Negative-weights suppression in Monte Carlo samples

5 May 2025, 09:00 → 9 May 2025, 18:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

Jeppe Rosenkrantz Andersen (IPPP, University of Durham), Michelangelo Mangano (CERN)

This Workshop provides a forum to review, discuss and improve techniques to reduce the impact of negative weights in LHC event generators working at the NLO and beyond. Negative weights induce a significant dilution of the statistical power of large MC event samples, leading to a huge burden for the computing resources required to match the HL-LHC needs. Negative weights pose challenges also to efficient numerical calculations of higher-order parton-level calculations at NNLO and beyond, an issue that will also be covered during the Workshop.

The workshop programme will consist of selected talks in the afternoons, and ample time for discussions and coordination between participants to advance the development and application of methods for negative weight suppression.

The workshop is embedded within the Next-Generation-Triggers (NGT) project, specifically task 1.5, whose aim includes the development of algorithms to improve and accelerate the performance of event generators and higher-order calculations for LHC physics.

A set of rooms has been reserved at the CERN Hostel for the Workshop participants. Check the "Accommodation" item in the left-side menu for details. 

Monday 5 May

10:00 → 10:30 Coffee

12:30 → 13:50 Presentations

12:30 KrKNLO Matching

Among NLO matching methods, the KrkNLO method is unique in exploiting a modification of the PDF factorisation scheme to allow NLO accuracy to be achieved by a multiplicative reweight. This gives positive weights by construction, since it does not use subtraction, and unlike other matching methods has no dependence on an unphysical choice of shower-scale or suppression-factor.
We summarise the recent implementation of the method for general colour-singlet processes in Herwig 7, and present results for LHC processes involving the production of massive and massless vector bosons. We will summarise the results of a systematic comparison with MC@NLO, and also review the properties of the Krk scheme among other factorisation schemes proposed as useful alternatives to MSbar, including their positivity properties.

Speaker: James Christopher Whitehead

KrkNLO matching for negative-weight reduction

KrkNLO matching for negative-weight reduction

13:15 Positive-weight event generation with ESME

In this talk we discuss a recent proposal for a family of NLO matching methods that are positive-definite by construction (Exponentiated Subtraction for Matching Events or ESME), and its implementation within PanScales. The method is general enough that it can be implemented in other frameworks in principle. The trade-off for guaranteed positive weights is the inclusion of higher-order spurious terms, but these can be controlled analytically. For the simple processes that we have so-far considered, the method is very efficient.
I will start by summarising the issue with negative weights and their origin within NLO matching methods, and then proceed to introduce ESME and show some results obtained with PanScales.

Speaker: Alexander Karlberg (CERN)

050525NEGATIVE.pdf

15:30 → 16:00 Coffee

16:00 → 17:00 Presentations

16:00 ARCANE Reweighting to reduce negative weights

Negative weights in next-to-leading-order (NLO) event generation pose a significant computational challenge in collider physics. In this talk, I will describe a new Monte Carlo technique called ARCANE reweighting for tackling the negative weights problem. By applying ARCANE reweighting, one can reduce or even completely eliminate the negative weights in Monte Carlo datasets a) without introducing any biases in the distribution of physical observables, b) without requiring any changes to the matching and merging prescriptions used in NLO event generation, and c) without introducing any uncertainties that will not be captured by the standard error formulas used in HEP data analyses.
I will demonstrate the technique for the generation of e+ e- --> q qbar + 1 jet events using the MC@NLO formalism. I will also discuss what the next steps to implement ARCANE reweighting for processes relevant for LHC experiments might look like.

Speaker: Prasanth Shyamsundar (Fermi National Accelerator Laboratory)

ARCANE talk - CERN neg wgts workshop.pdf

Tuesday 6 May

10:00 → 10:30 Coffee

13:30 → 15:30 Presentations

13:30 Challenge of negative weights in NNLO QCD calculations: insights from the MATRIX framework

Negative weights are a common challenge in higher-order perturbative calculations, impacting the statistical power of Monte Carlo samples and increasing computational costs. In this talk, we discuss our experience with the MATRIX framework, a state-of-the-art tool for next-to-next-to-leading order (NNLO) quantum chromodynamics (QCD) predictions widely used in LHC
precision physics. Due to its subtraction scheme, MATRIX inherently generates events with negative weights, which, while crucial for theoretical accuracy, pose significant challenges for event generation efficiency. We explore the effect of negative weights in MATRIX on statistical uncertainties and computational cost of NNLO QCD predictions across various processes.

