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$\nu$-Flows: Conditional Neutrino Regression

by Matthew Leigh, John Andrew Raine, Knut Zoch, Tobias Golling

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Submission summary

Authors (as registered SciPost users): John Raine
Submission information
Preprint Link: scipost_202208_00052v3  (pdf)
Code repository:
Data repository:
Date accepted: 2023-04-13
Date submitted: 2023-02-09 09:54
Submitted by: Raine, John
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Phenomenology
Approach: Phenomenological


We present $\nu$-Flows, a novel method for restricting the likelihood space of neutrino kinematics in high-energy collider experiments using conditional normalising flows and deep invertible neural networks. This method allows the recovery of the full neutrino momentum which is usually left as a free parameter and permits one to sample neutrino values under a learned conditional likelihood given event observations. We demonstrate the success of \mbox{$\nu$-Flows} in a case study by applying it to simulated semileptonic \ttbar events and show that it can lead to more accurate momentum reconstruction, particularly of the longitudinal coordinate. We also show that this has direct benefits in a downstream task of jet association, leading to an improvement of up to a factor of 1.41 compared to conventional methods.

Author comments upon resubmission

We would like to thank both reviewers for the valuable input and feedback. We have addressed all suggestions and implemented suggested corrections as well as drafted responses to particular issues that were raised.
This has helped polish the paper and bring it to an overall standard we are proud of.

Most changes are minor and listed in the following section, but some other points are addressed here.

A reviewer was interested to note how many of the events had to be rejected due to ambiguous jet-parton matching. Out of the number of events that pass the selection criteria (kinematics, multiplicities, tagging), approximately 9% were discarded due to ambiguous jet-to-parton matching. Out of those remaining, approximately 52% are fully matchable, i.e. all four quarks from the ttbar event are unambiguously matched to reconstructed jets.

We were requested to add extra discussion to the results shown in Fig 5 as well as address the idea that one could use the v-FF network to provide a weighting to the two kinematic solutions based on proximity.
This is a very interesting observation and suggestion, and isn’t something we had had in mind. It would certainly be an interesting avenue of study to improve the naive v-FF and mass constraint methods, however for this paper we prefer to remain focused on the flows for this paper without a deep dive into exactly what it learns. Certainly from the jets and labelling we know it is more than just the mass constraint that it learns. Furthermore, there would still be the instances where the mass constraint method leads to no real solutions, whereas in all instances v-Flows is able to provide a full prediction over the potential neutrino momentum solutions.

Best regards,
The authors

List of changes


Fixed a typo that was pointed out and has been changed
old: of potential process"
new: of potential processes

Case Study

The text has been changed to to reflect the correct truth parton matching of R=0.4.
old: a radius of R < 0.2
new: a radius of R < 0.4

It was pointed out that the wording of the following text bit messy and it has been modified to be more direct
old: This is in contrast to traditional approaches where different approaches need to be optimised for final states with other multiplicities of neutrino s in the final state, for example Neutrino Weighting [35–37] in the case of dilepton ttbar production
new: Furthermore, while performance is expected to degrade, the architecture of v-Flows can be trivially scaled to predict any fixed number of neutrino momenta, it would just need to be retrained on the new process. In contrast, traditional approaches differ from one channel to another. For example the kinematic constraint method is not applicable in dilepton tt production where other techniques, such as Neutrino Weighting [35–37], are used.


We have changed the text in the previous paragraphs to make it more clear where comparisons to the mass constraint method in Fig 5 are being made. As well as added the following paragraph to the discussion of Fig 5.
new: For all methods, including the mass constraint, to fail similarly points to an overall poor reconstruction of the objects in the event, namely ptmiss and the single lepton. We still wish to further investigate specific failure cases, but it is important to note that the relative width or uncertainty displayed by the likelihood plot of v-Flows has increased correspondingly.

We have increased the size of images with hard to read text.

Included extra references for machine learning approaches to jet-parton assignment. The requested references for Spatter and SAJA have been added along with:
Erdmann et al, J. Instrum. 14, P11015 (2019)
ATLAS, Phys. Rev. D 97, 072016 (2018)
ATLAS, Phys. Rev. Lett. 125, 061802 (2020)


We were asked to add to the discussion some of the comments we addressed in the previous round of changes, alluding to how including jet-parton assignment information into the network improves its performance. The following paragraph has been added to the conclusion.
new: It is interesting to note the relationship between the regression accuracy and the jet-parton assignment. When training the flow with full access to the truth parton labels for each jet, performance was observed to increase. When removing the jets as inputs to the network entirely, the performance is observed to decrease. This indicates a cyclic dependency, whereby the jet-parton assignment and the neutrino estimation both improve each other. A combined training approach with multiple tasks could be an avenue of further study.


We have performed a review of each reference and fixed those plus other small inconsistencies.

Published as SciPost Phys. 14, 159 (2023)

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