Controlled comparison of probabilistic architectures for Gaia XP asteroseismic inference

Determine, through controlled comparisons, whether Bayesian neural networks, Bayesian extensions of the present mixture density network, conditional diffusion models, and scalable Gaussian-process approximations can improve the inference of the asymptotic dipole gravity-mode period spacing ΔΠ₁ from 343-dimensional Gaia DR3 XP spectra, while providing practical computational performance for approximately 22 million stars.

Background

The paper infers the asymptotic dipole gravity-mode period spacing ΔΠ₁ and the large frequency separation Δν from corrected Gaia DR3 BP/RP (XP) spectra using a deterministic mixture density network (MDN). The adopted MDN uses a two-component Gaussian mixture for ΔΠ₁ to represent the bimodal distinction between red-giant-branch and red-clump stars, but its deterministic network weights do not capture epistemic uncertainty associated with limited or sparse training data.

The authors identify several alternative probabilistic approaches: Bayesian neural networks or Bayesian MDNs could model epistemic uncertainty; conditional diffusion models could represent more flexible conditional distributions; and scalable inducing-point or deep-kernel Gaussian-process approximations could be considered with a likelihood capable of representing the bimodal ΔΠ₁ distribution. These alternatives have not been systematically compared for this application, and their relative accuracy, uncertainty calibration, and computational feasibility remain unresolved.