This is demo code to generate the results in "Robust First and Second-Order Differentiation for Regularized Optimal Transport" (https://arxiv.org/pdf/2407.02015)

util.py: utility functions.

SinkhornHessian.py: Main function classes -- SinkhornHessian and ShuffledRegression.

CondH.py: It plots the delay of the smallest positive eigenvalue $\lambda_{2N-1}$ in $N$ and $\epsilon$ in two cases: (1) Equally spaced points on the unique circle and (2) Uniformly distributed point cloud in unit square $[0,1]^2$. (Figure 1)

Hessian_speed_uniform.py: It plots the comparison of runtime (in seconds) in Hessian computing among three approaches: unroll, implicit differentiation and analytic expression with regularization (ours). (Figure 2 Top)

Hessian_accuracy_uniform.py: It plots the comparison of marginal error for Hessian computing among three approaches: unroll, implicit differentiation and analytic expression with regularization (ours). (Figure 2 Bottom)

shuffled_regression.py: It plots the results in shuffled regression with Gaussian mixtures. (Figure 3)

3D_pointcloud_regist.py: It plots the results in 3D Point Cloud Registration. (Figure 4) The ModelNet10 dataset can be downloaded in https://vision.princeton.edu/projects/2014/3DShapeNets/ModelNet10.zip.