Interpretable Parameter Inference from Simulated 21 cm Power Spectra: Recoverability, Symbolic Compressibility, and Information Localization

The redshifted 21 cm signal from neutral hydrogen provides one of the most promising probes of the Cosmic Dawn and the Epoch of Reionization, encoding rich information regarding early structure formation, ionization morphology, and high-redshift astrophysical evolution. Recovering the underlying physical parameters from observable 21 cm statistics, however, constitutes a highly nonlinear and partially degenerate inverse problem. In this work, we investigate interpretable parameter inference from simulated 21 cm power spectra using a combination of machine-learning baselines, symbolic regression, feature-ablation analyses, perturbation robustness tests, and bootstrap uncertainty estimation. Synthetic 21 cm power-spectrum realizations are generated using 21cmFAST across a five-parameter space spanning both cosmological and astrophysical effects: zeta, log10(Tvir), Rmfp, log10(LX), and sigma8. Random Forest and multilayer perceptron regressors are first used to establish a baseline recoverability hierarchy, after which symbolic regression using PySR is employed to investigate whether the inferred parameter mappings admit compact analytic structure. Additional analyses explore information localization across redshift and spatial scales, perturbative robustness under controlled feature corruption, and uncertainty calibration behavior using bootstrap ensemble resampling. A broadly consistent complexity–recoverability hierarchy emerges across the different analyses. The cosmological parameter sigma8 exhibits strong recoverability, strong symbolic compressibility, coherent localization within restricted redshift-scale regions, substantial perturbative robustness, and comparatively meaningful uncertainty-error alignment. In contrast, the astrophysical parameters zeta, log10(Tvir), and log10(LX) remain weakly recoverable across nearly all tested frameworks, resist compact symbolic representation, and exhibit diffuse localization and weak robustness structure, while Rmfp consistently occupies an intermediate regime between these extremes. The results indicate that recoverability, symbolic compressibility, information localization, robustness, and uncertainty calibration are closely interconnected and reflect how physical information is distributed within the selected coeval 21 cm power-spectrum feature representation. More broadly, this work demonstrates that interpretable machine-learning analyses can provide substantially more than predictive surrogate models alone and may instead serve as probes of structural organization within high-dimensional cosmological inverse problems. This is a preprint version of a manuscript submitted to Astronomy and Computing for peer review. Associated datasets, trained models, symbolic-regression analyses, and reproducibility materials:https://doi.org/10.5281/zenodo.20617535 Code repository:https://github.com/rudhresh1997/21cm-symbolic-regression/tree/production-n2000