Related papers: Discovering Mathematical Equations with Diffusion …
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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:…
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…
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…
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…
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…
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…
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…
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,…
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…
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,…