Cold-Start Protein–Protein Interaction Prediction Is Bounded by the Frozen Embedding, Not the Classifier: A Leakage-Controlled Audit and a Calibrated Conformal Baseline
Sequence-based protein–protein interaction (PPI) prediction has reached an empirical plateau on leakage-controlled benchmarks, where the dominant signal under the cold-start regime—predicting interactions among proteins absent from training—comes from evolutionary-scale protein language models (PLMs) rather than from the downstream classifier. A natural hypothesis is that elaborate head-only optimization over a frozen PLM can narrow the in-domain-to-cold-start gap cheaply. We test this hypothesis and report a negative-but-constructive result. We build a many-objective NSGA-III search that attaches a compact head to a frozen ESM-2 t33 backbone and jointly optimizes the head architecture, a physicochemical feature mask, and a contrastive-pretraining curriculum against a fitness vector that explicitly contains the cold-start gap; we then subject it to a controlled audit. On a leakage-controlled yeast DIP benchmark with Park–Marcotte stratification (homology-disjoint at 40% identity), the searched contrastive head, trained to a fair budget, reaches cold-start (C3) average precision (AUPR) 0.683, whereas an off-the-shelf random forest on the same embeddings reaches 0.734; gradient boosting and an RBF-SVM also exceed it. Seven design axes—objective, architecture, pair operator, embedding compression, pooling, training budget, and training-set size—each fail to close the gap, indicating the achievable level is set by the frozen representation, not the classifier. On a second, human benchmark (Bernett), simple classifiers again reach the published state-of-the-art range ( $\approx 0.65$ vs. 0.69 AUPR) at a fraction of the cost. Finally, we add distribution-free calibrated selective prediction via split conformal, turning a frozen-ESM classifier into a deployable cold-start predictor with finite-sample coverage. We release all code and reproduction drivers.