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In recent years, large language models (LLMs) have witnessed remarkable advancements, with the test-time scaling law consistently enhancing the reasoning capabilities. Through systematic evaluation and exploration of a diverse spectrum of…

Computation and Language · Computer Science 2025-11-03 Chenyang Shao , Sijian Ren , Fengli Xu , Yong Li

Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the…

Machine Learning · Computer Science 2025-03-21 Parshin Shojaee , Kazem Meidani , Shashank Gupta , Amir Barati Farimani , Chandan K Reddy

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…

Machine Learning · Computer Science 2025-12-12 Geoffrey F. Bomarito , Patrick E. Leser

Mathematical formulas are the crystallization of human wisdom in exploring the laws of nature for thousands of years. Describing the complex laws of nature with a concise mathematical formula is a constant pursuit of scientists and a great…

Machine Learning · Computer Science 2024-09-20 Yanjie Li , Jingyi Liu , Weijun Li , Lina Yu , Min Wu , Wenqiang Li , Meilan Hao , Su Wei , Yusong Deng

Unsupervised out-of-distribution (OOD) detection aims to identify out-of-domain data by learning only from unlabeled In-Distribution (ID) training samples, which is crucial for developing a safe real-world machine learning system. Current…

Computer Vision and Pattern Recognition · Computer Science 2026-02-03 Ying Yang , De Cheng , Chaowei Fang , Yubiao Wang , Changzhe Jiao , Lechao Cheng , Nannan Wang

In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress…

Machine Learning · Statistics 2025-09-30 Zhengyi Guo , Jiatu Li , Wenpin Tang , David D. Yao

This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize…

Fluid Dynamics · Physics 2023-01-24 Hongwei Tang , Yan Wang , Tongguang Wang , Linlin Tian

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

Graphics · Computer Science 2025-05-20 Javier E. Santos , Agnese Marcato , Roman Colman , Nicholas Lubbers , Yen Ting Lin

Symbolic regression (SR) aims to find symbolic expressions that describe datasets. Due to its inherent interpretability, is a powerful paradigm for scientific discovery. Recent advances have expanded SR to describe related phenomena using a…

Machine Learning · Computer Science 2026-03-31 Viktor Martinek , Roland Herzog

Recently, diffusion models have emerged as a new paradigm for generative models. Despite the success in domains using continuous signals such as vision and audio, adapting diffusion models to natural language is under-explored due to the…

Computation and Language · Computer Science 2023-02-15 Shansan Gong , Mukai Li , Jiangtao Feng , Zhiyong Wu , Lingpeng Kong

Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…

Machine Learning · Computer Science 2026-02-17 Jing Xiao , Xinhai Chen , Jiaming Peng , Qinglin Wang , Menghan Jia , Zhiquan Lai , Guangping Yu , Dongsheng Li , Tiejun Li , Jie Liu

Symbolic regression algorithms search a space of mathematical expressions for formulas that explain given data. Transformer-based models have emerged as a promising, scalable approach shifting the expensive combinatorial search to a…

Machine Learning · Computer Science 2025-09-25 Henrik Voigt , Paul Kahlmeyer , Kai Lawonn , Michael Habeck , Joachim Giesen

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…

Machine Learning · Statistics 2023-06-12 Aaron Lou , Stefano Ermon

Diffusion models have recently emerged as powerful learners for simulation-based inference (SBI), enabling fast and accurate estimation of latent parameters from simulated and real data. Their score-based formulation offers a flexible way…

Machine Learning · Statistics 2026-01-30 Jonas Arruda , Niels Bracher , Ullrich Köthe , Jan Hasenauer , Stefan T. Radev

Diffusion models (DMs) have recently been introduced in image deblurring and exhibited promising performance, particularly in terms of details reconstruction. However, the diffusion model requires a large number of inference iterations to…

Computer Vision and Pattern Recognition · Computer Science 2023-09-26 Zheng Chen , Yulun Zhang , Ding Liu , Bin Xia , Jinjin Gu , Linghe Kong , Xin Yuan

Diffusion probabilistic models have demonstrated an outstanding capability to model natural images and raw audio waveforms through a paired diffusion and reverse processes. The unique property of the reverse process (namely, eliminating…

Audio and Speech Processing · Electrical Eng. & Systems 2021-11-23 Yen-Ju Lu , Yu Tsao , Shinji Watanabe

Precise and accurate predictions over boundary areas are essential for semantic segmentation. However, the commonly-used convolutional operators tend to smooth and blur local detail cues, making it difficult for deep models to generate…

Computer Vision and Pattern Recognition · Computer Science 2023-02-07 Haoru Tan , Sitong Wu , Jimin Pi

Robustness is essential for deep neural networks, especially in security-sensitive applications. To this end, randomized smoothing provides theoretical guarantees for certifying robustness against adversarial perturbations. Recently,…

Computer Vision and Pattern Recognition · Computer Science 2025-07-02 Jiachen Lei , Julius Berner , Jiongxiao Wang , Zhongzhu Chen , Zhongjia Ba , Kui Ren , Jun Zhu , Anima Anandkumar

Variable selection for high-dimensional, highly correlated data has long been a challenging problem, often yielding unstable and unreliable models. We propose a resample-aggregate framework that exploits diffusion models' ability to…

Methodology · Statistics 2025-08-20 Minjie Wang , Xiaotong Shen , Wei Pan

Pre-trained diffusion models have demonstrated remarkable proficiency in synthesizing images across a wide range of scenarios with customizable prompts, indicating their effective capacity to capture universal features. Motivated by this,…

Computer Vision and Pattern Recognition · Computer Science 2024-11-22 Yuxiang Ji , Boyong He , Chenyuan Qu , Zhuoyue Tan , Chuan Qin , Liaoni Wu