Interaction as Interference: A Quantum-Inspired Aggregation Approach

TL;DR

This paper introduces a quantum-inspired aggregation method that models interaction effects as interference, enabling controlled synergy or antagonism, and demonstrates its effectiveness in classification tasks.

Contribution

It proposes a novel interference-based aggregation approach inspired by quantum mechanics, with a lightweight classifier and diagnostics for interaction analysis.

Findings

IKC outperforms baselines on synthetic XOR task

Coherent aggregation improves model calibration and likelihood

Diagnostics effectively measure interference effects

Abstract

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), \emph{coherent} aggregation sums complex amplitudes before squaring, creating an interference cross-term, whereas an \emph{incoherent} proxy sums squared magnitudes and removes it. In a minimal linear-amplitude model, this cross-term equals the standard potential-outcome interaction contrast \(\Delta_{\mathrm{INT}}\) in a \(2\times 2\) factorial design, giving relative phase a direct, mechanism-level control over synergy versus antagonism. We instantiate this idea in a lightweight \emph{Interference Kernel Classifier} (IKC) and introduce two diagnostics: \emph{Coherent Gain} (log-likelihood gain of coherent over the incoherent proxy) and \emph{Interference Information} (the induced Kullback-Leibler gap). A controlled phase sweep recovers the identity. On a high-interaction synthetic task (XOR), IKC outperforms strong baselines under paired, budget-matched comparisons; on real tabular data (\emph{Adult} and \emph{Bank Marketing}) it is competitive overall but typically trails the most capacity-rich baseline in paired differences. Holding learned parameters fixed, toggling aggregation from incoherent to coherent consistently improves negative log-likelihood, Brier score, and expected calibration error, with positive Coherent Gain on both datasets.