Beyond Solver Verdicts: Generative Reward Models for Autoformalization
Mirrored from arXiv — NLP / Computation & Language for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
arXiv:2609.11085 (cs)
[Submitted on 10 Sep 2026]
Title:Beyond Solver Verdicts: Generative Reward Models for Autoformalization
Authors:Vikash Singh, Debargha Ganguly, Aman Goel, Ali Torkamani, Xiaoxue Han, Joseph Lilien, Ferhat Erata, Vipin Chaudhary
View a PDF of the paper titled Beyond Solver Verdicts: Generative Reward Models for Autoformalization, by Vikash Singh and Debargha Ganguly and Aman Goel and Ali Torkamani and Xiaoxue Han and Joseph Lilien and Ferhat Erata and Vipin Chaudhary
View PDF
HTML (experimental)
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.
| Subjects: | Machine Learning (cs.LG); Computation and Language (cs.CL) |
| Cite as: | arXiv:2609.11085 [cs.LG] |
| (or arXiv:2609.11085v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.11085
arXiv-issued DOI via DataCite (pending registration)
|
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Beyond Solver Verdicts: Generative Reward Models for Autoformalization, by Vikash Singh and Debargha Ganguly and Aman Goel and Ali Torkamani and Xiaoxue Han and Joseph Lilien and Ferhat Erata and Vipin Chaudhary
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.