Beyond Solver Verdicts: Generative Reward Models for Autoformalization
Updated 14 min ago · first seen 11 Sept 2026
paper_01M294FNZJW0HN8ERJR76VZZMF
- Published
- 11 Sept 2026
- T1 · 15 min ago
- arXiv
- 2609.11085
- T1 · 15 min ago
- Category
- cs.LG
- T1 · 15 min ago
Abstract
Neurosymbolic systems rely on mathematical solvers to guarantee reasoning correctness, yet solvers are fundamentally blind to whether a formal translation maintains strict reference-equivalence to a designated formalization. We formalize this vulnerability as Verdict-Preserving-Unfaithfulness (VPU): a failure mode where an incorrect encoding executes successfully and matches the expected verdict. We theoretically prove that structural, verdict-only verification heuristics are mathematically bounded to chance-level detection on these deceptively valid traces. To resolve this, we introduce Generative Verification (GenV), which distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score by repurposing the language model's native vocabulary space. Mechanistic analysis via decision-projected logit lenses and sparse autoencoders shows this generative readout natively extracts precise spatial error coordinates without explicit localization training. Empirically, our oracle-mined verifier (GenV+HN) achieves 0.961 AUROC in reference-equivalence verification, generalizes zero-shot across unseen translators and divergent formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation.
Authors 8
Vikash Singh, Debargha Ganguly, Aman Goel, Ali Torkamani, Xiaoxue Han, Joseph Lilien, Ferhat Erata, Vipin Chaudhary
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Arxiv announce type
- cross
Source:arXiv (Atom API + RSS)T1observed 14 min agohigh
- arXiv id
- 2609.11085
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Categories
- cs.LG, cs.CL
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 15 min agohigh
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Provenance
Attributed facts
9
Source tiers
T19
Freshest observation
14 min ago
Conflicts
None
No models linked to this paper yet.
- Authors
- Vikash Singh, Debargha Ganguly, Aman Goel
As of
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Claim history
Official pageofficial_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/abs/2609.11085 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Abstractabstract1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| Neurosymbolic systems rely on mathematical solvers to guarantee reasoning correctness, yet solvers are fundamentally blind to whether a formal translation maintains strict reference-equivalence to a designated formalization. We formalize this vulnerability as Verdict-Preserving-Unfaithfulness (VPU): a failure mode where an incorrect encoding executes successfully and matches the expected verdict. We theoretically prove that structural, verdict-only verification heuristics are mathematically bounded to chance-level detection on these deceptively valid traces. To resolve this, we introduce Generative Verification (GenV), which distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score by repurposing the language model's native vocabulary space. Mechanistic analysis via decision-projected logit lenses and sparse autoencoders shows this generative readout natively extracts precise spatial error coordinates without explicit localization training. Empirically, our oracle-mined verifier (GenV+HN) achieves 0.961 AUROC in reference-equivalence verification, generalizes zero-shot across unseen translators and divergent formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation. | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Arxiv announce typearxiv_announce_type2
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cross | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
| new | → | superseded | arXiv (Atom API + RSS)T1 | high | deterministic |
arXiv idarxiv_id1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 2609.11085 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Categoriescategories1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG, cs.CL | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Hf paper urlhf_paper_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://huggingface.co/papers/2609.11085 | → current | current | Hugging Face Hub (public pages, model cards, papers)T2 | medium | deterministic |
Hf commentsmetric.hf_comments1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 1 | → current | current | Hugging Face Hub (public pages, model cards, papers)T2 | medium | deterministic |
Upvotesmetric.upvotes1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 1 | → current | current | Hugging Face Hub (public pages, model cards, papers)T2 | medium | deterministic |
PDFpdf_url1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| https://arxiv.org/pdf/2609.11085 | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Primary categoryprimary_category1
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| cs.LG | → current | current | arXiv (Atom API + RSS)T1 | high | deterministic |
Publishedpublished_at3conflicting claims
| Value | Valid from → to | Status | Source | Confidence | Extractor |
|---|---|---|---|---|---|
| 10 Sept 2026 | → current | conflicting | Hugging Face Hub (public pages, model cards, papers)T2 | medium | deterministic |
| 10 Sept 2026 | → current | conflicting | Hugging Face Hub (public pages, model cards, papers)T2 | medium | deterministic |
| 11 Sept 2026 | → current | current | arXiv (Atom API + RSS)T1 | conflicted | deterministic |
Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
Beyond Solver Verdicts: Generative Reward Models for Autoformalization: arxiv announce type changed from new to cross
Arxiv announce typenew→crossarxivNew paper: Beyond Solver Verdicts: Generative Reward Models for Autoformalization
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.CL | feed | T1· Official | 14 min ago | 1 |
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 15 min ago | 1 |
Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.