This supplementary has an extended version of the paper, and contains two notebooks for reproducing Figures from this submission. We encourage the reviewers the run this notebook after reading the submission.

hippo_function_approximation.ipynb:
- checks the function approximation interpretation of these HiPPO variants (Proposition 1), including the new methods introduced HiPPO-LegS (time-invariant) and HiPPO-FouT
- includes animations that show the "online function reconstruction" in action. These animations are a more informative version of Figures 2 and 5

ssm_kernels.ipynb:
- shows how individual SSM basis functions are defined (Figures 1 and 3)
