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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. 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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5. StarFlow: Leveraging Normalizing Flows for Stellar Age Estimation in SDSS-V DR19

   https://doi.org/10.3847/1538-3881/addd18  

   Stone-Martinez, Alexander; Holtzman, Jon A; Lu, YuxiLucy; Hasselquist, Sten; Imig, Julie; Griffith, Emily J; Bellinger, Earl P; Saydjari, Andrew K (July 2025, The Astronomical Journal)

   Abstract Understanding the ages of stars is crucial for unraveling the formation history and evolution of our Galaxy. Traditional methods for estimating stellar ages from spectroscopic data often struggle with providing appropriate uncertainty estimations and are severely constrained by the parameter space. In this work, we introduce a new approach using normalizing flows—a type of deep generative model—to estimate stellar ages for evolved stars with improved accuracy and robust uncertainty characterization. The model is trained on stellar masses for evolved stars derived from asteroseismology and predicts the relationship between the carbon and nitrogen abundances of a given star and its age. Unlike standard neural network techniques, normalizing flows enable the recovery of full likelihood distributions for individual stellar ages, offering a richer and more informative perspective on uncertainties. Our method yields age estimations for 378,720 evolved stars and achieves a typical absolute age uncertainty of approximately 2 Gyr. By intrinsically accounting for the coverage and density of the training data, our model ensures that the resulting uncertainties reflect both the inherent noise in the data and the completeness of the sampled parameter space. Applying this method to data from the fifth-generation Sloan Digital Sky Survey Milky Way Mapper, we have produced the largest stellar age catalog for evolved stars to date. 

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