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This paper introduces the Linear Fitness Subspace (LFS) hypothesis, positing that protein fitness variation induced by mutations is linearly accessible within a compact, assay-specific subspace of PLM representations. Building on this, Subspace-Guided Evolutionary Search (SGES) leverages this LFS for sample-efficient surrogate modeling and uncertainty estimation in directed evolution. SGES demonstrates superior fitness prediction and search efficiency across numerous assays compared to zero-shot PLMs and existing ML-guided optimization methods.
Protein fitness landscapes are surprisingly linear in a low-dimensional subspace of PLM representations, enabling dramatically more efficient directed evolution.
Model-guided directed evolution seeks to identify high-fitness protein variants under limited oracle budgets. Protein language models (PLMs) provide rich representations for this task, but task-agnostic zero-shot scores can be misaligned with a target assay, while supervised search in high-dimensional embedding spaces can make surrogate modeling and uncertainty estimation sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: within mutation-induced residue-level representation changes, a compact, assay-specific set of directions makes fitness variation linearly accessible from few labeled variants. This is a local, supervision-recoverable statement rather than a claim that protein fitness landscapes or global PLM geometry are universally linear. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which estimates an LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition in the learned subspace. Across 10 core ProteinGym assays, 87 extended static-validation assays, and an 18-assay budgeted-search evaluation, SGES improves fitness prediction and search efficiency over zero-shot PLMs and recent ML-guided protein optimization baselines. Controlled comparisons with PCA, random projections, label-shuffled PLS, classical mutation features, and acquisition ablations further isolate the benefit of a fitness-aligned site-delta coordinate.
