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NaturalProofs: Mathematical Theorem Proving in Natural Language
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use joint parameterization instead of pairwise | BERT (P/S) · ProofWiki retrieval | mAP: 16.82 -> 36.75 | Helped |
| use joint parameterization instead of pairwise | BERT (P/S) · Stacks retrieval | mAP: 20.93 -> 28.32 | Helped |
| joint parameterization on out-of-domain textbooks | BERT-pair (P) · Real Analysis zero-shot | mAP: 13.24 -> 11.24 | Hurt |
| train on ProofWiki+Stacks combined rather than per-domain | BERT joint · ProofWiki retrieval | mAP: 36.75 -> 32.71 | Hurt |
| add pairwise-model initialization of theorem encoder and reference embeddings (ablation) | Joint model · ProofWiki retrieval | mAP: 18.71 -> 37.51 | Helped |
| add pairwise initialization (ablation) | Autoregressive model · ProofWiki retrieval | mAP: 17.77 -> 35.37 | Helped |
| add NaturalProofs finetuning to language-pretrained BERT (ablation) | BERT pairwise · ProofWiki | mAP: 0.14 -> 16.99 | Helped |
| add language pretraining before NaturalProofs training (ablation) | BERT pairwise · ProofWiki | mAP: 0.04 -> 16.99 | Helped |
| add content to title-only input (ablation) | BERT pairwise · ProofWiki | mAP: 24.48 -> 16.99 | Hurt |
| add title to content-only input (ablation) | BERT pairwise · Stacks | mAP: 19.12 -> 21.21 | Helped |
| use autoregressive model instead of joint top-5 retrieval | reference generation · ProofWiki generation | Edit distance: 93.03 -> 84.30 | Helped |
| use BERT pairwise instead of TF-IDF | zero-shot Real Analysis · Real Analysis zero-shot | mAP: 15.79 -> 13.24 | Hurt |
Closest papers by meaning
- FaithSieve: Fine-Grained Evaluation of Math Proofs with Faithful Formal Evidence (NeurIPS 2026 · similarity 0.89)
- RealMath: A Continuous Benchmark for Evaluating Language Models on Research-Level Mathematics (NeurIPS 2025 · similarity 0.89)
- Semantic Search over 9 Million Mathematical Theorems (NeurIPS 2026 · similarity 0.89)
- Not All Proofs Are Equal: Evaluating LLM Proof Quality Beyond Correctness (NeurIPS 2026 · similarity 0.88)
- Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning (ICLR 2025 · similarity 0.88)
- miniCTX: Neural Theorem Proving with (Long-)Contexts (ICLR 2025 · similarity 0.88)
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