{"slug": "sage-formalization-with-semantic-correction", "title": "Sage: Formalization with Semantic Correction", "summary": "Sage, an agentic formalization framework described in arXiv paper 2609.35790v1, suppresses answer leakage to 2.7% while reaching 73.3% pass@4 joint compilation and semantic fidelity on Omni-MATH without proofs, versus 42.0% for a fine-tuned Goedel-Formalizer-V2 baseline. The four-stage decomposed generation pipeline with a dual-signal semantic correction loop pairs Lean 4 compiler diagnostics with multi-dimensional semantic feedback, addressing a 70.9% answer leakage rate in prior models that guess unverified answers. On IMO-Unformalized, a set of 175 unformalized International Mathematical Olympiad problems, Sage achieved 87.4% pass@4 verified fidelity against 19.4% for the baseline and won over 79% of blind pairwise evaluations.", "body_md": "arXiv:2609.35790v1 Announce Type: new \nAbstract: While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 formal statements are already provided. Translating informal natural language into a formal language is a critical data bottleneck plagued by an \"illusion of rigor\": standard type-checkers accept statements that compile but drop hypotheses, introduce vacuous truths, or subtly alter mathematical bounds. To resolve this, we introduce Sage (Semantic Agent-Guided Formalization Engine), an agentic framework that replaces monolithic translation with a four-stage decomposed generation pipeline coupled with a dual-signal semantic correction loop. By pairing Lean 4 compiler diagnostics with multi-dimensional semantic feedback, our correction loop enforces mathematical fidelity alongside syntactic validity. By explicitly accounting for the gap between open-ended queries and declarative formal targets, our pipeline prevents models from achieving high formalization rates by guessing unverified answers (exhibiting a 70.9% answer leakage rate). Consequently, Sage suppresses leakage to 2.7% while achieving 73.3% pass@4 joint compilation and semantic fidelity on the Omni-MATH without proofs (compared to 42.0% for a fine-tuned Goedel-Formalizer-V2 baseline). Finally, on IMO-Unformalized, a novel frontier of 175 unformalized International Mathematical Olympiad problems, Sage demonstrates effective zero-shot generalization with 87.4% pass@4 verified fidelity compared to just 19.4% for the baseline, winning over 79% of blind pairwise evaluations.", "url": "https://wpnews.pro/news/sage-formalization-with-semantic-correction", "canonical_source": "https://arxiv.org/abs/2609.35790", "published_at": "2026-09-30 04:00:00+00:00", "updated_at": "2026-09-30 04:19:10.414783+00:00", "lang": "en", "topics": ["artificial-intelligence", "machine-learning", "ai-research", "ai-agents", "large-language-models"], "entities": ["Sage", "Lean 4", "Omni-MATH", "Goedel-Formalizer-V2", "IMO-Unformalized", "International Mathematical Olympiad", "arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/sage-formalization-with-semantic-correction", "markdown": "https://wpnews.pro/news/sage-formalization-with-semantic-correction.md", "text": "https://wpnews.pro/news/sage-formalization-with-semantic-correction.txt", "jsonld": "https://wpnews.pro/news/sage-formalization-with-semantic-correction.jsonld"}}