A Normalized Autoencoder for LHC Triggers

We appreciate the feedback from the referees. We reviewed the manuscript based on the reports. We discuss the major and minor issues below.

We would like to point out that the detailed report by the first referee suggests the publication in Scipost Physics.
We think that the introduction of Normalized AutoEncoders is an important step towards necessary anomaly detection searches with robust autoencoders in Particle Physics. Therefore, we believe the paper should be published in Scipost Physics.

Changes based on report 1:

Major issue:
We agree with the referee that, given two datasets A and B, an over-density in the low probability region p_A doesn't imply an over-density in the low p_B.
However, the underlying physics suggests this is true when comparing QCD and top jets. A top jet will likely decay (> 70% of the time) to a three prong jet, therefore it is expected that a large region of phase space will be populated exclusively by QCD jets which must look differently.
The differences between the average images of QCD and top jets and in high-level observables (e.g. tau_3/tau_2) corroborate this point.
Given these differences, it is indeed surprising that an AE is not able to tag QCD jets, and we argue that this is connected to the ability of the network to interpolate simple features.
Additionally, it has been shown that the complexity bias is an issue for AE since reconstruction heavily correlates with the number of active pixels (e.g. see arXiv:2104.09051).

In this work, we show that an NAE is symmetric in the sense that we can reliably find overdensities in low-probability regions without modifying the network architecture and fine-tuning the parameters. We see the difference between
performing density estimation on the direct or inverse task, as shown in Figs. 3-4, so there's no indication that we are not approximating the true data distribution.
We rephrased the first paragraph of the "QCD vs top jets" section to make this clear.

Minor changes:
- abstract:
"Autoencoders are the ideal analysis tool for the LHC" -> "Autoencoders are an effective analysis tool for the LHC"
"its main goal of finding physics beyond the Standard Model" -> "one of its main"

- introduction:
"that no assumption" -> "that as few assumptions as possible"
"The problem with these studies...":
The end of the paragraph addresses this point. QCD jets are easier to compress since they have a simple structure. In other words, the effective dimensionality of a QCD jet is on average smaller than a top jet. Therefore, the network is still able to interpolate these features.
We modified the corresponding paragraph to explain our claims on applications of NAEs for LHC triggers.

- network and dataset:
"by using the reconstruction error ..." -> "The NAE training includes two steps... The pre-training phase builds an approximate..."
A new paragraph describes the training procedure and the role of the modified loss function.

-Preprocessing:
We do not expect to lose physical information. The picked preprocessing does not modify the structure of the jet (e.g. prongness).
Additionally, n-reweighting has been selected to enhance features in jets with low complexity. Therefore, the improvement found in our dark jets example is not an accident.

- QCD vs top and QCD vs dark jets:
added black line label in captions

- Outlook:
"However, density-based autoencoders have not been shown to work properly and have a massive dependence on data preprocessing"
rephrased and added citations.