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An unfolding method based on conditional Invertible Neural Networks (cINN) using iterative training

by Mathias Backes, Anja Butter, Monica Dunford, Bogdan Malaescu

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Submission summary

Authors (as registered SciPost users): Anja Butter
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-10-04
Date submitted: 2023-01-04 10:58
Submitted by: Butter, Anja
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Experiment
  • High-Energy Physics - Phenomenology
Approaches: Experimental, Computational, Phenomenological


The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding techniques while retaining the full dimensionality. Generative networks like invertible neural networks~(INN) enable a probabilistic unfolding, which map individual events to their corresponding unfolded probability distribution. The accuracy of such methods is however limited by how well simulated training samples model the actual data that is unfolded. We introduce the iterative conditional INN~(IcINN) for unfolding that adjusts for deviations between simulated training samples and data. The IcINN unfolding is first validated on toy data and then applied to pseudo-data for the $pp \to Z \gamma \gamma$ process.

Published as SciPost Phys. Core 7, 007 (2024)

Reports on this Submission

Anonymous Report 1 on 2023-8-16 (Contributed Report)

  • Cite as: Anonymous, Report on arXiv:2212.08674v2, delivered 2023-08-16, doi: 10.21468/SciPost.Report.7659


1- Novel use of the conditional Invertible Neural Networks (cINN) method, which is well-regarded in other disciplines.
2- Well written, well presented.


1- The paper showcases the cINN method primarily through simple, low-dimensional examples. More examples would be helpful.
2- There is a gap in the paper, as there is no comparative study against contemporary unfolding methods, making it challenging to ascertain its advantages.


The study first introduces the collider data unfolding problem, as well as the prevalent methodologies used to tackle it, underscoring their limitations. The second section proceeds to redefine the problem through Bayesian framework. Within this framework, the manuscript introduces the cINN unfolding algorithm and the iterative approach involving training-unfolding-reweighting. The authors then put their method to the test in two distinct scenarios. The initial test (third section) involves a simplistic 1D toy model utilizing a Gaussian distribution. The subsequent scenario revolves around a more complex pp->Z\gamma\gamma process.

In summary, while the manuscript presents a novel approach to unfolding detector data, certain areas could be refined to provide a more comprehensive and clearer picture of the methodology's potential and comparative advantages.

Requested changes

Here are some minor feedbacks, which would be good to addressed but not necessary.

1- Very few typos: a ... flow which have, reweigthing. Some minor British/American difference in word usage.
2- I would give ref to ADAM.
3- Figure (6) is hard to follow. To enhance clarity, adopting a 3-color scheme would be recommended. This would allow readers to distinguish between positive and negative correlations.
4- Section 4 parameter space truncates at a relatively low energy level. The manuscript could benefit from elaborating on training time/complexity for extended parameter spaces.
5- The concluding remarks of the manuscript seem rather concise. Expanding this section could provide a clearer picture of the manuscript's impacts. Specifically, it would be insightful to:
5.1- Dive into the potential of the method when applied to processes with higher dimensions, i.e. more complicated processes beyond two jets.
5.2- Pit the cINN approach against other methods. If a direct comparison isn't feasible, providing quantitative evidence highlighting its superior efficiency would be beneficial, e.g. quantifying the reduction in variance, how much bias is reduced in distribution.

  • validity: top
  • significance: top
  • originality: high
  • clarity: high
  • formatting: perfect
  • grammar: perfect

Author:  Anja Butter  on 2024-01-11  [id 4238]

(in reply to Report 1 on 2023-08-16)

Dear Referee,

Thank you very much for the positive feedback and your suggestions. We have addressed them in the following way:

1 -> We have corrected the typos. We try to write everything in American English now.

2 -> The reference to ADAM has been included.

3 -> We adapted a new color scheme which should visualize the correlations better.

4 -> We have added a comment on the expected training behavior towards higher dimensions.

5 -> In the conclusions of this paper the goal was mainly to summarize its content. We especially wanted to avoid putting somewhat speculative comments about more comparisons with other methods, which were left for later studies. The referee can actually find a follow-up study on such comparisons in a more recent preprint (arxiv:2310.17037). Still, we have slightly expanded the conclusions to better emphasize the benefits of the IcINN method and the way it was tested.

Anonymous on 2024-01-16  [id 4246]

(in reply to Anja Butter on 2024-01-11 [id 4238])

Dear authors,

We have happy with these changes and recommend the updated version ( for publication. Please go ahead and submit the revision.

Best regards,

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