Venue: ICLR 2023 TinyPapers

Reviews:

final_score: rating: High Impact (HI): a submission which meets the reviewing criteria and is predicted to make an impact on the field
review_content: summary_of_contributions: The authors propose a differentiable variant of sequential Monte Carlo sampling for estimating normalisation constants of sampled distributions. They systematically compare Langevin and Hamiltonian dynamics with the proposed dSMCS under different resampling variants. They conclude that resampling particle weights but omitting the resampling gradients during differentiation, results in better estimates for the normalisation constants and smaller variance in the gradients.
strengths_and_weaknesses: 
Strengths:

- This is very well written paper with well designed figures.

- Touches a rather important topic for sampling.

- Has nice structure with outlining the experimental/numerical results first, and then providing theoretical explanations.


Weakness:

- The article is too dense (reasonably for the size of the paper) and includes a lot of acronyms (also reasonably given the permitted length and the number of variants employed here).

- Authors might not need the DEI initiative to publish...

- It is not entirely clear which methods are contributed by the present paper and which are already in the literature and are only used for comparison.
suggested_changes: - Please increase size of Figure 3.

- A comparison with DAIS (if not too computationally demanding) may be helpful to compare the resulting ESS and ELBOs. 

- An implementation that supports the findings and details the proposed resampling variants would greatly facilitate the understanding of the proposed approach.
review_title: null

final_score: rating: High Potential (HP): a submission which meets the reviewing criteria and has potential to make an impact on the field
review_content: summary_of_contributions: This paper proposes using a resampling operation in (D)AIS, instead of prior methods which use a non-differentiable MH update step or a learned kernel.  The authors provide evidence that resampling achieves higher ESSs (with a similar feel to how SMC improves over regular IS) on an existing benchmark problem.  Some theoretical analysis is also provided. 
strengths_and_weaknesses: This is a strong submission, which actually has the feel of a full-length paper that has been aggressively cut down to length.  I query if this is the intention of TinyPapers as a venue (but the work itself cannot be faulted on that front).  There have been several recent papers on differentiable SMC/AIS-like algorithms (DAIS, SIXO), and so this work would be a nice addition to the literature.  

## Questions
1. The authors' methods achieve nearly perfect ESS, which, if true, is very compelling.  I query how the ESS is being computed.  The ESS should be computed from the weights prior to resampling.  It isn’t fully surprising that the methods with resampling get higher ESS, because the particles’ weights are reset after resampling.  A fully degenerate SMC sampler (where just one particle survives) can achieve a near-perfect ESS after resampling if a single particle is iterated into a flat region of the joint probability (all iterated particles are very similar and hence equally weighted).  I invite the authors to comment on this, clarify how they compute the ESS, and maybe provide additional context on how particles differ.  Why is the ESS for “No Resampling” so low at the start?  Should the ESS for all methods at step zero be approximately the same?  
2. I think theorem 2 is trivially correct?  If the ESS = N, then there is effectively no resampling, or rather, since the particles are all equally likely, then there is no preferential signal over the “wiring” of particles.  I think this is okay, it is always nice to write out foundational results, but this theorem could be dropped to the supplement to free space for more discussion.

I think the result in theorem 1 is however a nice parallel to the follow-up work to Maddison et al. (2017a), SIXO (Lawson et al., 2022), where the backwards message asymptotically makes the bound tight (and hence all particles are equally weighted and ESS = N).  Drawing an explicit parallel (in the discussion section) between the two works would be a nice way to link in to some more recent literature as well.  

*Slight edit from my original review*:  I think proving out that resampling gradients go to zero in the limit of perfect ESS is worthwhile, but it is especially important to explicitly link this to the fact that your experiments seem to recover near-perfect ESS.  I would like to see an additional comment/caveat that this proof (and associated benefit) only holds in an asymptotic range.  On more complex examples, where perfect ESS is not recovered, it doesn't apply, and you fall back to the empirical evidence of the benefit, as per Maddison.  

## Clarity

The paper itself is pretty well written and reads clearly to someone who is familiar with the topic.  The paper is very condensed and is intense technical for such a short paper, which may put some readers off, but, again, may be the result of the format.  

My main concern with the clarity is that I really struggle to parse the results.  Figure 1 is not super clear.  I think “No Resampling” is regular (D)AIS, and “GST” and “CAT” are two variants of the authors work? I am to take from this that no resampling is always almost entirely degenerate?  

I then have no idea what Figure 2 is showing.  The colors, markers, dashed lines etc are all very confusing.  For the main paper, I recommend thinning the results and focusing on just one of Langevin or Hamiltonian (include the other in the appendix), and really highlighting whatever the main result is.  

## Correctness 
I think the work is correct, modulo some clarification w.r.t. ESS above.

## Reproducibility
The authors have provided a lot of additional detail in the supplement.  I believe the work would be reproducible.  

suggested_changes: See above in “Clarity”.  My main request is “thinning” the results figures, and highlighting just a single positive result in the main text.  The more complete results can then be deferred to the supplement.  

With this distillation of *the* key result, drawing explicit connections to Lawson et al., and clarifying how ESS is computed/expanding on the weaknesses of ESS as a metric, I would be comfortable to rating this paper even higher.  

Good work, and good luck.
review_title: null

Decision: Invite to present