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HFEPX · Eval paper review

Evaluating the Robustness of Proof Autoformalization in Lean 4

Zhengtao Gui, Sheng Yang, Zhouxing Shi

Published

Jun 12, 2026

Citations

0

Trust level

Low

Usefulness score

0/100 (Low)

Extraction confidence

25% (Low)

Derived from extracted protocol signals and abstract evidence.

Rater population

Not reported

Signals refreshed

Oct 16, 2026

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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.

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

Use if you need

Background context only.

What to verify

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

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Human feedback signal
Not explicit
Not explicit in abstract metadata
Evaluation signal
Weak or implicit
Validate from full paper
Usefulness for eval research
0/100
Adjacent candidate

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

If you are doing eval pipeline work, start here

Human Eval Papers LLM-as-Judge Papers Pairwise Preference Papers Tool-Use Evaluation Search

Abstract

Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4. Existing LLM-based models for proof autoformalization are typically evaluated only on well-formed informal proofs from curated datasets. We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models. We formulate two categories of perturbations: a global perturbation paraphrases the informal theorem-proof pair in a different style, under which the formalization should remain consistent; a local perturbation alters a value, symbol, or proof step, possibly in a counterfactual way, and a robust formalization should faithfully reflect the perturbation rather than reverting to the original or inferring a different one on its own. We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations. We evaluate seven recent models: their correctness varies under global perturbations, and they mostly fail to remain faithful under local perturbations.

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.

"Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4."

Benchmarks / Datasets

partial

MATH 500, MiniF2F

Useful for quick benchmark comparison.

"We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4."

Benchmarks and datasets

MATH-500MiniF2F

Reported metrics

No metric terms were extracted from the available abstract.

Human feedback details
Uses human feedback
No
Feedback types
None
Rater population
Not reported
Expertise required
Math
Evaluation details
Evaluation modes
None
Agentic eval
None
Quality controls
Not reported
Evidence quality
Low
Use this page as
Background context only

Research brief

Metadata summary

Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4.

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

Key takeaways

  • Proof autoformalization aims to translate a mathematical informal proof in natural language into a formal proof in a formal language such as Lean 4.
  • Existing LLM-based models for proof autoformalization are typically evaluated only on well-formed informal proofs from curated datasets.
  • We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models.

Researcher actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • 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.

Recommended queries

Contribution summary

  • We argue that a robust proof autoformalizer must remain faithful even for informal proofs that diverge from these idealized ones, and we present the first study on the robustness of proof autoformalization models.
  • We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations.
  • We evaluate seven recent models: their correctness varies under global perturbations, and they mostly fail to remain faithful under local perturbations.

Why it matters for eval

  • We build a benchmark with both perturbations on miniF2F and MATH-500, and automatically measure how stable a proof autoformalization's correctness is under global perturbations and how faithfully its output reflects local perturbations.

Researcher checklist

  • Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Benchmark or dataset anchors are present

    Detected: MATH-500, MiniF2F

  • Metric reporting is present

    No metric terms extracted.