Casting a graph net to catch dark showers

1. This work is an application of DL techniques to the work [10], which is interesting.

1. This work is an application of "known" DL techniques on a specific physics example.

Once authors deal with questions in the requested changes part, I would like to recommend this work for a publication.

1. Learnings with low level information (particle level) generally suffer from pileups, especially dealing with jets. There are prescriptions to reduce effects from pileups. How much is DGCNN robust under these conventional procedures for pileups removals ?

2. It would be appreciated if authors perform comparison analyses between semi-invisible and hadronic tau. On top of this, W+jets (where W->hadronic tau+neutrino) study would be relevant for mono-jet study.

3. Authors "observe" performance of various DL techniques on a subject of "semi-invisible jet" (just like HEP-EX.) It would be very welcomed if authors provide some reasons (qualitative analyses) behind these performance dependency on Dark QCD model-parameters.

4. I guess that the Z' mass dependence in analysis is negligible as authors seem like to fix PT range of jet.
- For Z' = 2TeV where PT of jet are O(1) TeV, what would be expected performance over top-jet with O(1) TeV PT ?

The paper presents a study of the performance of several neural network architectures designed to act on low-level collider event inputs in improving the discrimination between QCD jets and semi-visible jets originating from a dark shower. The presentation is clear and writing is of high quality. The optimization of such searches is currently a subject of active development and this study contributes to that conversation. I am happy to recommend publication provided the more discussion on a few points is expanded and the changes requested here (and in the other report) are implemented, as detailed below.

1- The high level variables referred to at the bottom of p. 2 are conventionally referred to collectively as $N$-subjettiness, not subjettiness.
2- Given that baryons would be expected to have a mass $\sim \Lambda_d$, the same as the assumption made for the mesons in the text, better justification for ignoring baryons in the phenomenological study should be given. Since an $SU(3)$ gauge group is assumed, I would expect a combinatoric suppression of $\sim 1/9$ in collider production, as in the SM. The authors should comment on whether this is enough to ignore the baryons for their purposes or if additional suppression must be provided.
3- Since no hyperparameter optimization is performed for the networks going from top to semi-visible jet tagging, can the authors exclude the possibility that the performance differences in the networks would be reduced for a difference choice of hyperparameters?
4- While the DGCNN showed the best performance for a given choice of parameters when trained on those parameters, when ultimately trained with mixed samples (a much more realistic scenario) the performance is degraded by a factor of a few. Have the authors checked that the other architectures degrade similarly when training on mixed samples? If so, this should be stated; if not, it should be done. Perhaps the other architectures are more robust to model variation.
5- I want to second the other referee's concern about ignoring systematic uncertainties induced by the tagger. The uncertainty in the signal efficiency in real world events for a tagger trained on simulated signal where no calibration region exists can be significant and should be discussed.
6- Some measure of the effort of training the various networks in Table 4, perhaps wall clock time on equivalent systems, would be helpful as a metric in benchmarking the ultimate network performance in the absence of hyperparameter optimization.

1) Comparison of different network architectures
2) Exploration of model parameters affecting network performance
3) Forecast of limits

1) Explanation of model

This is a very strong paper and I suggest it for publication. The authors examine different supervised neural network architectures to search for semi-invisible jets. They find that a Dynamic Graph Convolutional Neural Network performs better than jet images or Lorentz Layer networks.

I have a few minor comments and requested changes.

1) In section 2, the authors describe the model and how it can lead to semi-invisible jets. While the diagram is nice, showing how the Z' decays, it would be very helpful to explicitly show the decay modes of the ${\rho^+}$, $\rho^0$. This would help explain why the $\rho^0$ is the only dark meson decaying on collider time scales and setting the R_inv = 0.75. For instance in [1809.10184], the $\rho^+$ decays promptly to q q$^{\prime}$ when $m_{\rho} < 2 m_{\pi}$.

2) In Figure 3 the CNN and LoLa change which is better for tops versus semi-visible. Do the authors have any insights into this?

3) Table 2 shows the results for training and testing on different meson masses. However, they never show results for testing on a lighter mass than was trained on, is there a reason for this.

4) Using a parameterized network would greatly help over the mixed samples. These allow the network to generalize between samples better. The authors mention this but do not cite the paper showing this [https://arxiv.org/abs/1601.07913 for hep]

5) On page 12, the number 3.84 seems to come out of nowhere. Rephrasing such that they are looking for the 95% CL exclusion, which is when q_mu = 3.84 would help the reader.

6) On page 13, there needs to be more explanation about why systematics can now safely be neglected, especially since the previous section was about how training on the wrong parameters (even on mixed samples) leads to a reduction in performance.

7) They should also cite the few other hep-ph papers utilizing graph neural networks such as https://arxiv.org/abs/1807.09088, (https://iml-wg.github.io/HEPML-LivingReview)

This paper demonstrates the application of graph networks applied to the jets of dark showers at the LHC. The work is timely, the analysis is thorough, and the paper is well-written. I congratulate the authors on this nice addition to the literature! Below are a small number of minor comments that it would be good to address before the paper is published.

- [36,48,49] block on p5, might be best to add 1902.09914.
- p5: "dense neural network" is Tensorflow jargon - perhaps "fully connected network" would be more appropriate.
- Discussion on p6, before Sec. 3.1: I'm not sure how this is different than a CNN; a CNN operator, just like the EdgeConv operator is local, but having many layers allows for global relations. Please either tell me why this is wrong or modify the text accordingly.
- "Normally, the network prediction is given by the class with the highest probability." -> I would never advocate to do this, since the best cut should depend on the relative abundance of signal and background which most certainly is not 50%-50% (=the prior used in your training).
- Fig. 3 right: can you please comment how this compares with the results shown in the community top tagging paper (1902.09914)?
- Why R = 0.8? That is not the radius used by ATLAS.
- p12: Please explain 3.84 (I am sure you have a good reason, but please don't make the reader guess!).
- "We can therefore safely neglect additional systematic uncertainties introduced by the dark shower tagger." -> the stat. uncertainty is at most 30% - it does not seem crazy to me that the systematic uncertainty would be comparable. Why is it then save to neglect?
- Last paragraph of the conclusions: unsupervised methods are not the only anomaly detection procedures that have been proposed - there are a variety of semi-supervised methods that may be (more) effective. See e.g. https://iml-wg.github.io/HEPML-LivingReview/.
- Delphes: what detector setup are you using?