SIGMA: Search-Augmented On-Demand Knowledge Integration for Agentic Mathematical Reasoning
This work addresses the problem of enhancing reasoning accuracy and efficiency in complex, knowledge-intensive tasks like mathematical problem-solving, offering a scalable approach that is incremental over existing multi-agent methods.
The paper tackled the problem of improving mathematical reasoning by addressing limitations in current retrieval-augmented models, such as inflexible search and poor multi-source integration, and introduced SIGMA, a multi-agent framework that achieved a 7.4% absolute performance improvement on benchmarks like MATH500 and AIME.
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.