Flows for Flows: Training Normalizing Flows Between Arbitrary Distributions with Maximum Likelihood Estimation

Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps to be found between arbitrary distributions. We demonstrate and explore the utility of this approach and show it is particularly interesting in the case of conditional normalizing flows and for introducing optimal transport constraints on maps that are constructed using normalizing flows

Decorrelation using Optimal Transport

Being able to decorrelate a feature space from protected attributes is an area of active research and study in ethics, fairness, and also natural sciences. We introduce a novel decorrelation method using Convex Neural Optimal Transport Solvers (Cnots), that is able to decorrelate continuous feature space against protected attributes with optimal transport. We demonstrate how well it performs in the context of jet classification in high energy physics, where classifier scores are desired to be decorrelated from the mass of a jet. The decorrelation achieved in binary classification approaches the levels achieved by the state-of-the-art using conditional normalising flows. When moving to multiclass outputs the optimal transport approach performs significantly better than the state-of-the-art, suggesting substantial gains at decorrelating multidimensional feature spaces

\nu-Flows: Conditional Neutrino Regression

We present $\nu$-Flows, a novel method for restricting the likelihood space of neutrino kinematics in high energy collider experiments using conditional normalizing 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 $\nu$-Flows in a case study by applying it to simulated semileptonic $t\bar{t}$ 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.Comment: 26 pages, 15 figure

ν2\nu^2-Flows: Fast and improved neutrino reconstruction in multi-neutrino final states with conditional normalizing flows

In this work we introduce $\nu^2$-Flows, an extension of the $\nu$-Flows method to final states containing multiple neutrinos. The architecture can natively scale for all combinations of object types and multiplicities in the final state for any desired neutrino multiplicities. In $t\bar{t}$ dilepton events, the momenta of both neutrinos and correlations between them are reconstructed more accurately than when using the most popular standard analytical techniques, and solutions are found for all events. Inference time is significantly faster than competing methods, and can be reduced further by evaluating in parallel on graphics processing units. We apply $\nu^2$-Flows to $t\bar{t}$ dilepton events and show that the per-bin uncertainties in unfolded distributions is much closer to the limit of performance set by perfect neutrino reconstruction than standard techniques. For the chosen double differential observables $\nu^2$-Flows results in improved statistical precision for each bin by a factor of 1.5 to 2 in comparison to the Neutrino Weighting method and up to a factor of four in comparison to the Ellipse approach.Comment: 20 pages, 16 figures, 5 table

Flow Away your Differences: Conditional Normalizing Flows as an Improvement to Reweighting

We present an alternative to reweighting techniques for modifying distributions to account for a desired change in an underlying conditional distribution, as is often needed to correct for mis-modelling in a simulated sample. We employ conditional normalizing flows to learn the full conditional probability distribution from which we sample new events for conditional values drawn from the target distribution to produce the desired, altered distribution. In contrast to common reweighting techniques, this procedure is independent of binning choice and does not rely on an estimate of the density ratio between two distributions. In several toy examples we show that normalizing flows outperform reweighting approaches to match the distribution of the target.We demonstrate that the corrected distribution closes well with the ground truth, and a statistical uncertainty on the training dataset can be ascertained with bootstrapping. In our examples, this leads to a statistical precision up to three times greater than using reweighting techniques with identical sample sizes for the source and target distributions. We also explore an application in the context of high energy particle physics.Comment: 21 pages, 9 figure

Flows for Flows: Morphing one Dataset into another with Maximum Likelihood Estimation

