A Normalized Autoencoder for LHC Triggers

We thank the referee for the feedback. We carefully reviewed the manuscript and rephrased statements on the effect of preprocessing and trigger applications.
However, we are not stating that our network is insensitive to changes in the probability distribution (preprocessing).
In Section 4, we discuss the changes induced by the reweighting in the data space and the response of the NAE samples and reconstructions.
We provide clarification on statements about preprocessing below. Please let us know if your concerns arise from more specific claims.

Preprocessing:
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- Although the jets we study in the paper would pass trigger selection cuts already,
the results still demonstrate how our approach limits the assumptions
made on BSM signals to data preprocessing rather than latent space structure,
in favor of a more model-agnostic network architecture

- For phase space
regions with such modes the NAE training adjusts the energy as the
underlying structure of the latent space, such that the autoencoder
gets a robust OOD detector

- This way, the NAE training increases the energy for
Aachen jets, because the normalization forces the main prong to a
lower value. These effects are inevitable when training likelihood-based networks,
a different preprocessing will change the density and, therefore, the anomaly scores.

- Once again focusing on the $p_T$-reweightings we show the energy
distributions for the QCD training data and the two signals in Fig.~\ref{fig:djmse}.
We see that unlike in our earlier study~\cite{Buss:2022lxw} the effect of the preprocessing
on the whole distribution is limited. A shift in performance at low signal
efficiency can be seen by varying $n$ with the ordering between
the two dataset being switched around $n = 0.2~...~0.3$.
The energy distribution of the Heidelberg dataset has a shifted
main peak at $n=0.5$ which is washed out by smaller reweighting factors,
while the QCD distribution undergoes a slight shift and develops a
longer high-energy tail. For the Aachen dataset, lowering $n$ moves the mean away
from the QCD background and at the same time increases the width of the distribution.
These patterns will affect the ROC curves at low signal efficiency and large background
suppression.

- Removed: However, already looking at the AUC as a performance
measure this changes, because the performance ordering as a function
of $n$ changes towards larger signal efficiencies.

- For the more challenging Aachen and Heidelberg dark jets, the NAE works
for a reasonable single choice of preprocessing. The performance gain
from using different reweighting factors on the two datasets is explainable
in terms of the changes induced on the features of the two signals.

- Autoencoders are ML-analysis tools which effectively represent the idea
behind LHC searches.

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Triggers:
Highlight using autoencoders as of the idea of triggers: not necessarily hardware/online triggers
but tools to extract "interesting" events. Left hardware applications for future work.

- One of the goals of this work is to develop an autoencoder which is a robust anomalous jets tagger.
We explore the concept of using autoencoders as of triggers, i.e. tools that can extract
interesting events from a given background with as little bias as possible.

- The next step will be to benchmark our architecture on more
realistic datasets, optimize it for performace, and study the
possibility of implementing the network on hardware for
online triggering.