Beyond Solver Verdicts: Generative Reward Models for Autoformalization — Paper

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 35 min agohigh
Arxiv announce type: cross
Source:arXiv (Atom API + RSS)T1observed 34 min agohigh
arXiv id: 2609.11085
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Categories: cs.LG, cs.CL
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Hf paper url: https://huggingface.co/papers/2609.11085
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 27 min agomedium
Hf comments: 1
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 25 min agomedium
Upvotes: 1
Source:Hugging Face Hub (public pages, model cards, papers)T2observed 25 min agomedium
PDF: arxiv.org/pdf/2609.11085
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Primary category: cs.LG
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 35 min agohigh

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Attributed facts

12

Source tiers

T1T29 / 3

Freshest observation

25 min ago

Conflicts

2 flagged

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Authors: Vikash Singh, Debargha Ganguly, Aman Goel

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Claim history · Upvotes

1 claims · 1 propertiesShow all properties

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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

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 →

11 Sept 2026
Property changedPaperBeyond Solver Verdicts: Generative Reward Models for Autoformalization
Beyond Solver Verdicts: Generative Reward Models for Autoformalization: arxiv announce type changed from new to cross
Arxiv announce typenew→crossarxiv
rss.arxiv.org
11 Sept 2026
New paperPaperBeyond Solver Verdicts: Generative Reward Models for Autoformalization
New paper: Beyond Solver Verdicts: Generative Reward Models for Autoformalization
arxiv
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.CL	feed	T1· Official	34 min ago	1
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	35 min ago	1
Hugging Face Hub (public pages, model cards, papers)	huggingface.co/papers	listing	T2· Quality secondary	25 min ago	2

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