[Paper Review] Efficiently Moving Instead of Reweighting Collider Events with Machine Learning

Radha Mastandrea, Benjamin Nachman|arXiv (Cornell University)|Dec 12, 2022

Anomaly Detection Techniques and Applications4 citations

TL;DR

This paper proposes using normalizing flows to morph collider physics events from a reference dataset to better match a target dataset, instead of relying on traditional reweighting. It finds that training strategies like identity initialization and movement penalties yield more faithful mappings closer to optimal transport, significantly improving fidelity in signal regions compared to double base methods.

ABSTRACT

There are many cases in collider physics and elsewhere where a calibration dataset is used to predict the known physics and / or noise of a target region of phase space. This calibration dataset usually cannot be used out-of-the-box but must be tweaked, often with conditional importance weights, to be maximally realistic. Using resonant anomaly detection as an example, we compare a number of alternative approaches based on transporting events with normalizing flows instead of reweighting them. We find that the accuracy of the morphed calibration dataset depends on the degree to which the transport task is set up to carry out optimal transport, which motivates future research into this area.

Motivation & Objective

• To improve calibration of collider physics datasets by replacing traditional reweighting with event morphing via normalizing flows.
• To evaluate how different training procedures affect the fidelity of morphed reference datasets in matching target distributions.
• To investigate whether morphing based on optimal transport principles enhances performance in resonant anomaly detection tasks.
• To explore whether minimizing event movement during morphing leads to more accurate and realistic calibration.

Proposed method

• Uses conditional normalizing flows to map events from a reference distribution to a target distribution, conditioned on a resonant mass variable M.
• Compares four training strategies: Double Base (two flows to standard normal), Base to Data (flow from reference to target), Identity Initialization (transfer learning from self-mapping), and Movement Penalty (L2 loss on displacement).
• Employs a binary classifier to evaluate morphing fidelity by testing if the target can be distinguished from the morphed reference in the signal region.
• Trains flows using a 1M background and 100k signal event dataset from the LHC 2020 Olympics R&D, with ReLU activations and cosine annealing learning rate.
• Quantifies performance using ROC scores for the post-hoc classifier, with scores near 0.5 indicating indistinguishability and thus high fidelity.
• Applies the morphing function to reference events and evaluates the resulting distribution against the true target in different phase space regions (sidebands, signal, outer bands).

Experimental results

Research questions

• RQ1 How does the choice of training procedure affect the fidelity of event morphing in collider physics calibration?
• RQ2 Can morphing via normalizing flows outperform traditional reweighting in matching target distributions, especially when support overlaps are limited?
• RQ3 To what extent do movement penalties and identity initialization improve morphing accuracy toward optimal transport solutions?
• RQ4 Does the Double Base method, which maps through a standard normal, produce suboptimal morphing due to indirect transport?
• RQ5 How well do different morphing strategies preserve indistinguishability between the morphed reference and the true target in the signal region?

Key findings

• The Double Base method produced the lowest fidelity, with a ROC score of 0.630 ± 0.024 in the low-mass outer band, indicating poor indistinguishability from the target.
• All methods except Double Base achieved ROC scores below 0.51 in the signal region, indicating high fidelity and successful morphing.
• The Identity Initialization and Movement Penalty methods achieved ROC scores of 0.508 ± 0.004 and 0.507 ± 0.002 in the signal region, respectively, showing excellent fidelity.
• The Base to Data method achieved a ROC score of 0.503 ± 0.001 in the signal region, also indicating strong performance.
• All methods showed good fidelity in sideband regions (ROC < 0.503), confirming effective training on the reference data.
• The Double Base method showed a significant drop in performance in outer bands, suggesting it fails to preserve distributional similarity when support is non-overlapping.