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

[Submitted on 31 Oct 2025 (v1), last revised 18 Jun 2026 (this version, v2)]

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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.

Submission history

From: Ali Asgarov [view email]
[v1] Fri, 31 Oct 2025 15:51:00 UTC (651 KB)
[v2] Thu, 18 Jun 2026 02:08:20 UTC (648 KB)