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This paper introduces Product-Unit Residual Networks (PURe), which integrate multiplicative product units with residual connections to explicitly model nonlinear feature interactions, showing improved accuracy, robustness, and interpretability over standard MLPs.
TBP-mHC introduces a novel parameterization for manifold-constrained hyper connections in residual networks, achieving full expressivity of the Birkhoff polytope with O(n^2) degrees of freedom and improved stability and scalability.