FFNN–TabNet: An Enhanced Stellar Age Determination Method Based on TabNet
Abstract
:1. Introduction
- 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). This step not only optimizes the functionality of the module but also significantly enhances its ability to process complex data structures and capture nonlinear relationships, thereby effectively increasing the accuracy of stellar age determination.
- To address the issue of gradient vanishing or diminishing that may be caused by the Rectified Linear Unit (ReLU) activation function [13] within TabNet, this study has replaced it with the Parametric Rectified Linear Unit (PReLU) activation function [14]. The PReLU function dynamically adjusts activation thresholds to avoid gradient vanishing, effectively enhancing the model’s learning speed and stability. This improvement is particularly crucial for enhancing the model’s ability to process complex nonlinear relationships, contributing to increased accuracy and efficiency in stellar age determination.
- To further optimize the performance of the model, this study incorporated the Bayesian optimization algorithm (BOA) [15,16] for hyperparameter tuning. This method effectively resolves the issues of inefficiency and inaccuracy inherent in traditional hyperparameter tuning approaches, significantly enhancing the model’s capability to process complex data structures and improving the accuracy of its determination. Additionally, the algorithm accelerates the hyperparameter search process and more accurately identifies the optimal combination of hyperparameters, thereby increasing the model’s stability and robustness.
- To verify the effectiveness of the FFNN–TabNet model, we conducted detailed ablation experiments and compared it comprehensively with six other different models. Through these experiments, we were able to clearly observe the performance differences between the models. The results show that in the challenging task of determining stellar ages, the FFNN–TabNet model excels, surpassing the other models in terms of accuracy and stability. The comparative experiment on feature contribution leads to the conclusion that there has been an enhancement in the model’s ability to capture nonlinear relationships among features.
2. Related Works
2.1. Traditional Stellar Age Determination Methods
- 5.
- Spectroscopic Method
- 6.
- Gyrochronology Method
- 7.
- Asteroseismology Method
- 8.
- Method Based on Stellar Activity
2.2. Machine-Learning and Deep-Learning Methods
3. Method
3.1. Data
3.2. The FFNN–TabNet
3.2.1. TabNet Neural Network Decision Process
3.2.2. The FFNN–TabNet Architecture
- (1)
- Initially, the primal feature vector undergoes normalization in a batch normalization (BN) [58] layer, followed by computational processing in the Feature Transformer layer. Within this layer, data traverses a shared parameter layer constituted of two FC + BN + GLU units, connected via a residual network and subsequently normalized by a factor of 5.0. This layer’s chief purpose is to deduce commonalities among features. Subsequent to this layer, data proceeds to an independent parameter layer, mirroring the preceding layer’s architecture [12]. The feature transformer layer architecture is depicted in Figure 3.
- (2)
- Subsequent to its processing through the Feature Transformer layer, the red giant dataset advances into the Split module. This module functions to segregate the output derived from the initial Feature Transformer, thereby isolating and acquiring the features in the first step, specifically when . The formula is shown in Equation (3).
- (3)
- Subsequent to traversing the Split module, the dataset proceeds into the Attentive Transformer layer, analogous to the Mask layer depicted in Figure 1. The primary role of this layer is the computation of the current step’s Mask, which is essential for feature selection. The Attentive Transformer layer is intricately composed of an FC layer, BN layer, and a Sparsemax layer, along with a weighted scaling factor as a foundational scale component [12]. Owing to the intricate non-linear interrelations among the features of red giant star data, in the current research, we have strategically integrated a FFNN upstream of the BN layer. The attentive transformer architecture is illustrated in Figure 4.
- (1)
- Feedforward Neural Network (FFNN)
- (2)
- Sparsemax [59]
4. Construction of the FFNN–TabNet Determination Model
4.1. Data Preprocessing
4.2. Bayesian Optimization
- (1)
- Initialization: Based on the aforementioned search range, a set of initial hyperparameters is randomly selected, denoted as T(0).
- (2)
- Selection of Candidate Combination: Based on T(0), select a potential set of candidate hyperparameter combinations, denoted as R[t].
- (3)
- Construction of Probability Model: Build a Bayesian network based on the current distribution of hyperparameters to represent the probabilistic relationship between hyperparameters and the objective function.
