SEVerA uses Formally Guarded Generative Models and a three-stage Search-Verification-Learning process to synthesize self-evolving agents that satisfy hard formal constraints while improving task performance.
hub Mixed citations
Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl
Mixed citation behavior. Most common role is background (57%).
31
Pith papers citing it
Background
57% of classified citations
abstract
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, and is built on a high-performance distributed back-end, a flexible search algorithm, and interfaces with several deep learning packages. PySR's internal search algorithm is a multi-population evolutionary algorithm, which consists of a unique evolve-simplify-optimize loop, designed for optimization of unknown scalar constants in newly-discovered empirical expressions. PySR's backend is the extremely optimized Julia library SymbolicRegression.jl, which can be used directly from Julia. It is capable of fusing user-defined operators into SIMD kernels at runtime, performing automatic differentiation, and distributing populations of expressions to thousands of cores across a cluster. In describing this software, we also introduce a new benchmark, "EmpiricalBench," to quantify the applicability of symbolic regression algorithms in science. This benchmark measures recovery of historical empirical equations from original and synthetic datasets.
hub tools
citation-role summary
background 4
method 2
baseline 1
citation-polarity summary
representative citing papers
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
A two-stage symbolic regression plus generative model framework recovers governing interaction terms and forcing in stochastic triad models while accurately predicting statistical moments up to order five.
A knowledge-first approach to LLM-driven automatic heuristic design in combinatorial optimization yields better discovery efficiency, transfer, and generalization than code-centric baselines by formalizing a distortion-compression trade-off.
Transformers reconstruct the constituent RCFTs in tensor-product theories from low-energy spectra, reaching 98% accuracy on WZW models and generalizing to larger central charges with few out-of-domain examples.
A derivative algebra with EML and SOL primitives plus additive atomic forests enables simultaneous symbolic recovery of functions and antiderivatives from data, matching or exceeding XGBoost on 13 of 17 benchmarks with interpretable formulas.
Machine collective intelligence uses coordinated AI agents to evolve symbolic hypotheses and recover governing equations from observations in deterministic, stochastic, and uncharacterized systems, achieving up to six orders of magnitude better extrapolation than neural networks with 5-40 parameters
Latent Grammar Flow discovers ODEs by placing grammar-based equation representations in a discrete latent space, using a behavioral loss to cluster similar equations, and sampling via a discrete flow model guided by data fit and constraints.
First direct constraints on total cosmic backreaction over a significant redshift range are consistent with vanishing backreaction within 1 sigma but are too weak to exclude meaningful backreaction.
LLM-ODE integrates large language models into genetic programming to guide symbolic search for governing equations of dynamical systems, outperforming classical GP on 91 test cases in efficiency and solution quality.
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
AlphaEvolve is an LLM-orchestrated evolutionary coding agent that discovered a 4x4 complex matrix multiplication algorithm using 48 scalar multiplications, the first improvement over Strassen's algorithm in 56 years, plus optimizations for Google data centers and hardware.
Tensor perturbations from first-order phase transitions and domain wall annihilation induce curvature fluctuations at second order that form primordial black holes, allowing asteroid-mass PBHs to comprise all dark matter for specific parameter ranges with associated gravitational wave peaks in LISA,
FePySR uses a neural network to pre-extract valid features before PySR search, recovering more equations than baselines on benchmarks and identifying governing ODEs in 24 of 100 biological cases where PySR finds none.
GESR uses two BERT models to intelligently direct mutations and crossovers inside genetic programming, yielding higher efficiency and competitive accuracy on symbolic regression benchmarks.
AutoSINDy automatically builds a tailored basis library from PySR symbolic regression and applies SINDy to recover ground-truth nonlinear dynamics with 92.8% success under noise.
DoLQ employs a sampler agent, parameter optimizer, and LLM-based scientist agent to iteratively propose, refine, and evaluate ODE candidates, yielding higher success rates and better symbolic term recovery than prior symbolic regression methods on multi-dimensional benchmarks.
Programmatic context augmentation lets LLM-based symbolic regression perform code-driven data analysis during search, yielding superior efficiency and accuracy over baselines on LLM-SRBench.
