Related papers: Symbolic Density Estimation: A Decompositional App…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. 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:…
As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…
Partial differential equations (PDEs) are ubiquitous in the world around us, modelling phenomena from heat and sound to quantum systems. Recent advances in deep learning have resulted in the development of powerful neural solvers; however,…
Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both…
We discuss an acceptance-rejection algorithm for the random number generation from the Kolmogorov distribution. Since the cumulative distribution function (CDF) is expressed as a series, in order to obtain the density function we need to…
Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
The computational cost of geochemical solvers is a challenging matter. For reactive transport simulations, where chemical calculations are performed up to billions of times, it is crucial to reduce the total computational time. Existing…
Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…
In this paper, we propose ISDE (Independence Structure Density Estimation), an algorithm designed to estimate a multivariate density under Kullback-Leibler loss and the Independence Structure (IS) model. IS tackles the curse of…
In this paper, we propose a novel Multi-Modal Scene Graph with Kolmogorov-Arnold Expert Network for Audio-Visual Question Answering (SHRIKE). The task aims to mimic human reasoning by extracting and fusing information from audio-visual…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…
Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…
Understanding and predicting the activity of oxide perovskite catalysts for the oxygen evolution reaction (OER) requires descriptors that are both accurate and physically interpretable. While symbolic regression (SR) offers a path to…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
Dense object detection is widely used in automatic driving, video surveillance, and other fields. This paper focuses on the challenging task of dense object detection. Currently, detection methods based on greedy algorithms, such as…
In this work, we observe a counterintuitive phenomenon in self-supervised learning (SSL): longer training may impair the performance of dense prediction tasks (e.g., semantic segmentation). We refer to this phenomenon as Self-supervised…
The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…
We study the problem of space and time efficient evaluation of a nonparametric estimator that approximates an unknown density. In the regime where consistent estimation is possible, we use a piecewise multivariate polynomial interpolation…