Set Transformer inference of the neutron star equation of state from stellar observations
Abstract
We develop a permutation-invariant Set Transformer to reconstruct the equation of state (EoS) of dense matter from variable-size, unordered sets of neutron star (NS) observations. The model takes stellar masses together with radii, tidal deformabilities, or both, and predicts either the pressure P(n) or the sound speed cs2(n) on a fixed density grid, along with density-dependent uncertainties. Nothing in the architecture prescribes which star informs which density: self-attention couples all observations nonlinearly, and each density point reads the full set through its own learnable query, so the star-to-density mapping is learned from the data. Trained on independent piecewise-polytropic and Gaussian-process EoS ensembles, the model provides well-calibrated predictions whose uncertainty increases in density regions that stable stars cannot probe. Reconstruction errors decrease with the number of observations, while tidal deformability generally improves accuracy at a fixed observation count, even when it carries its own measurement noise. Sensitivity analysis reveals a density-local mapping: in the pressure models, predictions at density n depend most strongly on stars whose central densities are near n. We also show that the sensitivity of the model to the inferred stellar compactness provides information on the minimum central density. These results demonstrate that set-based neural inference, in which the star-to-density mapping is learned rather than assumed, can extract physically interpretable EoS information with calibrated uncertainties.
Related
- The Goldilocks Prior: Physically Consistent Inference of Neutron Star Properties from Gravitational Wave Observations
- NS-UNO: Neutron Star EoS Inference from an Unconstrained Number of Observations
- An Analytical Toy Equation of State for Neutron Stars Consistent with Current Observations
- An Analytical Toy Equation of State for Neutron Stars Consistent with Current Observations
- Extracting the Central Sound Speed of Neutron Stars through Intrinsic Stellar Structure Scaling with Reduced Equation-of-State Model Dependence
BibTeX
@misc{ferreira2026transformer,
title = {{Set Transformer inference of the neutron star equation of state from stellar observations}},
author = {Márcio Ferreira and Valéria Carvalho and Michał Bejger and Constança Providência},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31081},
eprint = {2609.31081},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31081},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Set Transformer inference of the neutron star equation of state from stellar observations
AU - Márcio Ferreira
AU - Valéria Carvalho
AU - Michał Bejger
AU - Constança Providência
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31081
UR - https://arxiv.org/abs/2609.31081
AB - We develop a permutation-invariant Set Transformer to reconstruct the equation of state (EoS) of dense matter from variable-size, unordered sets of neutron star (NS) observations. The model takes stellar masses together with radii, tidal deformabilities, or both, and predicts either the pressure P(n) or the sound speed c_s^2(n) on a fixed density grid, along with density-dependent uncertainties. Nothing in the architecture prescribes which star informs which density: self-attention couples all observations nonlinearly, and each density point reads the full set through its own learnable query, so the star-to-density mapping is learned from the data. Trained on independent piecewise-polytropic and Gaussian-process EoS ensembles, the model provides well-calibrated predictions whose uncertainty increases in density regions that stable stars cannot probe. Reconstruction errors decrease with the number of observations, while tidal deformability generally improves accuracy at a fixed observation count, even when it carries its own measurement noise. Sensitivity analysis reveals a density-local mapping: in the pressure models, predictions at density n depend most strongly on stars whose central densities are near n. We also show that the sensitivity of the model to the inferred stellar compactness provides information on the minimum central density. These results demonstrate that set-based neural inference, in which the star-to-density mapping is learned rather than assumed, can extract physically interpretable EoS information with calibrated uncertainties.
ER -