Boltzmann Classifier: A Thermodynamic-Inspired Approach to Supervised Learning

Abstract

We present the Boltzmann classifier, a novel distance based probabilistic classification algorithm inspired by the Boltzmann distribution. Unlike traditional classifiers that produce hard decisions or uncalibrated probabilities, the Boltzmann classifier assigns class probabilities based on the average distance to the nearest neighbors within each class, providing interpretable, physically meaningful outputs. We evaluate the performance of the method across three application domains: molecular activity prediction, oxidation state classification of transition metal complexes, and breast cancer diagnosis. In the molecular activity task, the classifier achieved the highest accuracy in predicting active compounds against two protein targets, with strong correlations observed between the predicted probabilities and experimental pIC50 values. For metal complexes, the classifier accurately distinguished between oxidation states II and III for Fe, Mn, and Co, using only metal-ligand bond lengths extracted from crystallographic data, and demonstrated high consistency with known chemical trends. In the breast cancer dataset, the classifier achieved 97% accuracy, with low confidence predictions concentrated in inherently ambiguous cases. Across all tasks, the Boltzmann classifier performed competitively or better than standard models such as logistic regression, support vector machines, random forests, and k-nearest neighbors. Its probabilistic outputs were found to correlate with continuous physical or biological properties, highlighting its potential utility in both classification and regression contexts. The results suggest that the Boltzmann classifier is a robust and interpretable alternative to conventional machine learning approaches, particularly in scientific domains where underlying structure property relationships are important.