Learning what to preserve: Grammar constrained search across scientific domains

Scientific strings encode structure directly in their notation. A chemical formula such as $\mathrm{LiM}{\mathrm{n}}_2{\mathrm{O}}_4$ specifies elemental identities and stoichiometric quantities, while a protein mutation such as M105K specifies residues and a positional coordinate. Yet pretrained models typically process such inputs using tokenizers learned from corpus statistics rather than from the structure of the notation itself. Existing solutions often introduce domain-specific parsers, vocabularies, or tokenizers, requiring a new representation strategy for each scientific domain. We ask whether a shared input representation rule can instead be discovered from downstream tasks across domains with different structural requirements. We introduce GCMS, a grammar-constrained multi-domain search framework that uses a policy gradient search over interpretable input rewrites. Joint search on crystal-system classification and protein mutation fitness discovers a common representation without an element inventory, residue classifier, or domain-specific parser. The learned rule transfers across unseen tasks and notation systems, including held-out materials properties, additional protein assays, modified peptides, and genomic variants. GCMS reduces band-gap MAE from $0.6161$ to $0.4918$ relative to WordPiece and reaches $0.8789$ Spearman on the held-out ProteinGym BLAT assay. These results show that transferable structure in scientific notation can be discovered from task supervision rather than engineered separately for each domain.