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Introduces geometry-constrained Kolmogorov-Arnold Networks that learn edge geometry via Banach duality, demonstrating superior performance in symbolic regression tasks, especially under measurement noise.
InsightSR is a framework that leverages Large Language Models to refine the search space for symbolic regression, improving accuracy and physical consistency through iterative semantic and structural guidance.
This paper proposes an adaptive protection mechanism for evolutionary feature construction in symbolic regression to preserve important constructed features during evolution, demonstrating improved performance on regression benchmarks and credit classification tasks.
This paper proposes a symbolic machine learning approach to discover interpretable corrections to the Peng-Robinson equation of state for predicting vapor-liquid equilibrium in hydrocarbon-nitrogen binary mixtures, improving accuracy over the original EOS.
This paper introduces a verifier-guided workflow around ODEFormer, a pretrained symbolic transformer, to discover interpretable equations for physical dynamical systems. It demonstrates transfer to vortex shedding and other systems using dynamical and physical-admissibility criteria to select equations from a candidate pool.
This paper introduces DDRSR, a method that broadens expression decomposition and reduction in symbolic regression, avoiding brute-force sub-structure searches and providing theoretical correctness, with empirical advantages over prior approaches.
This paper studies the LSR-Synth benchmark and finds that a fixed vocabulary covers most tasks, while language-model-generated candidates rarely expand the set of solvable instances except when vocabulary coverage is disrupted.
This paper investigates using symbolic regression to discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks, achieving an aggregate MSE reduction of 44.47% in 25 out of 30 benchmark/network combinations.
This paper introduces MEDA, an LLM- and symbolic regression-powered agentic framework for automatically discovering ordinary differential equation (ODE) models of biological dynamical systems. It retrieves background knowledge, proposes candidate ODEs, and evaluates them across canonical model retrieval, extrapolation, and open-ended discovery tasks, demonstrating strong structural recovery and biologically plausible models.
GAE introduces a framework combining graph neural networks, reinforcement learning, and LLM fine-tuning to overcome bottlenecks in evolutionary program search, achieving state-of-the-art performance on symbolic regression for complex nonlinear oscillator systems.
This paper introduces LLM-PySR, a method where language models guide symbolic equation discovery by controlling search parameters while using numerical symbolic regression for fitting. The approach achieves strong balance of accuracy and complexity across benchmark tasks.
GP_ELITE is a pure-Python library for genetic-programming based symbolic regression, enabling discovery of interpretable mathematical formulas from small experimental datasets. Version 0.2.0 introduces Levenberg–Marquardt constant fitting, multi-restart reliability, Pareto front output, and extrapolation mode.
This paper introduces Minimalist Genetic Programming (MGP), a novel algorithm that replaces evolution with a syntactic derivation process inspired by the Minimalist Program from linguistics, using a MERGE operator to construct symbolic expressions. MGP consistently finds exact ground truth models on symbolic regression tasks where standard GP struggles due to bloat.
EditSR proposes a two-layer framework combining a neural symbolic regression model with an edit-based Rectifier to efficiently rectify structural errors in generated expressions, reducing error accumulation and improving recovery of complex symbolic structures with limited extra cost.
A comprehensive survey on uncertainty quantification in symbolic regression, reviewing frequentist, Bayesian, and model selection approaches to address the lack of reliability support in real-world decision processes.
Deliberate Evolution (DE) is an agentic framework that improves LLM-based symbolic regression by decoupling candidate generation from search control, using adaptive operators, structural diagnosis tools, and reflective memory to achieve better results with only 40% of the standard sample budget.
This paper presents 'Additive Atomic Forests,' a framework for simultaneous symbolic recovery of functions and their antiderivatives using derivative algebra and self-expanding atom libraries. The method achieves strong performance on classification benchmarks and Feynman symbolic regression tasks while offering interpretable results.
This paper introduces DoLQ, a multi-agent framework that uses Large Language Models to perform both qualitative and quantitative evaluations for discovering ordinary differential equations from observational data.