Library Reachability in LSR-Synth: How Anti-Memorization Design Changes the Measurement of Symbolic Discovery

Computer Science > Artificial Intelligence [Submitted on 30 Jul 2026] Library Reachability in LSR-Synth: How Anti-Memorization Design Changes the Measurement of Symbolic Discovery Zhan'ao Yao, Liang Yin, Zhihao Gao, Boxuan Zhang, Xiaoyu Wu, Linjing Li, Rongyan Wang, Tingwei Chen, Youwei Wang, Xiaolin Zhao, Jiahui Shi, Jianjun Liu Existing benchmarks for scientific equation discovery are largely composed of well-known equations available in the public domain, making it difficult to determine whether a model is discovering laws from data or merely recalling answers from its training corpus. LSR-Synth mitigates this problem by introducing novel synthetic terms into established scientific mechanisms and filtering the resulting tasks for novelty, solvability, and scientific plausibility. This paper examines a narrower measurement question: can these tasks further distinguish scientific priors supplied by language models from conventional operator search that does not access task semantics? We construct a semantics-free baseline using a fixed vocabulary with publicly documented provenance, and assess the role of candidate coverage through semantic blinding, library weakening, and matched operator-family knockouts. Under the current task snapshot, search budget, and scoring protocol, the fixed vocabulary already covers most tasks, while language-model-generated candidates rarely expand the set of solvable instances. Their marginal contribution becomes substantial only when vocabulary coverage is selectively disrupted. Strict out-of-distribution evaluation lowers the absolute success rates of all methods but does not alter this relationship. These findings neither invalidate LSR-Synth's controls against memorization of complete formulas nor imply that language-model priors are generally unhelpful. Rather, they support a more limited conclusion: most current tasks remain suitable for evaluating the fitting and recombination of previously unseen expressions, but are insufficient on their own to identify contributions from priors beyond a fixed search space. Subjects: Artificial Intelligence (cs.AI) Cite as: arXiv:2607.28684 [cs.AI]   (or arXiv:2607.28684v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2607.28684 Focus to learn more Submission history From: Zhan'ao Yao [view email] [v1] Thu, 30 Jul 2026 02:36:26 UTC (561 KB) Access Paper: HTML (experimental) view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-07 Change to browse by: cs References & Citations NASA ADS 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)