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We present a novel integrator based on normalizing flows which can be used to improve the unweighting efficiency of Monte-Carlo event generators for collider physics simulations. In contrast to machine learning approaches based on surrogate models, our method generates the correct result even if the underlying neural networks are not optimally trained. We exemplify the new strategy using the example of Drell-Yan type processes at the LHC, both at leading and partially at next-to-leading order QCD.
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Recently normalizing flows (NFs) have demonstrated state-of-the-art performance on modeling 3D point clouds while allowing sampling with arbitrary resolution at inference time. However, these flow-based models still require long training times and large models for representing complicated geometries. This work enhances their representational power by applying mixtures of NFs to point clouds. We show that in this more general framework each component learns to specialize in a particular subregion of an object in a completely unsupervised fashion. By instantiating each mixture component with a comparatively small NF we generate point clouds with improved details compared to single-flow-based models while using fewer parameters and considerably reducing the inference runtime. We further demonstrate that by adding data augmentation, individual mixture components can learn to specialize in a semantically meaningful manner. We evaluate mixtures of NFs on generation, autoencoding and single-view reconstruction based on the ShapeNet dataset.
For many applications, such as computing the expected value of different magnitudes, sampling from a known probability density function, the target density, is crucial but challenging through the inverse transform. In these cases, rejection and importance sampling require suitable proposal densities, which can be evaluated and sampled from efficiently. We will present a method based on normalizing flows, proposing a solution for the common problem of exploding reverse Kullback-Leibler divergence due to the target density having values of 0 in regions of the flow transformation. The performance of the method will be demonstrated using a multi-mode complex density function.
Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layers exact update from $mathcal{O}(D^3)$ to $mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while training more quickly and surpassing the performance of functionally constrained counterparts.
Deep learning based image compression has recently witnessed exciting progress and in some cases even managed to surpass transform coding based approaches that have been established and refined over many decades. However, state-of-the-art solutions for deep image compression typically employ autoencoders which map the input to a lower dimensional latent space and thus irreversibly discard information already before quantization. Due to that, they inherently limit the range of quality levels that can be covered. In contrast, traditional approaches in image compression allow for a larger range of quality levels. Interestingly, they employ an invertible transformation before performing the quantization step which explicitly discards information. Inspired by this, we propose a deep image compression method that is able to go from low bit-rates to near lossless quality by leveraging normalizing flows to learn a bijective mapping from the image space to a latent representation. In addition to this, we demonstrate further advantages unique to our solution, such as the ability to maintain constant quality results through re-encoding, even when performed multiple times. To the best of our knowledge, this is the first work to explore the opportunities for leveraging normalizing flows for lossy image compression.
In this paper the current release of the Monte Carlo event generator Sherpa, version 1.1, is presented. Sherpa is a general-purpose tool for the simulation of particle collisions at high-energy colliders. It contains a very flexible tree-level matrix-element generator for the calculation of hard scattering processes within the Standard Model and various new physics models. The emission of additional QCD partons off the initial and final states is described through a parton-shower model. To consistently combine multi-parton matrix elements with the QCD parton cascades the approach of Catani, Krauss, Kuhn and Webber is employed. A simple model of multiple interactions is used to account for underlying events in hadron--hadron collisions. The fragmentation of partons into primary hadrons is described using a phenomenological cluster-hadronisation model. A comprehensive library for simulating tau-lepton and hadron decays is provided. Where available form-factor models and matrix elements are used, allowing for the inclusion of spin correlations; effects of virtual and real QED corrections are included using the approach of Yennie, Frautschi and Suura.
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