The age and mass of red giants are essential for understanding the structure
and evolution of the Milky Way. Traditional isochrone methods for these
estimations are inherently limited due to overlapping isochrones in the
Hertzsprung-Russell diagram, while asteroseismology, though more precise,
requires high-precision, long-term observations. In response to these
challenges, we developed a novel framework, Spectral Transformer (SPT), to
predict the age and mass of red giants aligned with asteroseismology from their
spectra. A key component of SPT, the Multi-head Hadamard Self-Attention
mechanism, designed specifically for spectra, can capture complex relationships
across different wavelength. Further, we introduced a Mahalanobis
distance-based loss function to address scale imbalance and interaction mode
loss, and incorporated Monte Carlo dropout for quantitative analysis of
prediction uncertainty.Trained and tested on 3,880 red giant spectra from
LAMOST, the SPT achieved remarkable age and mass estimations with average
percentage errors of 17.64% and 6.61%, respectively, and provided uncertainties
for each corresponding prediction. The results significantly outperform those
of traditional machine learning algorithms and demonstrate a high level of
consistency with asteroseismology methods and isochrone fitting techniques. In
the future, our work will leverage datasets from the Chinese Space Station
Telescope and the Large Synoptic Survey Telescope to enhance the precision of
the model and broaden its applicability in the field of astronomy and
astrophysics.

使用 Spectral Transformer（SPT）模型，通过红巨星的光谱预测其年龄和质量，具有较高的精度和一致性，超越传统机器学习算法，并与天体测量和恒星等值线拟合技术表现出较高的相关性。

红巨星的年龄和质量估计的光谱变换器（SPT）

SPT: Spectral Transformer for Red Giant Stars Age and Mass Estimation

The Kepler mission has provided exquisite data to perform an ensemble
asteroseismic analysis on evolved stars. In this work we systematically
characterize solar-like oscillations and granulation for 16,094 oscillating red
giants, using end-of-mission long-cadence data. We produced a homogeneous
catalog of the frequency of maximum power (typical uncertainty
$\sigma_{\nu_{\rm max}}$=1.6\%), the mean large frequency separation
($\sigma_{\Delta\nu}$=0.6\%), oscillation amplitude ($\sigma_{\rm A}$=4.7\%),
granulation power ($\sigma_{\rm gran}$=8.6\%), power excess width ($\sigma_{\rm
width}$=8.8\%), seismically-derived stellar mass ($\sigma_{\rm M}$=7.8\%),
radius ($\sigma_{\rm R}$=2.9\%), and thus surface gravity ($\sigma_{\log
g}$=0.01 dex). Thanks to the large red giant sample, we confirm that
red-giant-branch (RGB) and helium-core-burning (HeB) stars collectively differ
in the distribution of oscillation amplitude, granulation power, and width of
power excess, which is mainly due to the mass difference. The distribution of
oscillation amplitudes shows an extremely sharp upper edge at fixed $\nu_{\rm
max}$, which might hold clues to understand the excitation and damping
mechanisms of the oscillation modes. We find both oscillation amplitude and
granulation power depend on metallicity, causing a spread of 15\% in
oscillation amplitudes and a spread of 25\% in granulation power from
[Fe/H]=-0.7 to 0.5 dex. Our asteroseismic stellar properties can be used as
reliable distance indicators and age proxies for mapping and dating galactic
stellar populations observed by Kepler. They will also provide an excellent
opportunity to test asteroseismology using Gaia parallaxes, and lift
degeneracies in deriving atmospheric parameters in large spectroscopic surveys
such as APOGEE and LAMOST.

文章利用 Kepler 任务提供的数据对 1.6 万个震动红巨星进行了系统的恒星地震学研究，发现振动幅度和颗粒功率与金属丰度有关，这些研究可以作为已观测到的银河恒星种群的可靠距离指标和年龄代理，并为 APOGEE 和 LAMOST 等大型光谱调查中的大气参数导出消除退化提供了良好的机会。