Interaction as Interference: A Quantum-Inspired Aggregation Approach for Classification

Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule (probability as squared amplitude), coherent aggregation sums complex amplitudes before squaring, creating an interference cross-term, whereas an incoherent proxy sums squared magnitudes and removes it. Representing input contributions as complex amplitudes, the relative phase between amplitudes modulates the sign and magnitude of this cross-term, providing a mechanism-level account of synergy versus antagonism. In a minimal amplitude-linear model over a 2×2 design—the simplest setting for feature interaction—this cross-term equals the standard interaction contrast ΔINT, which can be interpreted as the potential-outcome interaction measure under randomized assignment. We instantiate this idea in a lightweight Interference Kernel Classifier (IKC) and introduce two diagnostics: Coherent Gain (log-likelihood gain of coherent aggregation over the incoherent proxy) and Interference Information (the induced Kullback–Leibler gap). A controlled phase sweep recovers this identity. On a high-interaction synthetic task (XOR), IKC attains predictive performance closely matching that of the evaluated classical baselines under paired, budget-matched comparisons; on real tabular data, its competitiveness is dataset-dependent, trailing the best evaluated baseline on Adult while outperforming it on Bank Marketing. In coherent–incoherent ablations with learned parameters held fixed, removing the coherent cross-terms degrades negative log-likelihood, Brier score, and expected calibration error on both datasets, with positive Coherent Gain. This quantum-inspired approach offers an interpretable mechanism for modeling and diagnosing feature interactions in probabilistic classification.