CRIQ: Feature Interaction Quantification in Deep Neural Networks with Coordinate-Ray Integrals

Higher-order game-theoretic interactions reveal critical neural network behaviors. However, existing black-box approximations suffer from combinatorial subset sampling bottleneck in high dimensions. To address this limitation, we introduce Coordinate-Ray Interaction Quantification (CRIQ), a scalable framework for interaction estimation in deep neural networks that maps discrete derivatives to coordinate-ray integrals. To resolve non-differentiability in continuous piecewise-linear (CPWL) models and bypass high-order tensor differentiation in feature embeddings, we also introduce Iterated Dimensional Reduction (IDR), which decomposes discrete derivatives into an alternating sum of 1D first-order derivative integrals. We derive CRIQ's sample complexity, propose an estimation algorithm and measure its convergence stability empirically, showing that CRIQ makes feature-level interaction quantification in high-dimensional neural networks computationally feasible.