# FFNN-TabNet: An Enhanced Stellar Age Determination Method Based on TabNet
## 1 Introduction  
The age of stars constitutes one of the most fundamental parameters in the study of stellar characteristics, as well as the current structure and formation history of the Milky Way galaxy [1]. The accurate determination of stellar ages is crucial for conducting a comprehensive census of stellar populations within the Milky Way, revealing its origins and understanding its integrated history of formation and evolution. Contemporary large-scale astronomical surveys have amassed a significant collection of high-quality spectral data, including but not limited to the LAMOST (Large Sky Area Multi-Object Fiber Spectroscopic Telescope) survey data [2, 3], GAIA (Global Astrometric Interferometer for Astrophysics) [4, 5], and the SDSS (Sloan Digital Sky Survey) [6]. These spectral analyses have enabled the determination of highly accurate atmospheric parameters and chemical abundances for a substantial number of stars [7]. However, determining the age of stars via spectral analysis proves challenging. Typically, it requires the correlation of observed data with stellar evolution models, such as spectroscopic methods. Unfortunately, these approaches often yield age determinations with relatively low precision. In recent years, the field of stellar age determination based on machine learning and deep learning has rapidly evolved with the proposition of several models, including but not limited to Artificial Neural Networks (ANN) [8], Kernel Principal ComponentAnalysis (KPCA) [9], and Random Forests (RF) [10]. These models, thanks to their progressively refined mechanisms and functionalities, have demonstrated considerable potential in this domain. Traditional methods typically specialize in distinct data types, with the spectroscopic method, for instance, being devoted to the analysis of stellar spectra to ascertain stellar ages. However, the spectroscopic method is limited for low-mass cooling main-sequence stars or giants with narrow and indistinct isochrone intervals. The gyrochronology method's utility is limited by its reliance on rotational periods and stellar chromatic attributes, reducing its overall applicability. The asteroseismology method deduces stellar attributes like mass and age from oscillation frequencies but is mainly suitable for stars with solar-like oscillations. The method based on stellar activity has lower age determination accuracy. A comprehensive review of traditional methods is provided in Section 2.1. In contrast, machine-learning methods have wide applicability, being able to identify and extract relevant features from various data sources (such as spectral data and asteroseismic parameters) through training, and they exhibit higher accuracy. However, the stellar data derived from spectroscopic analysis and asteroseismology encompass a wealth of physical and chemical attributes. Current models often struggle to accurately discern the key features significantly impacting age determination, resulting in suboptimal precision. Additionally, there exist complex nonlinear relationships among these datasets, and current models exhibit significant shortcomings in capturing these complexities. Further optimization and improvement are necessary to enhance their accuracy and efficiency in determining stellar ages. Addressing the aforementioned issues, this study introduces an improved model for determining stellar ages: FFNN-TabNet, which combines Feedforward Neural Network (FFNN) [11] and TabNet [12]. This model aims to resolve the challenges of low precision and the inadequate capture of complex nonlinear relationships inherent in existing models. Specifically, the main contribution of this work can be summarized as follows:  
1. This study introduces an enhanced model for stellar age determination based on TabNet, named FFNN-TabNet. We have made significant improvements to the attentive transformer module within TabNet, specifically by incorporating a Feedforward Neural Network (FFNN).