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

Abstract

Protein fitness landscapes contain nonlinear interactions in which mutation effects depend on other residues. We introduce ORBIT, an Order-Resolved Benchmarking of Interaction Transformations framework that separates interaction presence, representation accessibility, and functional recovery. ORBIT first validates Walsh-based diagnostics on synthetic landscapes with known interaction order, then analyzes the experimentally measured GB1 fitness landscape under the FLIP 2-vs-rest setting. We compare ridge regression, a standard MLP, independent tokens, nonlinear independent tokens, and Residual Interaction Tokenization (RIT). Across 20 paired training seeds, the primary two-hidden-layer comparison found no significant architecture differences in FLIP test R^2, third- or fourth-order functional recovery, or final-layer third- or fourth-order accessibility. However, RIT significantly increased pairwise accessibility at the token stage relative to both independent-token controls (Delta A_tok,2 = 0.2468, d_z = 1.67, Holm-adjusted p = 1.14 x 10^-5), without a detectable downstream higher-order advantage. A pre-specified depth/capacity analysis showed that deeper MLPs improved FLIP prediction, third-order functional recovery, and final-layer third-order accessibility; fourth-order accessibility also improved relative to the shallow MLP but remained below zero in absolute held-out R^2. ORBIT therefore reveals representation-level changes hidden by conventional prediction metrics and distinguishes early interaction-aware encoding from higher-order structure constructed by downstream nonlinear capacity.