Galactic Margin Machines: A physics-inspired framework for nonlinear classification

Margin-based classifiers such as support vector machines achieve strong generalization by maximizing geometric separation in feature space, yet their decision boundaries are often constrained by implicit kernel geometry and offer limited physical interpretability. This paper introduces Galactic Margin Machines (GMM), a physics-inspired classification framework that formulates learning as the interaction of competing potential fields generated by labeled training samples. Each sample is assigned a non-negative mass that determines its influence, generating a smooth potential landscape whose equilibrium surface defines the decision boundary. In this formulation, classification corresponds to partitioning feature space into regions of dominant potential, while the margin is interpreted as the minimum potential advantage of the correct class. The proposed framework naturally yields curved, geometry-aware decision boundaries and promotes sparsity through mass regularization, leading to a compact set of influential training samples termed support stars. A theoretical analysis establishes stability guarantees based on potential margins and connects the model to classical potential theory. Extensive experiments on synthetic datasets with complex geometric structure and on standard UCI benchmark datasets demonstrate that GMM achieves competitive performance comparable to strong baseline classifiers across multiple error metrics, including linear and nonlinear support vector machines, logistic regression, k-nearest neighbors, and random forests. Qualitative visualizations further illustrate the interpretability of the learned decision surfaces and the emergence of sparsity. Overall, the results demonstrate that potential-field learning provides an interpretable and competitive alternative to conventional kernel-based classifiers.