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Related papers: Towards Scaling Laws for Symbolic Regression

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Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step"…

Machine Learning · Computer Science 2026-03-17 Mingkun Xia , Weiwei Zhang

Representation learning algorithms are designed to learn abstract features that characterize data. State representation learning (SRL) focuses on a particular kind of representation learning where learned features are in low dimension,…

Artificial Intelligence · Computer Science 2018-10-30 Timothée Lesort , Natalia Díaz-Rodríguez , Jean-François Goudou , David Filliat

Symbolic regression (SR) with genetic programming (GP) aims to discover interpretable mathematical expressions directly from data. Despite its strong empirical success, the theoretical understanding of why GP-based SR generalizes beyond the…

Machine Learning · Computer Science 2026-04-21 Masahiro Nomura , Ryoki Hamano , Isao Ono

Synthetic-to-real transfer learning is a framework in which a synthetically generated dataset is used to pre-train a model to improve its performance on real vision tasks. The most significant advantage of using synthetic images is that the…

Machine Learning · Computer Science 2021-10-12 Hiroaki Mikami , Kenji Fukumizu , Shogo Murai , Shuji Suzuki , Yuta Kikuchi , Taiji Suzuki , Shin-ichi Maeda , Kohei Hayashi

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior,…

Machine Learning · Computer Science 2026-02-25 Qian Li , Yuxiao Hu , Juncheng Liu , Yuntian Chen

Neural scaling laws--power-law relationships between generalization errors and characteristics of deep learning models--are vital tools for developing reliable models while managing limited resources. Although the success of large language…

Machine Learning · Computer Science 2026-03-27 Tilen Cadez , Kyoung-Min Kim

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

Machine Learning · Computer Science 2024-11-12 Alex Havrilla , Wenjing Liao

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

Machine Learning · Computer Science 2026-03-25 Fateme Memar , Tao Zhe , Dongjie Wang

This paper revisits datasets and evaluation criteria for Symbolic Regression (SR), specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on…

Machine Learning · Computer Science 2025-01-06 Yoshitomo Matsubara , Naoya Chiba , Ryo Igarashi , Yoshitaka Ushiku

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

Neural scaling laws have revolutionized the design and optimization of large-scale AI models by revealing predictable relationships between model size, dataset volume, and computational resources. Early research established power-law…

Computation and Language · Computer Science 2025-05-28 Ayan Sengupta , Yash Goel , Tanmoy Chakraborty

Recent works have shown that machine learning models improve at a predictable rate with the total amount of training data, leading to scaling laws that describe the relationship between error and dataset size. These scaling laws can help…

Machine Learning · Computer Science 2024-06-03 Ian Covert , Wenlong Ji , Tatsunori Hashimoto , James Zou

Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the…

Machine Learning · Computer Science 2022-04-25 Pierre-Alexandre Kamienny , Stéphane d'Ascoli , Guillaume Lample , François Charton

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the Random…

Machine Learning · Computer Science 2025-05-13 Francesco Cagnetta , Alessandro Favero , Antonio Sclocchi , Matthieu Wyart

Symbolic regression (SR) searches for analytical expressions representing the relationship between a set of explanatory and response variables. Current SR methods assume a single dataset extracted from a single experiment. Nevertheless,…

While scaling laws for large language models (LLMs) during pre-training have been extensively studied, their behavior under reinforcement learning (RL) post-training remains largely unexplored. This paper presents a systematic empirical…

Symbolic regression (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing…

Machine Learning · Computer Science 2026-03-31 Giorgio Morales , John W. Sheppard

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare…

Machine Learning · Computer Science 2025-06-04 Leshem Choshen , Yang Zhang , Jacob Andreas

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

We study empirical scaling laws for transfer learning between distributions in an unsupervised, fine-tuning setting. When we train increasingly large neural networks from-scratch on a fixed-size dataset, they eventually become data-limited…

Machine Learning · Computer Science 2021-02-03 Danny Hernandez , Jared Kaplan , Tom Henighan , Sam McCandlish