Speaker: Oleksandr Zenaiev

Zenaiev-negweights.pdf

14:15 Cell Resampling to reduce negative weights

Cell resampling is a method for suppressing negative weights and generally improving statistical convergence in Monte Carlo event generation. I review the lessons learned from applications to showered and large fixed-order event samples and present a new phase-space metric designed to better match the sensitivity of experimental analyses. I conclude with an overview over some of open questions: systematic uncertainty estimates, optimisation of event generation, and the definition of the objects entering the metric.

Speaker: Andreas Maier (IFAE)

cell_resampling.pdf

15:00 Cell resampling in McMule at NNLO

McMule, a Monte Carlo for MUons and other LEptons, implements many major QED processes at NNLO (eg. $ee\to ee$, $e\mu\to e\mu$, $ee\to\mu\mu$, $\ell p\to \ell p$, $\mu \to \nu\bar\nu e$) including effects from the lepton masses.
This makes McMule suitable for predictions for low-energy experiments such as MUonE, CMD-III, ULQ2, or KLOE.
In this talk I will discuss how we are implementing cellular resampling (2109.07851 & 2303.15246) directly as part of the generation step which further reduces the fraction of negative weights.
I will show some preliminary results at NNLO for $ep\to ep$ for the ULQ2 experiment.

Speaker: Yannick Ulrich (University of Liverpool (GB))

cres-mcmule.pdf

Slides

15:30 → 16:00 Coffee

Wednesday 7 May

10:00 → 10:30 Coffee

16:00 → 18:30 Presentations

16:00 Treatment of non-positive definite integrands with Normalising Flows

We showcase the application of neural importance sampling for the evaluation of NNLO QCD scattering cross sections. We consider trainable Normalizing Flows in the form of discrete coupling layers and time continuous flows for the integration of the various cross-section contributions when using the sector-improved residue subtraction scheme, the so-called STRIPPER method. We thereby consider the stratification of the integrands into their positive and negative contributions, and separately optimize the phase-space sampler. We exemplify the novel methods for the case of gluonic top-quark pair production at the LHC at NNLO QCD accuracy. We find significant gains with respect to the current default methods used in STRIPPER in terms of reduced cross-section variances and increased unweighting efficiencies.

Speaker: Rene Poncelet (IFJ PAN Krakow)

2025.05.07-CERN-negativeweights-poncelet.pdf

16:45 Stay Positive: Neural Refinement of Simulated Event Weights

Monte Carlo simulations are an essential tool for data analysis in particle physics. Simulated events are typically produced alongside weights, that redistribute the cross section across the phase space. The presence of latent degrees of freedom can lead to a distribution of weights with negative values, often complicating analysis. Traditional post-hoc reweighting methods aim to approximate the average weight as a function of phase space. In contrast, we propose a novel approach that refines the initial weights to eliminate negative values through a scaling transformation utilizing a phase space dependent factor. Our method uses neural networks to process high-dimensional and unbinned phase spaces. We will show that our neural weight refinement method achieves comparable or superior accuracy to existing reweighting schemes, and demonstrate its behavior on realistic and synthetic examples.

Speaker: Dennis Daniel Nick Noll (Lawrence Berkeley National Lab (US))

250507_noll-weight_refiner.pdf

17:30 Improving QCD Simulations via Information-Theoretic Reweighting

We begin by reviewing how NLL accuracy is achieved in modern parton showers—highlighting the recent Sherpa implementation—and then introduce our new information-theoretic matching framework to achieve beyond NLL accuracy. By minimizing a Kullback–Leibler functional under constraints set by precision QCD inputs observables (including theory uncertainties), we embed high-order predictions into fully differential, particle-level simulations with strictly positive event weights and the ability to impose multiple observable constraints simultaneously. As a proof of concept, we apply the method to the thrust distribution in e⁺e⁻ collisions, revealing the overlooked role of logarithmic moments of thrust and related event shapes.

Speaker: Ben Assi

CERN_2025.pdf

Thursday 8 May

10:00 → 10:30 Coffee

11:00 → 11:45 Presentations

11:00 Resampling for event generators

Speaker: Simon Platzer (University of Graz (AT))

slides.pdf

14:00 → 16:00 Presentations

14:00 Open discussion

16:00 → 16:30 Coffee

Friday 9 May

10:00 → 10:30 Coffee