Beyond Tokens: Probing Higher-Order Epistasis in Learned Protein Representations

Protein foundation models support mutation-effect and structural prediction, but predictive performance alone does not reveal which forms of biological interaction information remain accessible through model depth. We ask whether ESM-2 retains higher-order epistatic information as strongly as first- and second-order information across its representation hierarchy, introducing ORBIT-FMIB, a diagnostic framework combining Walsh-based interaction decomposition with subset-conditioned neural dependence estimation. The method is validated on synthetic landscapes with known interaction structure before being applied to the dense four-site GB1 fitness landscape using frozen ESM-2 representations. An initial production run suggested ESM-2 retains higher-order epistatic information less well than lower-order information ($Δ_{\mathrm{HO-LO}}=-0.107$). An independent replication of the complete measurement grid, under matched GPU hardware and identical critic seeds, substantially reduced this contrast ($Δ_{\mathrm{HO-LO}}=-0.017$), and its sign was unstable across otherwise-defensible evaluation-pairing choices applied to the same trained critics ($-0.011$ to $+0.015$). We therefore do not currently have robust evidence that ESM-2 selectively loses higher-order epistatic information, nor that retention is equal across orders; the directional question remains open. The measurement protocol itself, including its documented removal of a positional-subset shortcut in pooled critics, remains validated and is unaffected by this finding. ORBIT-FMIB is offered as a diagnostic framework for probing interaction structure in protein foundation models; this study's own replication result illustrates why such probing requires adequately-powered reproducibility checks before its output is treated as a biological finding.

Recently, there has been a growing adoption of protein language models (PLMs) in biomedical science. Their embeddings provide a rich numerical representation of protein sequences which achieve state-of-the-art performance on several downstream tasks including protein fitness prediction. However, PLM embeddings are not directly interpretable and, thereby, it remains unclear what features they encode. To gain insight into which biochemical properties of the protein are driving the prediction, we leverage an orthogonal projection technique that removes linear effects of known tabular features from embeddings and extend it to high-order and interaction effects. In this way, we remove the effects of interpretable biochemical features from PLM embeddings. In an ablation study, we show that this leads to a decrease in performance for a downstream classifier trained only on the embeddings to predict protein fitness. In an additional evaluation, we find that these biochemical features explain a substantial part of the variance in the predictions of this classifier. Hence, we can show that PLM embeddings encode patterns correlated with biochemical properties and quantify their contribution to predicting protein fitness. This computationally efficient approach is not limited to the features or embeddings considered here and is readily transferable to problem settings beyond protein fitness prediction.

Masked language modeling (MLM) is the standard objective for training protein language models, typically implemented by randomly masking individual residues at a fixed rate (e.g., 15%). This practice implicitly assumes that all sequence positions contribute equally to representation learning. In downstream fitness prediction tasks, however, protein sequences are governed by three-dimensional structural dependencies and long-range residue contacts that induce strong nonlocal couplings between residues. We introduce Bucket Masking, a structure-aware masking strategy that selects groups of residues based on their proximity in three-dimensional space, preferentially masking structurally coupled regions during training. By conditioning the masking distribution on residue contacts, Bucket Masking shifts the learning objective toward modeling long-range interactions that are critical for protein function. Across four downstream protein fitness prediction tasks, Bucket Masking enables up to a 14% improvement over standard random masking, excelling at predicting higher-order mutational interactions. Through controlled ablations, we show that these improvements arise from mask placement rather than span size, establishing masking as a positional inductive bias.