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

Ali Asgarov, Umid Suleymanov, Aadyant Khatri

TL;DR

Mathematical reasoning requires both accurate knowledge and careful multi-step deduction, and single-perspective retrieval often fails on knowledge-intensive tasks. SIGMA introduces a multi-agent framework with four specialist agents (Factual, Logical, Computational, Completeness) plus a moderator to perform independent reasoning-search cycles and integrate results via Hypothetical Document Enhancement for on-demand retrieval. The approach yields consistent gains over strong baselines on $MATH500$, $AIME$, $AMC$, and $GPQA$, including an absolute improvement of $7.4\%$ over competing methods, while remaining efficient at smaller model scales. This work demonstrates that on-demand, multi-perspective knowledge integration is a scalable and effective paradigm for complex mathematical problem solving and potentially other knowledge-intensive domains.

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.

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

TL;DR

Mathematical reasoning requires both accurate knowledge and careful multi-step deduction, and single-perspective retrieval often fails on knowledge-intensive tasks. SIGMA introduces a multi-agent framework with four specialist agents (Factual, Logical, Computational, Completeness) plus a moderator to perform independent reasoning-search cycles and integrate results via Hypothetical Document Enhancement for on-demand retrieval. The approach yields consistent gains over strong baselines on , , , and , including an absolute improvement of over competing methods, while remaining efficient at smaller model scales. This work demonstrates that on-demand, multi-perspective knowledge integration is a scalable and effective paradigm for complex mathematical problem solving and potentially other knowledge-intensive domains.

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.

Paper Structure

This paper contains 9 sections, 4 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Methodology
  4. Experiments
  5. Results
  6. Conclusion
  7. SIGMA Multi-Agent Inference
  8. Problem and Multi-Agent Execution
  9. Framework Advantages

Figures (2)

  • Figure 1: MATH500 score versus model size. SIGMA variants (stars) form a shaded performance frontier at 1.5B, 3B, and 7B parameters, with arrows indicating SIGMA’s absolute improvement over the second-best method of the same size. Closed-source models are placed at $>100$B on the x-axis. SIGMA outperforms several larger closed-source models, including GPT‑4o gpt_4o_system_card, Gemini 8B GeminiTeam2025gemini25, and Claude‑3.5‑Haiku anthropic_claude_3_5_haiku_2024.
  • Figure 2: Overview of the SIGMA framework.