Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution
Abstract
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.
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BibTeX
@misc{ma2026linear,
title = {{Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution}},
author = {SiYuan Ma and Canran Xiao and Zikai Xiao and Albert Gao and Liang He and Xuan-Yu Wang and Shuying Cao and Xiaojun Jia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07607},
eprint = {2610.07607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07607},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution
AU - SiYuan Ma
AU - Canran Xiao
AU - Zikai Xiao
AU - Albert Gao
AU - Liang He
AU - Xuan-Yu Wang
AU - Shuying Cao
AU - Xiaojun Jia
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07607
UR - https://arxiv.org/abs/2610.07607
AB - 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.
ER -