Symbolic regression on GWTC-4 posteriors yields closed-form analytic formulae for merger-rate evolution, effective-spin dependencies on mass ratio and redshift, and conditional mass-ratio distributions at specific primary mass peaks.
BINNs are extended to 2D+t systems and combined with symbolic regression to recover reaction-diffusion models of lung cancer cell dynamics from time-lapse microscopy data.
ASRNNs recover Hamiltonian dynamics and symbolic equations from trajectories with only two irregularly spaced noisy points by preserving symplectic structure without derivative estimation.
Variational autoencoders combined with symbolic regression extract physically meaningful representations and order parameters from raw quantum measurement data, revealing new phenomena such as corner-ordering in Rydberg arrays.
A Gompertzian reionization model with three nuisance parameters demotes optical depth to a derived quantity, reducing its uncertainty by a factor of three and revealing potential neutrino mass tension in CMB analyses.
citing papers explorer
-
SEVerA: Verified Synthesis of Self-Evolving Agents
SEVerA uses Formally Guarded Generative Models and a three-stage Search-Verification-Learning process to synthesize self-evolving agents that satisfy hard formal constraints while improving task performance.
-
KAN: Kolmogorov-Arnold Networks
KANs with learnable univariate spline activations on edges achieve better accuracy than MLPs with fewer parameters, faster scaling, and direct visualization for scientific discovery.
-
The finite expression method for turbulent dynamics with high-order moment recovery
A two-stage symbolic regression plus generative model framework recovers governing interaction terms and forcing in stochastic triad models while accurately predicting statistical moments up to order five.
-
Back to the Beginning of Heuristic Design: Bridging Code and Knowledge with LLMs
A knowledge-first approach to LLM-driven automatic heuristic design in combinatorial optimization yields better discovery efficiency, transfer, and generalization than code-centric baselines by formalizing a distortion-compression trade-off.
-
Reconstructing conformal field theoretical compositions with Transformers
Transformers reconstruct the constituent RCFTs in tensor-product theories from low-energy spectra, reaching 98% accuracy on WZW models and generalizing to larger central charges with few out-of-domain examples.
-
Additive Atomic Forests for Symbolic Function and Antiderivative Discovery
A derivative algebra with EML and SOL primitives plus additive atomic forests enables simultaneous symbolic recovery of functions and antiderivatives from data, matching or exceeding XGBoost on 13 of 17 benchmarks with interpretable formulas.
-
Machine Collective Intelligence for Explainable Scientific Discovery
Machine collective intelligence uses coordinated AI agents to evolve symbolic hypotheses and recover governing equations from observations in deterministic, stochastic, and uncharacterized systems, achieving up to six orders of magnitude better extrapolation than neural networks with 5-40 parameters
-
Neuro-Symbolic ODE Discovery with Latent Grammar Flow
Latent Grammar Flow discovers ODEs by placing grammar-based equation representations in a discrete latent space, using a behavioral loss to cluster similar equations, and sampling via a discrete flow model guided by data fit and constraints.
-
First observational constraints on cosmic backreaction over an extended redshift range
First direct constraints on total cosmic backreaction over a significant redshift range are consistent with vanishing backreaction within 1 sigma but are too weak to exclude meaningful backreaction.
-
LLM-ODE: Data-driven Discovery of Dynamical Systems with Large Language Models
LLM-ODE integrates large language models into genetic programming to guide symbolic search for governing equations of dynamical systems, outperforming classical GP on 91 test cases in efficiency and solution quality.
-
In-Context Symbolic Regression for Robustness-Improved Kolmogorov-Arnold Networks
In-context symbolic regression methods improve robustness of symbolic formula recovery from KANs, cutting median OFAT test MSE by up to 99.8 percent across hyperparameter sweeps.
-
Symbolic recovery of PDEs from measurement data
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
-
AlphaEvolve: A coding agent for scientific and algorithmic discovery
AlphaEvolve is an LLM-orchestrated evolutionary coding agent that discovered a 4x4 complex matrix multiplication algorithm using 48 scalar multiplications, the first improvement over Strassen's algorithm in 56 years, plus optimizations for Google data centers and hardware.
