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In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…

Numerical Analysis · Mathematics 2018-07-18 Selin Aslan , Eric de Sturler , Misha E. Kilmer

Autoregressive Language Models instantiate a factorized likelihood over token sequences, yet their strictly sequential decoding process imposes an intrinsic lower bound on inference latency. This bottleneck has emerged as a central obstacle…

Computation and Language · Computer Science 2025-09-30 Maxim Divilkovskiy , Vitaly Malygin , Sergey Zlobin , Stanislav Ilyushin , Sultan Isali , Vasily Kalugin , Nuriza Aitassova , Fei Yi , Weidi Zeng

Discrete diffusion models have recently shown significant progress in modeling complex data, such as natural languages and DNA sequences. However, unlike diffusion models for continuous data, which can generate high-quality samples in just…

Machine Learning · Computer Science 2025-03-20 Anji Liu , Oliver Broadrick , Mathias Niepert , Guy Van den Broeck

Autoregressive models have emerged as a powerful framework for modeling exchangeable sequences - i.i.d. observations when conditioned on some latent factor - enabling direct modeling of uncertainty from missing data (rather than a latent).…

Machine Learning · Computer Science 2025-03-04 Daksh Mittal , Ang Li , Tzu-Ching Yen , Daniel Guetta , Hongseok Namkoong

Normalizing Flows (NFs) are likelihood-based models for continuous inputs. They have demonstrated promising results on both density estimation and generative modeling tasks, but have received relatively little attention in recent years. In…

Computer Vision and Pattern Recognition · Computer Science 2025-06-09 Shuangfei Zhai , Ruixiang Zhang , Preetum Nakkiran , David Berthelot , Jiatao Gu , Huangjie Zheng , Tianrong Chen , Miguel Angel Bautista , Navdeep Jaitly , Josh Susskind

Bayesian inference with computationally expensive likelihood evaluations remains a significant challenge in many scientific domains. We propose normalizing flow regression (NFR), a novel offline inference method for approximating posterior…

Machine Learning · Statistics 2025-04-17 Chengkun Li , Bobby Huggins , Petrus Mikkola , Luigi Acerbi

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…

Machine Learning · Computer Science 2024-04-24 Qinglong Meng , Chongkun Xia , Xueqian Wang

High fidelity scientific simulations modeling physical phenomena typically require solving large linear systems of equations which result from discretization of a partial differential equation (PDE) by some numerical method. This step often…

Mathematical Software · Computer Science 2020-07-01 Mohammad Shafaet Islam , Qiqi Wang

Normalizing flows have emerged as a powerful brand of generative models, as they not only allow for efficient sampling of complicated target distributions but also deliver density estimation by construction. We propose here an in-depth…

Machine Learning · Statistics 2025-08-05 Andrea Coccaro , Marco Letizia , Humberto Reyes-Gonzalez , Riccardo Torre

Previously, non-autoregressive models were widely perceived as being superior in generation efficiency but inferior in generation quality due to the difficulties of modeling multiple target modalities. To enhance the multi-modality modeling…

Computation and Language · Computer Science 2023-11-30 Lihua Qian , Mingxuan Wang , Yang Liu , Hao Zhou

Much recent effort has been invested in non-autoregressive neural machine translation, which appears to be an efficient alternative to state-of-the-art autoregressive machine translation on modern GPUs. In contrast to the latter, where…

Computation and Language · Computer Science 2021-06-28 Jungo Kasai , Nikolaos Pappas , Hao Peng , James Cross , Noah A. Smith

Traditional source separation approaches train deep neural network models end-to-end with all the data available at once by minimizing the empirical risk on the whole training set. On the inference side, after training the model, the user…

Multistep inference is a bottleneck for real-time generative speech enhancement because flow- and diffusion-based systems learn an instantaneous velocity field and therefore rely on iterative ordinary differential equation (ODE) solvers. We…

Sound · Computer Science 2026-03-05 Duojia Li , Shenghui Lu , Hongchen Pan , Zongyi Zhan , Qingyang Hong , Lin Li

Normalizing Flows (NFs) are a classical family of likelihood-based methods that have received revived attention. Recent efforts such as TARFlow have shown that NFs are capable of achieving promising performance on image modeling tasks,…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Tianrong Chen , Jiatao Gu , David Berthelot , Joshua Susskind , Shuangfei Zhai

Generative Large Language Models (LLMs) based on the Transformer architecture have recently emerged as a dominant foundation model for a wide range of Natural Language Processing tasks. Nevertheless, their application in real-time scenarios…

Computation and Language · Computer Science 2024-01-04 Coleman Hooper , Sehoon Kim , Hiva Mohammadzadeh , Hasan Genc , Kurt Keutzer , Amir Gholami , Sophia Shao

Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of…

Machine Learning · Statistics 2021-02-25 Ilyes Khemakhem , Ricardo Pio Monti , Robert Leech , Aapo Hyvärinen

Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book…

Machine Learning · Statistics 2026-03-11 Shinto Eguchi

Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes…

Machine Learning · Computer Science 2023-10-30 Federico Danieli , Miguel Sarabia , Xavier Suau , Pau Rodríguez , Luca Zappella

A normalizing flow models a complex probability density as an invertible transformation of a simple density. The invertibility means that we can evaluate densities and generate samples from a flow. In practice, autoregressive flow-based…

Machine Learning · Statistics 2019-06-06 Conor Durkan , Artur Bekasov , Iain Murray , George Papamakarios

Distributed inference serves as a promising approach to enabling the inference of large language models (LLMs) at the network edge. It distributes the inference process to multiple devices to ensure that the LLMs can fit into the device…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-13 Xing Liu , Lizhuo Luo , Ming Tang , Chao Huang , Xu Chen
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