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HFEPX · Eval paper review

QED-Nano: Teaching a Tiny Model to Prove Hard Theorems

LM-Provers, Yuxiao Qu, Amrith Setlur, Jasper Dekoninck +5 more

Published

Apr 6, 2026

Citations

0

Trust level

Moderate

Usefulness score

65/100 (Medium)

Extraction confidence

70% (Moderate)

Derived from extracted protocol signals and abstract evidence.

Rater population

Not reported

Signals refreshed

Apr 6, 2026

Should you rely on this paper?

This paper has useful evaluation signal, but protocol completeness is partial; pair it with related papers before deciding implementation strategy.

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

Best use

Secondary protocol comparison source

Use if you need

A secondary eval reference to pair with stronger protocol papers.

What to verify

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

Main weakness

No major weakness surfaced.

Human feedback signal
Detected
From extracted signals
Evaluation signal
Detected
Eval setup described
Usefulness for eval research
65/100
Moderate-confidence candidate

Useful as a secondary reference; validate protocol details against neighboring papers.

Abstract

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

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

strong

Rubric Rating

Directly usable for protocol triage.

"Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO)."

Evaluation Modes

strong

Automatic Metrics

Includes extracted eval setup.

"Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO)."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO)."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO)."

Reported Metrics

strong

Inference cost

Useful for evaluation criteria comparison.

"QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost."

Benchmarks and datasets

No benchmark or dataset names were extracted from the available abstract.

Reported metrics

inference cost
Human feedback details
Uses human feedback
Yes
Feedback types
Rubric Rating
Rater population
Not reported
Unit of annotation
Multi Dim Rubric
Expertise required
Math, Coding
Evaluation details
Evaluation modes
Automatic Metrics
Agentic eval
None
Quality controls
Not reported
Evidence quality
Moderate
Use this page as
Secondary protocol comparison source

Research brief

Metadata summary

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO).

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

Key takeaways

  • Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO).
  • However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon.
  • This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math?

Researcher actions

  • Compare this paper against others mentioning MATH.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • 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.

Contribution summary

  • To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

Why it matters for eval

  • To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

Researcher checklist

  • Human feedback protocol is explicit

    Detected: Rubric Rating

  • Evaluation mode is explicit

    Detected: Automatic Metrics

  • Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Metric reporting is present

    Detected: inference cost