Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification

[2606.01160] Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification Skip to main content Search Submit Donate Log in Computer Science > Artificial Intelligence arXiv:2606.01160 (cs) This paper has been withdrawn by Mingyu Li [Submitted on 31 May 2026 ( v1 ), last revised 22 Aug 2026 (this version, v2)] Title: Expected Value Alignment for Generative Reward Modeling in Formal Mathematics Verification Authors: Shihao Ji , Haotao Tan , Zihui Song , Mingyu Li No PDF available, click to view other formats Abstract: Large Language Models (LLMs) are increasingly used with formal interactive theorem provers such as Lean 4. Scaling these systems with reinforcement learning or search methods requires process reward models (PRMs) that can evaluate intermediate reasoning steps. Existing reward-model designs expose a practical trade-off. Value-head models provide continuous scores but modify the generative model interface, while generative reward models preserve textual rationales but are poorly matched to continuous floating-point regression because numeric values are split across tokens. We introduce Expected Value Alignment (EVA), a reward-modeling procedure that keeps the surface output discrete while extracting continuous scores from the model's token distribution. The model emits integer scores in a structured JSON format, and EVA computes a continuous score as the expectation over the logits of the corresponding anchor tokens. Training combines the causal language modeling objective with an auxiliary mean squared error loss on these expected values. We instantiate EVA in \textit{Leibniz}, a reward model for Lean 4 formal verification, and evaluate it against zero-shot and reward-modeling baselines. The evaluation demonstrates that continuous logit-based scoring significantly reduces discretization artifacts while retaining the interpretability of generative critiques. Comments: Withdrawn due to serious concerns regarding the authenticity and accuracy of the listed authorship. The identity of one or more listed authors cannot presently be verified, and the author list may not represent distinct contributors. The manuscript is withdrawn pending institutional review Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2606.01160 [cs.AI] (or arXiv:2606.01160v2 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2606.01160 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mingyu Li [ view email ] [v1] Sun, 31 May 2026 11:06:48 UTC (17 KB) [v2] Sat, 22 Aug 2026 07:08:50 UTC (1 KB) (withdrawn) Full-text links: Access Paper: Withdrawn Additional Features Audio Summary Current browse context: cs.AI < prev | next > new | recent | 2026-06 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools 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, Media 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 Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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 . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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