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Beyond Solver Verdicts: Generative Reward Models for Autoformalization

Updated 3 h ago · first seen 11 Sept 2026

paper_01M294FNZJW0HN8ERJR76VZZMF

Published: 11 Sept 2026; T1 · 4 h ago
arXiv: 2609.11085; T1 · 4 h ago
Category: cs.LG; T1 · 4 h 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: arxiv.org/abs/2609.11085
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
arXiv id: 2609.11085
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Categories: cs.LG, cs.CL
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Hf paper url: https://huggingface.co/papers/2609.11085
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 4 h agomedium
Hf comments: 1
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 3 h agomedium
Upvotes: 1
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 3 h agomedium
PDF: arxiv.org/pdf/2609.11085
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 4 h agohigh

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Provenance

Attributed facts

Source tiers

T1T29 / 3

Freshest observation

3 h ago

Conflicts

2 flagged

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Claim history

15 claims · 12 properties2 conflicting

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2609.11085	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
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.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type2

Claim history for Arxiv announce type
Value	Valid from → to	Status	Source	Confidence	Extractor
cross	11 Sept 2026 21:03 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic
new	11 Sept 2026 21:02 UTC → 11 Sept 2026 21:03 UTC	superseded	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2609.11085	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

Claim history for Authors
Value	Valid from → to	Status	Source	Confidence	Extractor
Vikash Singh, Debargha Ganguly, Aman Goel, Ali Torkamani, Xiaoxue Han, Joseph Lilien, Ferhat Erata, Vipin Chaudhary	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

Claim history for Categories
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG, cs.CL	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Hf paper urlhf_paper_url1

Claim history for Hf paper url
Value	Valid from → to	Status	Source	Confidence	Extractor
https://huggingface.co/papers/2609.11085	11 Sept 2026 21:10 UTC → current	current	Hugging Face Hub (public pages, model cards, papers)T2	medium	deterministic

Hf commentsmetric.hf_comments1

Claim history for Hf comments
Value	Valid from → to	Status	Source	Confidence	Extractor
1	11 Sept 2026 21:10 UTC → current	current	Hugging Face Hub (public pages, model cards, papers)T2	medium	deterministic

Upvotesmetric.upvotes1

Claim history for Upvotes
Value	Valid from → to	Status	Source	Confidence	Extractor
1	11 Sept 2026 21:10 UTC → current	current	Hugging Face Hub (public pages, model cards, papers)T2	medium	deterministic

PDFpdf_url1

Claim history for PDF
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/pdf/2609.11085	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
cs.LG	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at3conflicting claims

Claim history for Published
Value	Valid from → to	Status	Source	Confidence	Extractor
10 Sept 2026	11 Sept 2026 21:12 UTC → current	conflicting	Hugging Face Hub (public pages, model cards, papers)T2	medium	deterministic
10 Sept 2026	11 Sept 2026 21:10 UTC → current	conflicting	Hugging Face Hub (public pages, model cards, papers)T2	medium	deterministic
11 Sept 2026	11 Sept 2026 21:02 UTC → 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 →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.CL	feed	T1· Official	4 h ago	1
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	4 h ago	1
Hugging Face Hub (public pages, model cards, papers)	huggingface.co/papers	listing	T2· Quality secondary	3 h ago	2

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.