Orthogonal Polynomial Approximation for Matrix-Log Normalization in Global Covariance Pooling

Global Covariance Pooling (GCP) typically relies on matrix-logarithm normalization, whose SVD/EIG-based computation is CPU-bound and costly. This work derives orthogonal-polynomial approximations of the matrix logarithm on symmetric positive definite matrices that are GPU-friendly, reducing computational cost and moving a previously CPU-bound operation onto the GPU.

We benchmark polynomial families in terms of numerical accuracy, runtime, and classification performance on large-scale vision datasets, showing that carefully designed polynomials offer a strong efficiency–fidelity trade-off for scalable log-normalization in GCP-based networks.

Recommended citation: Md Rifat Ur Rahman, Md Raihan Khan, Md Sakib Hossain Shovon, Pietro Liò, and Mohammad Ali Moni, "Orthogonal Polynomial Approximation for Matrix Log Normalization in Global Covariance Pooling," BMVC 2026 (accepted).