiple sources. We introduce SIGMA (Search-Augmented On-Demand Knowledge Integration for AGentic Mathematical reAsoning), a unified framework that orchestrates specialized agents to independently reason, perform targeted searches, and synthesize findings through a moderator mechanism. Each agent generates hypothetical passages to optimize retrieval for its analytic perspective, ensuring knowledge integration is both context-sensitive and computation-efficient. When evaluated on challenging benchmarks such as MATH500, AIME, and PhD-level science QA GPQA, SIGMA consistently outperforms both open- and closed-source systems, achieving an absolute performance improvement of 7.4%. Our results demonstrate that multi-agent, on-demand knowledge integration significantly enhances both reasoning accuracy and efficiency, offering a scalable approach for complex, knowledge-intensive problem-solving. We will release the code upon publication.