Order-Resolved Interaction Attribution in Noisy Quantum Machine Learning

Feature-interaction explanations determine whether a model uses features jointly or independently. For a deployed quantum classifier, reliable attribution requires separating interactions learned from data from those induced by the circuit and accounting for hardware noise. We develop an interaction-attribution framework that addresses these effects through the encoding, entangler graph, and noise channel. The encoding fixes the trigonometric degree of the decision function, allowing low-order Sobol variances to be identified exactly from a fixed grid. The entangler graph determines where architecture-induced interactions can occur. For the circuits studied here, the pairwise reach is $2(L-1)$ when the entangler commutes with the readout, and a hardware experiment on ibm_fez confirms this prediction for a distance-four interaction. Noise has a separate effect: its mode-wise contraction does not imply contraction of interaction variances, which can increase when noise breaks cancellations. We derive the attenuation law that holds and find that attenuation increases with interaction order for depolarizing and amplitude-damping noise. Across twelve datasets, the completeness residual is biased downward in all 60 single-encoding runs, while interaction rankings remain stable with mean Spearman correlation above $0.997$. At higher noise, the two-point correction reduces the residual error from $0.0334\pm 0.0087$ without correction to $0.0018\pm 0.0011$. These results provide a circuit-aware framework for attributing interaction structure in deployed quantum models. Code: https://anonymous.4open.science/r/ORIAN.