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Symbolic Regression tries to find a mathematical expression that describes the relationship of a set of explanatory variables to a measured variable. The main objective is to find a model that minimizes the error and, optionally, that also…

Artificial Intelligence · Computer Science 2018-02-27 Fabricio Olivetti de Franca

The linear representation hypothesis states that neural network activations encode high-level concepts as linear mixtures. However, under superposition, this encoding is a projection from a higher-dimensional concept space into a…

Machine Learning · Computer Science 2026-03-31 Vitória Barin Pacela , Shruti Joshi , Isabela Camacho , Simon Lacoste-Julien , David Klindt

Sparse Autoencoders (SAEs) are a promising approach for extracting neural network representations by learning a sparse and overcomplete decomposition of the network's internal activations. However, SAEs are traditionally trained considering…

Machine Learning · Computer Science 2025-04-02 Jeffrey Olmo , Jared Wilson , Max Forsey , Bryce Hepner , Thomas Vin Howe , David Wingate

Symbolic Regression (SR) plays a central role in scientific knowledge discovery by distilling mathematical equations from observational data. Most existing SR methods function within a bi-level optimization framework: an outer loop that…

Machine Learning · Computer Science 2026-05-25 Boxiao Wang , Kai Li , Zhiwei Chen , Yang Huang , Runxiang Wang , Ziwen Zhang , Yifan Zhang , Jian Cheng

Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as ``black boxes''. In contrast to standard regression models that require a prescribed functional…

Artificial Intelligence · Computer Science 2026-05-05 Theofanis Aravanis , Grigorios Chrimatopoulos , Mohammad Ferdows , Michalis Xenos , Efstratios Em Tzirtzilakis

Symbolic regression (SR) is the task of learning a model of data in the form of a mathematical expression. By their nature, SR models have the potential to be accurate and human-interpretable at the same time. Unfortunately, finding such…

Neural and Evolutionary Computing · Computer Science 2022-07-12 Marco Virgolin , Solon P. Pissis

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness,…

Learning effective policies for sparse objectives is a key challenge in Deep Reinforcement Learning (RL). A common approach is to design task-related dense rewards to improve task learnability. While such rewards are easily interpreted,…

Machine Learning · Computer Science 2020-10-12 Hassam Sheikh , Shauharda Khadka , Santiago Miret , Somdeb Majumdar

Different from universal object detection, referring expression comprehension (REC) aims to locate specific objects referred to by natural language expressions. The expression provides high-level concepts of relevant visual and contextual…

Computer Vision and Pattern Recognition · Computer Science 2023-06-08 Wei Su , Peihan Miao , Huanzhang Dou , Yongjian Fu , Xi Li

Symbolic regression is essential for deriving interpretable expressions that elucidate complex phenomena by exposing the underlying mathematical and physical relationships in data. In this paper, we present an advanced symbolic regression…

Machine Learning · Computer Science 2025-03-13 Sikai Huang , Yixin Berry Wen , Tara Adusumilli , Kusum Choudhary , Haizhao Yang

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

Machine Learning · Computer Science 2023-03-17 Mengge Du , Yuntian Chen , Dongxiao Zhang

The growing environmental footprint of artificial intelligence (AI), especially in terms of storage and computation, calls for more frugal and interpretable models. Sparse models (e.g., linear, neural networks) offer a promising solution by…

Machine Learning · Statistics 2025-09-23 Sylvain Sardy , Maxime van Cutsem , Xiaoyu Ma

Evolutionary symbolic regression (SR) fits a symbolic equation to data, which gives a concise interpretable model. We explore using SR as a method to propose which data to gather in an active learning setting with physical constraints. SR…

Machine Learning · Computer Science 2024-08-13 Jorge Medina , Andrew D. White

Learned sparse retrieval (LSR) is a family of first-stage retrieval methods that are trained to generate sparse lexical representations of queries and documents for use with an inverted index. Many LSR methods have been recently introduced,…

Information Retrieval · Computer Science 2023-03-28 Thong Nguyen , Sean MacAvaney , Andrew Yates

Deep latent generative models have attracted increasing attention due to the capacity of combining the strengths of deep learning and probabilistic models in an elegant way. The data representations learned with the models are often…

Machine Learning · Computer Science 2023-04-04 Zhao Xu , Daniel Onoro Rubio , Giuseppe Serra , Mathias Niepert

Sparse autoencoders (SAEs) decompose large language model (LLM) activations into latent features that reveal mechanistic structure. Conventional SAEs train on broad data distributions, forcing a fixed latent budget to capture only…

Machine Learning · Computer Science 2025-08-14 Charles O'Neill , Mudith Jayasekara , Max Kirkby

Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic…

Machine Learning · Computer Science 2026-05-11 Jakub Stępień , Marcin Mazur , Jacek Tabor , Przemysław Spurek

Sparse autoencoders (SAEs) have recently emerged as a powerful tool for interpreting the internal representations of large language models (LLMs), revealing latent latent features with semantical meaning. This interpretability has also…

Other Quantitative Biology · Quantitative Biology 2025-07-11 Haoxiang Guan , Jiyan He , Jie Zhang

Expansion-enhanced sparse lexical representation improves information retrieval (IR) by minimizing vocabulary mismatch problems during lexical matching. In this paper, we explore the potential of jointly learning dense semantic…

Machine Learning · Computer Science 2024-05-24 Biplob Biswas , Rajiv Ramnath

Conventional compressed sensing theory assumes signals have sparse representations in a known, finite dictionary. Nevertheless, in many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the…

Information Theory · Computer Science 2014-12-19 Jun Fang , Huiping Duan , Jing Li , Hongbin Li , Rick S. Blum