[25] Conor Durkan, Artur Bekasov, Iain Murray, and George Papamakarios. Neural spline flows. In Advances in Neural Information Processing Systems, 2019.
[26] Rianne van den Berg, Leonard Hasenclever, Jakub Tomczak, and Max Welling. Sylvester normalizing flows for variational inference. In Conference on Uncertainty in Artificial Intelligence, 2018.
[27] Sameera Ramasinghe, Kasun Fernando, Salman Khan, and Nick Barnes. Robust normalizing flows using Bernstein-type polynomials. arXiv:2102.03509, 2021.
[28] Sergei Yu Pilyugin. Theory of pseudo-orbit shadowing in dynamical systems. Differential Equations, 47 (13):1929-1938, 2011.
[29] Abbas Fakhari and Helen Ghane. On shadowing: ordinary and ergodic. Journal of Mathematical Analysis and Applications, 364(1):151-155, 2010.
[30] Robert Corless and Sergei Yu Pilyugin. Approximate and real trajectories for generic dynamical systems. Journal of mathematical analysis and applications, 189(2):409-423, 1995.
[31] Jonathan Meddaugh. Shadowing as a structural property of the space of dynamical systems. arXiv:2106.01957, 2021.
[32] Sergei Yu Pilyugin and O.B. Plamenevskaya. Shadowing is generic. Topology and its Applications, 97(3): 253-266, 1999.
[33] Ivan Dokmanić and Rémi Gribonval. Beyond moore-penrose part i: generalized inverses that minimize matrix norms. arXiv:1706.08349, 2017.
[34] Michelle Schatzman. Numerical Analysis: a Mathematical Introduction. Oxford University Press, 2002.
[35] Cornelius Lanczos. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. 1950.
[36] Ed S. Coakley and Vladimir Rokhlin. A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices. Applied and Computational Harmonic Analysis, 2013.
[37] Juntang Zhuang, Nicha C Dvornek, sekhar tatikonda, and James s Duncan. MALI: A memory efficient and reverse accurate integrator for neural ODEs. In International Conference on Learning Representations, 2021.
[38] Juntang Zhuang, Nicha Dvornek, Xiaoxiao Li, Sekhar Tatikonda, Xenophon Papademetris, and James Duncan. Adaptive checkpoint adjoint method for gradient estimation in neural ODE. In International Conference on Machine Learning, 2020.
[39] Ricky T. Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. Neural ordinary differential equations. In Advances in Neural Information Processing Systems, 2018.
[40] Patrick Kidger. On neural differential equations. arXiv:2202.02435, 2022.
[41] Yu Qiao and Nobuaki Minematsu. A study on invariance of  $f$ -divergence and its application to speech recognition. IEEE Transactions on Signal Processing, 58(7):3884-3890, 2010.
[42] George Birkhoff. Proof of the ergodic theorem. Proceedings of the National Academy of Sciences, 17(12): 656-660, 1931.
[43] Tanja Eisner, Balint Farkas, Markus Haase, and Rainer Nagel. Operator Theoretic Aspects of Ergodic Theory. Graduate Texts in Mathematics. Springer, 2015.
[44] Brian Coomes, Hüseyin Koçak, and Kenneth Palmer. Rigorous computational shadowing of orbits of ordinary differential equations. Numerische Mathematik, 69:401-421, 1995.
[45] Joseph Frederick Elliott. The characteristic roots of certain real symmetric matrices. Master's thesis, University of Tennessee - Knoxville, 1953.
[46] Sergey Yu Pilyugin. Spaces of dynamical systems. de Gruyter,  $2^{\mathrm{nd}}$  edition, 2019.
[47] Tomas Geffner and Justin Domke. MCMC variational inference via uncorrected Hamiltonian annealing. In Advances in Neural Information Processing Systems, 2021.
[48] Guodong Zhang, Kyle Hsu, Jianing Li, Chelsea Finn, and Roger Grosse. Differentiable annealed importance sampling and the perils of gradient noise. In Advances in Neural Information Processing Systems, 2021.