anyakrakusuma: A Python Library for Entropic Schrödinger Bridges on Idealized Geometries
This work addresses the numerical instability of discrete static Schrödinger bridge problems—equivalently, entropy-regularized optimal transport—under high cost-to-regularization ratios by introducing a log-domain Sinkhorn–Knopp iteration algorithm. The proposed method achieves high-precision solutions even in extreme parameter regimes where the Gibbs kernel suffers severe underflow. A diagnostic framework based on information entropy, covariance analysis, and geometric metrics is developed to precisely characterize the structural properties of optimal couplings and intermediate distributions. The algorithm maintains marginal residuals as low as 10⁻⁹ and perfect marginal fidelity at cost-to-regularization ratios up to 400, demonstrating convergence across approximately eight orders of magnitude. It accurately recovers geometric transformations such as 90-degree rotations with an error of merely 0.07°, and exhibits empirical convergence rates significantly surpassing theoretical worst-case bounds.