Speaker
Description
We introduce TN-SHAP-Q, a multilinear framework for computing Shapley values and interactions in quantum neural networks (QNNs). For QNNs with \emph{finite-lift} data encodings, we show that the circuit output is multilinear in the lifted coordinates and, moreover, coincides exactly with the \emph{multilinear extension} (MLE) of the induced cooperative game. This connection unifies feature and gate attribution within a common game-theoretic framework, and allows attribution to be computed directly from the multilinear structure of the model, without explicit coalition enumeration or surrogate fitting. Three consequences follow from this exact MLE realization. First, first-order Shapley values are computed exactly by Owen diagonal integration. Second, order-$k$ interaction indices are obtained from the same extension, with a Gauss--Legendre exactness threshold $M \ge \lceil (P-k+1)/2 \rceil$ that decreases with interaction order, where $P$ is the number of players (features or gates). Third, exact first-order Shapley values are recovered with polynomially many extension evaluations $O(P^2)$ rather than $2^P$ evaluations of coalition enumeration. Experiments on a trained Iris QNN, a breast-cancer variational quantum classifier, synthetic QNNs and the \texttt{qshaptools} QAOA benchmark reproduce exact Shapley values and interactions to machine precision, validate the predicted quadrature-exactness thresholds, exhibit the expected $1/\sqrt{N}$ degradation under finite-shot noise (where $N$ denotes the measurement shots) and reveal interaction structure that first-order attribution misses.
| Topic | Tensor methods and quantum-inspired machine learning |
|---|---|
| Additional Topic | Quantum variational circuits and their applications |