Many components of data analysis in high energy physics and beyond require morphing one dataset into another. This is commonly solved via reweighting, but there are many advantages of preserving weights and shifting the data points instead. Normalizing flows are machine learning models with impressive precision on a variety of particle physics tasks. Naively, normalizing flows cannot be used for morphing because they require knowledge of the probability density of the starting dataset. In most cases in particle physics, we can generate more examples, but we do not know densities explicitly. We propose a protocol called flows for flows for training normalizing flows to morph one dataset into another even if the underlying probability density of neither dataset is known explicitly. This enables a morphing strategy trained with maximum likelihood estimation, a setup that has been shown to be highly effective in related tasks. We study variations on this protocol to explore how far the data points are moved to statistically match the two datasets. Furthermore, we show how to condition the learned flows on particular features in order to create a morphing function for every value of the conditioning feature. For illustration, we demonstrate flows for flows for toy examples as well as a collider physics example involving dijet eventsComment: 15 pages, 17 figures. This work is a merger of arXiv:2211.02487 and arXiv:2212.0615

PC-Droid: Faster diffusion and improved quality for particle cloud generation

Building on the success of PC-JeDi we introduce PC-Droid, a substantially improved diffusion model for the generation of jet particle clouds. By leveraging a new diffusion formulation, studying more recent integration solvers, and training on all jet types simultaneously, we are able to achieve state-of-the-art performance for all types of jets across all evaluation metrics. We study the trade-off between generation speed and quality by comparing two attention based architectures, as well as the potential of consistency distillation to reduce the number of diffusion steps. Both the faster architecture and consistency models demonstrate performance surpassing many competing models, with generation time up to two orders of magnitude faster than PC-JeDi and three orders of magnitude faster than Delphes.Comment: 21 pages, 8 tables, 13 figure

Topological Reconstruction of Particle Physics Processes using Graph Neural Networks

We present a new approach, the Topograph, which reconstructs underlying physics processes, including the intermediary particles, by leveraging underlying priors from the nature of particle physics decays and the flexibility of message passing graph neural networks. The Topograph not only solves the combinatoric assignment of observed final state objects, associating them to their original mother particles, but directly predicts the properties of intermediate particles in hard scatter processes and their subsequent decays. In comparison to standard combinatoric approaches or modern approaches using graph neural networks, which scale exponentially or quadratically, the complexity of Topographs scales linearly with the number of reconstructed objects. We apply Topographs to top quark pair production in the all hadronic decay channel, where we outperform the standard approach and match the performance of the state-of-the-art machine learning technique.Comment: 25 pages, 24 figures, 8 table

The Interplay of Machine Learning--based Resonant Anomaly Detection Methods

Machine learning--based anomaly detection (AD) methods are promising tools for extending the coverage of searches for physics beyond the Standard Model (BSM). One class of AD methods that has received significant attention is resonant anomaly detection, where the BSM is assumed to be localized in at least one known variable. While there have been many methods proposed to identify such a BSM signal that make use of simulated or detected data in different ways, there has not yet been a study of the methods' complementarity. To this end, we address two questions. First, in the absence of any signal, do different methods pick the same events as signal-like? If not, then we can significantly reduce the false-positive rate by comparing different methods on the same dataset. Second, if there is a signal, are different methods fully correlated? Even if their maximum performance is the same, since we do not know how much signal is present, it may be beneficial to combine approaches. Using the Large Hadron Collider (LHC) Olympics dataset, we provide quantitative answers to these questions. We find that there are significant gains possible by combining multiple methods, which will strengthen the search program at the LHC and beyond.Comment: 23 pages, 17 figure

The sweet spot in sustainability: a framework for corporate assessment in sugar manufacturing

The assessment of corporate sustainability has become an increasingly important topic, both within academia and in industry. For manufacturing companies to conform to their commitments to sustainable development, a standard and reliable measurement framework is required. There is, however, a lack of sector-specific and empirical research in many areas, including the sugar industry. This paper presents an empirically developed framework for the assessment of corporate sustainability within the Thai sugar industry. Multiple case studies were conducted, and a survey using questionnaires was also employed to enhance the power of generalisation. The developed framework is an accurate and reliable measurement instrument of corporate sustainability, and guidelines to assess qualitative criteria are put forward. The proposed framework can be used for a company’s self-assessment and for guiding practitioners in performance improvement and policy decision-maki