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PySR is an open-source library for practical symbolic regression, a type of machine learning which aims to discover human-interpretable symbolic models. PySR was developed to democratize and popularize symbolic regression for the sciences,…

Instrumentation and Methods for Astrophysics · Physics 2023-05-08 Miles Cranmer

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of…

Machine Learning · Computer Science 2023-04-21 Tommaso Bendinelli , Luca Biggio , Pierre-Alexandre Kamienny

Discovering interpretable mathematical equations from observed data (a.k.a. equation discovery or symbolic regression) is a cornerstone of scientific discovery, enabling transparent modeling of physical, biological, and economic systems.…

Machine Learning · Computer Science 2025-08-28 Wangyang Ying , Jinghan Zhang , Haoyue Bai , Nanxu Gong , Xinyuan Wang , Kunpeng Liu , Chandan K. Reddy , Yanjie Fu

Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…

Symbolic Computation · Computer Science 2026-02-13 Nan Jiang , Ziyi Wang , Yexiang Xue

Self-supervision can dramatically cut back the amount of manually-labelled data required to train deep neural networks. While self-supervision has usually been considered for tasks such as image classification, in this paper we aim at…

Computer Vision and Pattern Recognition · Computer Science 2018-04-06 David Novotny , Samuel Albanie , Diane Larlus , Andrea Vedaldi

Unsupervised learning has grown in popularity because of the difficulty of collecting annotated data and the development of modern frameworks that allow us to learn from unlabeled data. Existing studies, however, either disregard variations…

Computer Vision and Pattern Recognition · Computer Science 2023-05-25 Yi-Zhan Xu , Chih-Yao Chen , Cheng-Te Li

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods…

Machine Learning · Computer Science 2024-12-11 Arya Grayeli , Atharva Sehgal , Omar Costilla-Reyes , Miles Cranmer , Swarat Chaudhuri

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…

Computational Physics · Physics 2020-04-16 Silviu-Marian Udrescu , Max Tegmark

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of…

Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…

Machine Learning · Computer Science 2026-05-25 Ziwen Liu , Meng Li

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

Exploration is essential in reinforcement learning, particularly in environments where external rewards are sparse. Here we focus on exploration with intrinsic rewards, where the agent transiently augments the external rewards with…

Machine Learning · Computer Science 2024-01-26 Changmin Yu , Neil Burgess , Maneesh Sahani , Samuel J. Gershman

We introduce AI-Kolmogorov, a novel framework for Symbolic Density Estimation (SymDE). Symbolic regression (SR) has been effectively used to produce interpretable models in standard regression settings but its applicability to density…

Machine Learning · Computer Science 2026-04-20 Angelo Rajendram , Xieting Chu , Vijay Ganesh , Max Fieg , Aishik Ghosh

Given the increase of publications, search for relevant papers becomes tedious. In particular, search across disciplines or schools of thinking is not supported. This is mainly due to the retrieval with keyword queries: technical terms…

Information Retrieval · Computer Science 2022-09-02 Lukas Pfahler , Katharina Morik

We explore semantic correspondence estimation through the lens of unsupervised learning. We thoroughly evaluate several recently proposed unsupervised methods across multiple challenging datasets using a standardized evaluation protocol…

Computer Vision and Pattern Recognition · Computer Science 2022-07-12 Mehmet Aygün , Oisin Mac Aodha

We introduce RIPE, an innovative reinforcement learning-based framework for weakly-supervised training of a keypoint extractor that excels in both detection and description tasks. In contrast to conventional training regimes that depend…

Computer Vision and Pattern Recognition · Computer Science 2025-07-15 Johannes Künzel , Anna Hilsmann , Peter Eisert

Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes,…

Machine Learning · Computer Science 2023-01-10 Tony Tohme , Dehong Liu , Kamal Youcef-Toumi

Unsupervised pre-training was a critical technique for training deep neural networks years ago. With sufficient labeled data and modern training techniques, it is possible to train very deep neural networks from scratch in a purely…

Computer Vision and Pattern Recognition · Computer Science 2017-03-29 Jianfeng Dong , Xiao-Jiao Mao , Chunhua Shen , Yu-Bin Yang

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…

Methodology · Statistics 2025-09-25 Somjit Roy , Pritam Dey , Debdeep Pati , Bani K. Mallick

Automated discovery of early visual concepts from raw image data is a major open challenge in AI research. Addressing this problem, we propose an unsupervised approach for learning disentangled representations of the underlying factors of…

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