Interaction as Interference: A Quantum-Inspired Aggregation Approach
This work addresses the challenge of controlling interaction effects in predictive models for researchers and practitioners in machine learning, offering a novel but incremental method with specific gains on synthetic tasks.
The paper tackles the problem of modeling interactions in machine learning by proposing a quantum-inspired aggregation approach that treats interaction as interference, enabling direct control over synergy versus antagonism through relative phase. The resulting Interference Kernel Classifier (IKC) outperforms strong baselines on a synthetic XOR task and shows consistent improvements in negative log-likelihood, Brier score, and expected calibration error on real datasets like Adult and Bank Marketing, with positive Coherent Gain observed.
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 \(Δ_{\mathrm{INT}}\) 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.