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

Ali Asgarov, Umid Suleymanov, Aadyant Khatri · Oct 31, 2025 · Citations: 0

Automatic Metrics Coding Long Horizon Math Multi Agent
Open arXiv Find Implementation RSS feed Shortlist (0)

How to use this page

Moderate trust

Use this for comparison and orientation, not as your only source.

Best use

Background context only

What to verify

Validate the evaluation procedure and quality controls in the full paper before operational use.

Evidence quality

Moderate

Derived from extracted protocol signals and abstract evidence.

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.

Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A benchmark-and-metrics comparison anchor.

Main weakness

No major weakness surfaced.

Trust level

Moderate

Usefulness score

25/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

Usefulness for eval research

Adjacent candidate

Extraction confidence 55%

If you are doing eval pipeline work, start here:

Human Eval Hub LLM-as-Judge Hub Pairwise Preference Hub Tool-Use Eval Hub

What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking."

Evaluation Modes

strong

Automatic Metrics

Includes extracted eval setup.

"Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking."

Benchmarks / Datasets

strong

MATH 500, GPQA, AIME, ScienceQA

Useful for quick benchmark comparison.

"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%."

Reported Metrics

strong

Accuracy

Useful for evaluation criteria comparison.

"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."

Human Feedback Details

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Not reported
  • Expertise required: Math, Coding

Evaluation Details

  • Evaluation modes: Automatic Metrics
  • Agentic eval: Long Horizon, Multi Agent
  • Quality controls: Not reported
  • Evidence quality: Moderate
  • Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

MATH-500GPQAAIMEScienceQA

Reported Metrics

accuracy

Research Brief

Metadata summary

Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • 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.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Validate inferred eval signals (Automatic metrics, Long-horizon tasks) against the full paper.
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Accuracy

Research Summary

Contribution Summary

  • 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…
  • 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.

Why It Matters For Eval

  • 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…
  • 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%.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Pass: Benchmark or dataset anchors are present

    Detected: MATH-500, GPQA, AIME, ScienceQA

  • Pass: Metric reporting is present

    Detected: accuracy

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Papers are ranked by protocol overlap, extraction signal alignment, and semantic proximity.

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