SlowGuess/NeurIPS_2023_OCR huggingface dataset:
(a) Banana
Figure 18: MixFlow forward (fwd) and backward (bwd) single transformation error  $\delta$  on both synthetic examples and real data examples. (a)-(d) show the distribution of forward error  $\left\{\| F^n x_0 - \hat{F} \circ F^{n-1} x_0\| : n = 1, \ldots, N\right\}$  (Fwd err.) and backward error  $\left\{\| F^n x_0 - \hat{B} \circ F^{n+1} x_0\| : n = 1, \ldots, N\right\}$  (Bwd err.). These errors are computed along precise forward trajectories that originate at  $x_0$ , which is sampled 50 times independently and identically from the reference distribution  $q_0$ .  $N$  here denotes the flow length for each example.
(a) Banana
Figure 19: MixFlow shadowing window computation time (wall time in second) for both the forward (Fwd) and backward (Bwd) orbits over increasing flow length. The lines indicate the median, and error regions indicate  $25^{\text{th}}$  to  $75^{\text{th}}$  percentile from 10 runs. Note that here the Monte Carlo error between different runs is so small that the error bar is too thin to be visualized.