Peer review Data-driven Discovery of Biophysical T Cell Receptor Co-specificity Rules Curtis Callan Princeston

Recent data-driven approaches to T cell receptor (TCR) specificity claim the discovery of generalizable “biophysical rules” through machine learning and contrastive optimization. In this work, we demonstrate that such claims rely on a categorical confusion between statistical inference and physical law. We provide a rigorous mathematical analysis showing that learned similarity metrics, defined as minimizers of dataset-dependent loss functions, are structurally non-equivalent to closed variational frameworks. The comparison is carried out explicitly against the Universal Ψ Equation, formulated as a single constrained variational principle independent of empirical training data. We prove that correlations inferred by data-driven models arise from optimization over finite datasets and lack closure, universality, and intrinsic falsifiability, whereas correlations in a variational framework are enforced by global stationarity constraints. No mapping exists between the two constructions. The results establish that data-driven TCR co-specificity models are statistical estimators rather than physical theories, and clarify the conceptual boundary between machine learning methodologies and foundational theoretical physics.