CapsNets Continuing the Convolutional Quest

We would like to thank the referee for their interest and careful reading of our paper, as well as their useful comments. We have clarified some points in our paper and addressed the points the referee has raised. Please find attached our list of changes.

1 - Add discussion of differences between original capsule implementation and
the current method.
- Both implementations are, by design, identical, to clarify this we added:
``Analogous to the original capsule paper, we transition between
convolutional and capsule part by re-shaping...'' in section 4.

2 - Add information about how many routings were used.
- We used 3 routings, as was shown to be optimal in other
studies. We have rephrased a sentence to reflect this:
``We repeated this for a chosen number of routings, where
three iterations have in other studies given the best results''
now reads
``We repeated this for 3 routings, which has been
shown in other studies to give the best results''

3 - More information about the preprocessing. The authors
mention that CapsNets need less preprocessing, and it sounds like
only scaling the images so the most intense pixel has a value of 1.0
was done. Is this the same for the benchmarks of the Rutgers DeepTop
Taggers as done here?
- We have added: ``In contrast to the minimal pre-processing
we use for the event image capsule network, for the Rutgers tagger and the
jet image capsule network we employ
the full pre-processing for each jet as described in Ref. [10].
The jets are selected and centered around the $p_T$ weighted centroid of the
jet, and rotated such that the major principal axis is vertical.
The image is then flipped to ensure that the maximum activity is in
the upper-right-hand quadrant. Finally, the images are pixelated and normalized."

4 - Compare CapsNets to networks of similar architecture but without
the Capsules for the Pooling CapsNets'' architecture of Figure 6.
- We have now made this comparison, and have included the plot in a response to the report.
We observe a small but persistent increase in performance by using
capsule networks over a dense network with a similar architecture. This
comes along with the advantage of having the capsule vectors themselves,
which provide a window into how the network is making decisions.

5 - Consider adding a W′ signal to see how CapsNets deal with signal
which has some substructure signals and similar kinematics. While
pre-selection should be able to deal with some of the differences here, it
would be for the study of the CapsNet themselves.
- A W' analysis would be an interesting new application for our
network, but it would be a whole project in itself and falls
outside the scope of our current publication.

6 - Some mention of how the results of [43] compare to the t¯tH classifier used here.
- We have added ``For this set-up we find comparable performance to
Ref. [43], with an AUC of 0.715, which is slightly above their
upper limit.''

7 - [Optional] Publicly available code or code snippets.
- Unfortunately, we are unable to dedicate the time to make a public code useful to the community.