We have simplified Figure 3 considerably, removing STL (which uses biased gradients), and removing 2 row C

We would like to thank the reviewers for their kind and thoughtful comments. Any attempt to mitigate particle degeneracy (e.g. Replicating Fig 1BD, we find similar, albeit less extreme results, with TMC always being faster than SMC. In particular, we have included Eq. 36 in the main text, and also included the corresponding choice of This should help to clarify that Eq. 11 applies to any directed graphical model (we have also included references In the example in Figure 1, we consider a model that does not have a chain-structure (see Appendix Figure 1A). IW AE performs arbitrarily badly due to the high-dimensionality of the state-space.