Factorizing LLM-Guided Search for Black-Box Protein Sequence Optimization

Protein sequence optimization must search combinatorial landscapes while spending only a small number of costly evaluations. LLMs provide adaptable biochemical priors, but mutation generation alone does not specify how a limited evaluation budget should be allocated across alternative search directions; unconstrained mutation proposals can therefore concentrate on a narrow set of positions and residues. We introduce Factorized LLM Search (FLS), an online optimization method that factorizes search control into parent selection, edit topology, source component, and concrete mutation generation. For each edit topology, FLS updates a two-stage Gibbs policy online, favoring high-reward parents and source components with fewer previously evaluated, chemistry-matched edit directions. A frozen LLM realizes concrete mutations within the sampled search subspaces. We compare FLS with matched prompt-only search, causal controls, and protein-optimization baselines on avGFP, Ube4b, GB1, and Bgl3 using 500 reward-model queries and ten runs per method. FLS improves mean endpoint reward over prompt-only search on all four benchmarks and ranks first in mean endpoint reward on three of four. These results support factorized search as a simple, auditable interface between LLM priors and budgeted protein design.