Interpretable Thermodynamic Score-based Classification of Relaxation Excursions

Classification and regression are cornerstones of computational biology and science at large, from identifying cell types to stratifying patients by disease state. Current deep learning classifiers provide accurate predictions but offer neither uncertainty estimates nor insight into which features matter most. On the other hand, while diffusion models excel at generating new samples from learned distributions, they have seen limited use in classification and prediction tasks. We introduce a physics-inspired conceptual approach, which we name Keeping SCORE, that transforms diffusion models into probabilistic engines for classification and regression. By measuring dissipation along noising trajectories under different class assumptions, we calculate exact class likelihoods and quantify prediction confidence. Our approach is naturally accompanied by feature attributions that identify which input variables drive each decision, providing interpretability without modifying existing trained models. We test our framework across image recognition tasks (handwritten digits, natural photos), single-cell genomics (distinguishing cell identities, mapping gene perturbation effects), and molecular biophysics (predicting mutation impacts on protein folding energy), showing accurate probability estimates alongside explanations through physically meaningful coordinates. This connection between non-equilibrium statistical mechanics and modern AI approaches creates interpretable, uncertainty-aware predictions for biological discovery.