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

• URL: http://arxiv.org/abs/2510.27568v1
• Date: Fri, 31 Oct 2025 15:51:00 GMT
• Title: SIGMA: Search-Augmented On-Demand Knowledge Integration for Agentic Mathematical Reasoning
• Authors: Ali Asgarov, Umid Suleymanov, Aadyant Khatri,
• Abstract summary: We introduce SIGMA (Search-Augmented On-Demand Knowledge Integration for AGentic Mathematical reAsoning), a unified framework that orchestrates specialized agents.<n>Each agent generates hypothetical passages to optimize retrieval for its analytic perspective, ensuring knowledge integration is both context-sensitive and computation-efficient.<n>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.
• Score: 0.054619385369457214
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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