Reconstructing partonic kinematics at colliders with Machine Learning

This paper uses machine learning to reconstruct the parton kinematics in proton proton collisions that produce a hadron and a photon. It is similar in spirit to the ep studies in [3,4], only there are not classical methods to compare with (as the kinematics of the initial state are less constrained by the final state). Overall, I found the paper to contain a lot of useful information, but many of the descriptions are not concise. For example, I'm not sure how much of Sec. 2 and 3 is really necesary to have in the main body of the paper. I also don't think it is necesary to explain what a neural network is in the main body.

- The references in the first paragraph are a bit random. This is not a problem per se, but I would encourage the authors to reconsider their list. I found the mention about EIC to also be a bit strange. It is true that there is interest in the EIC community to use AI/ML methods, but this is a relatively small part of the larger community (and the one referenced workshop is balanced by countless workshops in the context of the LHC).

- Please use vectorized graphics.

- I was missing a discussion / demonstration of model dependence. If you train with one model and test with another, how universal are the results?

- Related: the results seem very process dependent. Would one need to retrain for every process? What about processes that are ambiguous?

- It was not completely obvious to me what this method would be used for. In e+e- and ep, the event kinematics can be reconstructed and are used as inputs to theory comparisons / extractions. Would you please say a bit more about this? (sorry if it is alreayd included and I missed it!)

1. Problems that authors are going to solve are clearly stated.
2. Simple machine learning technique is used to solve the problems.

1. Uncertainties on their parton kinematics predictions are not discussed.
2. The selected kinematic region of the process may not be visible at the LHC.
3. The machine learning solution of their problems may have a numerical solution.

This paper is a proof-of-concept study of reconstructing parton-level kinematics in proton-proton collisions only using measurable final state data.
Authors attempt to reconstruct the initial state and final state momentum fractions of a hard process in a proton+proton->pion+photon (pp->pi+gamma) process as an illustrative example.
For this purpose, the authors introduced supervised regression techniques based on particle-level Monte-Carlo event simulation and three regression models: linear regression, Gaussian regression, and neural network.
Their method could reconstruct the parton-level kinematics with reasonable accuracy.

While this work is an interesting application of machine learning to collider physics, I think the following points must be addressed before I recommend this work for publication.

1. The selected process (pp->pi+gamma) with the mild selection criterion in Eq. 13 may be highly contaminated by busy hadron activities and pile-ups in (high-luminosity) LHC. Also, the trigger systems of ATLAS and CMS may wash out some of the kinematic regions considered in this paper. For example, this ATLAS report (arXiv:1909.00761) and CMS report (http://cds.cern.ch/record/2668901) say that the trigger efficiencies of photons are not good for pT < 15 GeV. Delphes uses 10 GeV cuts to photon for both ATLAS and CMS detector simulations. Do you have some idea about those?

2. Renormalization and factorization scale uncertainties and PDF/FF fitting uncertainty are not discussed. The parton level kinematics estimators are sensitive to those functions since it is trained by supervised learning from the dataset using those functions. The systematic uncertainty propagation should be reported together to strengthen the author's claim about the reconstructibility of the parton level kinematics.

3. Please state the loss functions for training the models.

4. If authors use mean square errors (MSE) for fitting x and z in their training dataset, I think authors could give us an asymptotic solution of their regressor. The regression using MSE loss has an asymptotic solution: the expectation of x (or z) given inputs of neural networks. Since the authors showed closed forms of differential cross-sections of their process and its Monte-Carlo simulation, I think the computation of the asymptotic solution is relatively straightforward.

5. The lower right of Figure 16 shows that some components still fail to be reconstructed. Have you tried larger-sized networks and used more training samples? There might be some underfitting since fitting performance keeps improving when you enlarge the network size.

6. Which dataset is used for drawing the correlation plots: fig 13, fig 14, fig 15, and fig 16? If the same simulated dataset is used, I think getting diagonal lines on those plots are somewhat natural. However, the simulation is always limited and different from nature, so sizable bias may occur in reality. Do you have any estimation of such bias by applying your trained networks to other simulated datasets from other Monte Carlo event simulations, such as Herwig, Pythia, Sherpa, and so on?


Minor comments:
- Page 15: MLP is a model of function, not an algorithm.

- Section 3.2 says that the following analyses are based on RHIC kinematics. If analysis on section 4 also uses data simulated at the RHIC energy scale, I think it's better to show that in the plots to improve readability because several energy scales are considered in previous sections.

- Section 4.5 is about future works. The analysis is not done in this paper yet, so it's better to move it to the conclusions and outlook section.