@inproceedings{ma-etal-2026-linear,
title = "Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution",
author = "Ma, SiYuan and
Xiao, Canran and
Xiao, Zikai and
Gao, Albert and
He, Liang and
Wang, Xuan-Yu and
Cao, Shuying and
Jia, Xiaojun",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.738/",
pages = "15490--15511",
ISBN = "979-8-89176-462-0",
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 existing methods either rely on task-agnostic zero-shot scores or perform search in high-dimensional embedding spaces where surrogate modeling and uncertainty estimation can be sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: mutation-induced fitness variation encoded by PLMs is concentrated in a low-dimensional linear subspace of residue-level representation changes. This view explains why zero-shot PLM scores are often useful but incomplete: they behave as fixed, task-agnostic projections, whereas few-shot supervision can recover assay-specific fitness directions. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which learns the LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition directly in the learned subspace. Across 10 core ProteinGym assays and an extended set of 87 assays, SGES improves fitness prediction, budgeted search efficiency, computational cost, and biological interpretability over zero-shot PLMs and recent ML-guided protein optimization baselines. These results suggest that PLMs encode protein fitness in a geometry that is more linear, lower-dimensional, and more directly exploitable than previously assumed."
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<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 existing methods either rely on task-agnostic zero-shot scores or perform search in high-dimensional embedding spaces where surrogate modeling and uncertainty estimation can be sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: mutation-induced fitness variation encoded by PLMs is concentrated in a low-dimensional linear subspace of residue-level representation changes. This view explains why zero-shot PLM scores are often useful but incomplete: they behave as fixed, task-agnostic projections, whereas few-shot supervision can recover assay-specific fitness directions. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which learns the LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition directly in the learned subspace. Across 10 core ProteinGym assays and an extended set of 87 assays, SGES improves fitness prediction, budgeted search efficiency, computational cost, and biological interpretability over zero-shot PLMs and recent ML-guided protein optimization baselines. These results suggest that PLMs encode protein fitness in a geometry that is more linear, lower-dimensional, and more directly exploitable than previously assumed.</abstract>
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%0 Conference Proceedings
%T Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution
%A Ma, SiYuan
%A Xiao, Canran
%A Xiao, Zikai
%A Gao, Albert
%A He, Liang
%A Wang, Xuan-Yu
%A Cao, Shuying
%A Jia, Xiaojun
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F ma-etal-2026-linear
%X 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 existing methods either rely on task-agnostic zero-shot scores or perform search in high-dimensional embedding spaces where surrogate modeling and uncertainty estimation can be sample-inefficient. We propose the Linear Fitness Subspace (LFS) hypothesis: mutation-induced fitness variation encoded by PLMs is concentrated in a low-dimensional linear subspace of residue-level representation changes. This view explains why zero-shot PLM scores are often useful but incomplete: they behave as fixed, task-agnostic projections, whereas few-shot supervision can recover assay-specific fitness directions. Building on this observation, we introduce Subspace-Guided Evolutionary Search (SGES), which learns the LFS from a small initial sample and performs surrogate modeling, uncertainty estimation, and acquisition directly in the learned subspace. Across 10 core ProteinGym assays and an extended set of 87 assays, SGES improves fitness prediction, budgeted search efficiency, computational cost, and biological interpretability over zero-shot PLMs and recent ML-guided protein optimization baselines. These results suggest that PLMs encode protein fitness in a geometry that is more linear, lower-dimensional, and more directly exploitable than previously assumed.
%U https://aclanthology.org/2026.findings-emnlp.738/
%P 15490-15511
Markdown (Informal)
[Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution](https://aclanthology.org/2026.findings-emnlp.738/) (Ma et al., Findings 2026)
ACL
- SiYuan Ma, Canran Xiao, Zikai Xiao, Albert Gao, Liang He, Xuan-Yu Wang, Shuying Cao, and Xiaojun Jia. 2026. Linear Fitness Subspace in Protein Language Models Enables Sample-Efficient Directed Evolution. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 15490–15511, Budapest, Hungary. Association for Computational Linguistics.