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1. Describing hadronization via histories and observables for Monte-Carlo event reweighting

   https://doi.org/10.21468/SciPostPhys.18.2.054  

   Bierlich, Christian; Ilten, Philip; Menzo, Tony; Mrenna, Stephen; Szewc, Manuel; Wilkinson, Michael K; Youssef, Ahmed; Zupan, Jure (February 2025, SciPost Physics)

   We introduce a novel method for extracting a fragmentation model directly from experimental data without requiring an explicit parametric form, called Histories and Observables for Monte-Carlo Event Reweighting (HOMER), consisting of three steps: the training of a classifier between simulation and data, the inference of single fragmentation weights, and the calculation of the weight for the full hadronization chain. We illustrate the use of HOMER on a simplified hadronization problem, aq\bar{q} $q\bar{q}$ string fragmenting into pions, and extract a modified Lund string fragmentation functionf(z) $f\left(z\right)$ . We then demonstrate the use of HOMER on three types of experimental data: (i) binned distributions of high-level observables, (ii) unbinned event-by-event distributions of these observables, and (iii) full particle cloud information. After demonstrating thatf(z) $f\left(z\right)$ can be extracted from data (the inverse of hadronization), we also show that, at least in this limited setup, the fidelity of the extractedf(z) $f\left(z\right)$ suffers only limited loss when moving from (i) to (ii) to (iii). Public code is available at https://gitlab.com/uchep/mlhad. 

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2. Normalizing Flows for Intelligent Manufacturing

   https://doi.org/10.1115/MSEC2023-101281  

   Russell, Matthew; Wang, Peng (June 2023, American Society of Mechanical Engineers)

   Abstract Monitoring machine health and product quality enables predictive maintenance that optimizes repairs to minimize factory downtime. Data-driven intelligent manufacturing often relies on probabilistic techniques with intractable distributions. For example, generative models of data distributions can balance fault classes with synthetic data, and sampling the posterior distribution of hidden model parameters enables prognosis of degradation trends. Normalizing flows can address these problems while avoiding the training instability or long inference times of other generative Deep Learning (DL) models like Generative Adversarial Networks (GAN), Variational Autoencoders (VAE), and diffusion networks. To evaluate normalizing flows for manufacturing, experiments are conducted to synthesize surface defect images from an imbalanced data set and estimate parameters of a tool wear degradation model from limited observations. Results show that normalizing flows are an effective, multi-purpose DL architecture for solving these problems in manufacturing. Future work should explore normalizing flows for more complex degradation models and develop a framework for likelihood-based anomaly detection. Code is available at https://github.com/uky-aism/flows-for-manufacturing. 

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3. VQ-Flows: Vector Quantized Local Normalizing Flows

   Sidheekh, Sahil; Dock, Chris B.; Jain, Tushar; Balan, Radu; Singh, Maneesh K. (August 2022, Uncertainty in artificial intelligence)

   Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their expressivity when the data distribution is supported on a lowdimensional manifold or has a non-trivial topology. We introduce a novel statistical framework for learning a mixture of local normalizing flows as “chart maps” over the data manifold. Our framework augments the expressivity of recent approaches while preserving the signature property of normalizing flows, that they admit exact density evaluation. We learn a suitable atlas of charts for the data manifold via a vector quantized autoencoder (VQ-AE) and the distributions over them using a conditional flow. We validate experimentally that our probabilistic framework enables existing approaches to better model data distributions over complex manifolds. 

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4. FlowSN: neural simulation-based inference under realistic selection effects applied to supernova cosmology

   https://doi.org/10.1093/mnras/stag1046  

   Boyd, Benjamin M; Mandel, Kaisey S; Grayling, Matthew; Mitra, Ayan; Kessler, Richard; Autenrieth, Maximilian; Do, Aaron; Ginolin, Madeleine; Kelsey, Lisa; Narayan, Gautham; et al (June 2026, Monthly Notices of the Royal Astronomical Society)

   ABSTRACT We present FlowSN, a statistical framework using simulation-based inference (SBI) with normalizing flows to account for selection effects in observational astronomy. Failure to account for selection effects can lead to biased inference on global parameters. An example is Malmquist bias, where detection limits result in a sample skewed towards brighter objects. In Type Ia supernova (SN Ia) cosmology, these selection effects can systematically shift the inferred posterior distributions of cosmological parameters, necessitating the development of robust statistical frameworks to account for the biases. SBI enables us to implicitly learn probability distributions that are analytically intractable to calculate. In this work, we introduce a novel approach that employs a normalizing flow to learn the non-analytic selected SN likelihood for a given survey from forward simulations, independent of the assumed cosmological model. The resulting likelihood approximation is incorporated into a hierarchical Bayesian framework, and posterior sampling is performed using Hamiltonian Monte Carlo to obtain constraints on cosmological parameters conditioned on the observed data. The modular learnt likelihood approximation can be reused without retraining to evaluate different cosmological models, providing a key advantage over other SBI approaches. We demonstrate the performance of this methodology by training and testing the SBI technique using realistic LSST-like SNANA simulations for the first time. Our FlowSN approach yields accurate posterior estimates on cosmological parameters, including the dark energy equation of state $$w_\text{0}$$, that are an order of magnitude less biased than those obtained with conventional techniques and also exhibit improved frequentist calibration. 

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5. Boosting Summarization with Normalizing Flows and Aggressive Training

   https://doi.org/10.18653/v1/2023.emnlp-main.165  

   Yang, Yu; Shen, Xiaotong (August 2023, The Proceeding of the 2023 Conference on Empirical Methods in Natural Language Processing)

   Bouamor, Houda; Pino, Juan; Bali, Kalia (Ed.)

   This paper presents FlowSUM, a normalizing flows-based variational encoder-decoder framework for Transformer-based summarization. Our approach tackles two primary challenges in variational summarization: insufficient semantic information in latent representations and posterior collapse during training. To address these challenges, we employ normalizing flows to enable flexible latent posterior modeling, and we propose a controlled alternate aggressive training (CAAT) strategy with an improved gate mechanism. Experimental results show that FlowSUM significantly enhances the quality of generated summaries and unleashes the potential for knowledge distillation with minimal impact on inference time. Furthermore, we investigate the issue of posterior collapse in normalizing flows and analyze how the summary quality is affected by the training strategy, gate initialization, and the type and number of normalizing flows used, offering valuable insights for future research. 

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