-
Primordial Black Hole from Tensor-induced Density Fluctuation: First-order Phase Transitions and Domain Walls
Tensor perturbations from first-order phase transitions and domain wall annihilation induce curvature fluctuations at second order that form primordial black holes, allowing asteroid-mass PBHs to comprise all dark matter for specific parameter ranges with associated gravitational wave peaks in LISA,
-
FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression
FePySR uses a neural network to pre-extract valid features before PySR search, recovering more equations than baselines on benchmarks and identifying governing ODEs in 24 of 100 biological cases where PySR finds none.
-
GESR: A Genetic Programming-Based Symbolic Regression Method with Gene Editing
GESR uses two BERT models to intelligently direct mutations and crossovers inside genetic programming, yielding higher efficiency and competitive accuracy on symbolic regression benchmarks.
-
Discovery of Nonlinear Dynamics with Automated Basis Function Generation
AutoSINDy automatically builds a tailored basis library from PySR symbolic regression and applies SINDy to recover ground-truth nonlinear dynamics with 92.8% success under noise.
-
Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation
DoLQ employs a sampler agent, parameter optimizer, and LLM-based scientist agent to iteratively propose, refine, and evaluate ODE candidates, yielding higher success rates and better symbolic term recovery than prior symbolic regression methods on multi-dimensional benchmarks.
-
Programmatic Context Augmentation for LLM-based Symbolic Regression
Programmatic context augmentation lets LLM-based symbolic regression perform code-driven data analysis during search, yielding superior efficiency and accuracy over baselines on LLM-SRBench.
-
Interpretable Analytic Formulae for GWTC-4 Binary Black Hole Population Properties via Symbolic Regression
Symbolic regression on GWTC-4 posteriors yields closed-form analytic formulae for merger-rate evolution, effective-spin dependencies on mass ratio and redshift, and conditional mass-ratio distributions at specific primary mass peaks.
-
Physics-Informed Neural Networks for Biological $2\mathrm{D}{+}t$ Reaction-Diffusion Systems
BINNs are extended to 2D+t systems and combined with symbolic regression to recover reaction-diffusion models of lung cancer cell dynamics from time-lapse microscopy data.
-
Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data
ASRNNs recover Hamiltonian dynamics and symbolic equations from trajectories with only two irregularly spaced noisy points by preserving symplectic structure without derivative estimation.
-
Discovering quantum phenomena with Interpretable Machine Learning
Variational autoencoders combined with symbolic regression extract physically meaningful representations and order parameters from raw quantum measurement data, revealing new phenomena such as corner-ordering in Rydberg arrays.
-
Into the Gompverse: A robust Gompertzian reionization model for CMB analyses
A Gompertzian reionization model with three nuisance parameters demotes optical depth to a derived quantity, reducing its uncertainty by a factor of three and revealing potential neutrino mass tension in CMB analyses.
-
Model-independent constraints on generalized FLRW consistency relations with bootstrap-based symbolic regression
Bootstrap-based symbolic regression on supernova and BAO data finds mild 2-4 sigma deviations from FLRW consistency relations, which if real would rule out most FLRW-based solutions to cosmological tensions.
-
Generating Literature-Driven Scientific Theories at Scale
Literature-grounded LLM synthesis of theories from 13.7k papers yields 2.9k theories that better match evidence and predict future results from 4.6k subsequent papers than parametric baselines.
-
Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves
GWAgent agentic workflow produces analytic surrogates for eccentric BBH waveforms with 6.9e-4 median mismatch and 8.4x speedup, outperforming baselines, and infers eccentricity for GW200129.
-
Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
BG-SINDy reformulates l0-constrained regression as term-level l2,0 regularization and uses progressive pruning guided by balance contributions to recover small-coefficient terms in multiscale PDEs.
-
Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches
The work introduces a modulation-based analytical method for singularity proofs in singular PDEs and refines ML techniques like PINNs and KANs to identify blowup solutions, with application to the open 3D Keller-Segel problem.
-
Identifying Topological Invariants of Non-Hermitian Systems via Domain-Adaptive Multimodal Model for Mathematics
A multimodal model with Qwen Math backbone identifies topological invariants of non-Hermitian systems from eigenvalues and eigenvectors in momentum space.
-
Experimental Design for Missing Physics
A sequential experimental design technique discriminates between model structures from symbolic regression to discover missing physics in process systems such as bioreactors.