- (4)
- Objective Function Fitting: Employ the constructed probability model to estimate the objective function, thereby generating a new set of hyperparameters, denoted as R1[t + 1].
- (5)
- Update of Parameter Combination: Substitute a part of R1[t + 1] into T[t] to form a new hyperparameter combination, T[t + 1].
- (6)
- Termination Condition Assessment: Evaluate whether the current candidate combination R[t] meets the predetermined termination criteria. If not, revert to Step 2 for further iteration; if satisfied, conclude the search.
4.3. Construction of the FFNN–TabNet Model
5. Experiments and Results
5.1. Loss Functions and Evaluation Metric
5.2. Experimental Results and Analysis
5.3. Ablation Experiment and Analysis
- (1)
- TabNet 1: The model excluding both PReLU activation function and FFNN module, termed TabNet without PReLU and FFNN;
- (2)
- TabNet 2: The model excluding only the FFNN module, termed TabNet without FFNN;
- (3)
- TabNet 3: The model excluding only the PReLU activation function, termed TabNet without PReLU;
- (4)
- FFNN–TabNet: The FFNN–TabNet model proposed in this study.
5.4. Model Comparison and Analysis
5.5. Feature Correlation and Analysis
6. Discussion
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Description |
---|---|
(K) | Effective temperature |
(dex) | Surface gravity |
mass | Red giant mass |
alpha | α elements |
Fe_H, N_H, Ca_H, V_H, C_H, P_H, Ni_H, Na_H, Mg_H, K_H, Co_H, Ti_H, Al_H, Mn_H, O_H, Cr_H | Chemical abundances, logarithm of the ratio of iron, nitrogen, calcium, vanadium, carbon, phosphorus, nickel, natrium, magnesium, potassium, cobalt, titanium, aluminum, manganese, oxygen, chromium to hydrogen atoms |
Age (Gyr) | red giant age |
Hyperparameter | Description | Value Range | Value |
---|---|---|---|
N_d | Width of the decision prediction layer | ~4–64 | 16 |
N_a | Width of the attention embedding for each mask | ~4–64 | 16 |
N_steps | Number of steps in the architecture | ~1–10 | 6 |
Lr | Learning rate | ~0.001–0.1 | 0.01 |
Optimizer_fn | Pytorch optimizer function | - | Adam |
Max Epochs | Maximum number of epochs for training | - | 100 |
Batch Size | Number of examples per batch | - | 64 |
Virtual Batch Size | Size of the mini batches used for GBN | - | 128 |
Early Stopping Patience | Early Stopping Patience | - | 20 |
Methods | MSE | RMSE | R2 |
---|---|---|---|
Tabnet 1 | 0.659 | 0.875 | 0.883 |
Tabnet 2 | 0.715 | 0.803 | 0.913 |
Tabnet 3 | 0.623 | 0.752 | 0.935 |
FFNN–TabNet | 0.535 | 0.711 | 0.946 |
Methods | Settings |
---|---|
LSTM | Learning rate = 0.001, batch size = 32, epochs = 50, optimizer = Adam, activation functions = tanh |
RF | n_estimators = 100, max_depth = 3 |
BPNN | Learning rate = 0.001, batch size = 64, epochs = 50, optimizer = Adam, activation functions = ReLU |
CNN | Learning rate = 0.001, batch size = 64, epochs = 50, optimizer = Adam, activation functions = ReLU |
RNN | Learning rate = 0.001, batch size = 32, epochs = 50, optimizer = Adam, activation functions = tanh |
TCN | Learning rate = 0.001, batch size = 64, epochs = 50, optimizer = Adam, activation functions = ReLU |
Methods | MSE | RMSE | R2 |
---|---|---|---|
LSTM | 0.860 | 1.146 | 0.802 |
RF | 0.749 | 0.981 | 0.848 |
BPNN | 0.697 | 0.913 | 0.856 |
CNN | 0.672 | 0.882 | 0.871 |
RNN | 0.681 | 0.876 | 0.878 |
TCN | 0.593 | 0.796 | 0.901 |
FFNN–TabNet | 0.535 | 0.711 | 0.946 |
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Zhang, H.; Wu, Y.; Zhang, W.; Zhang, Y. FFNN–TabNet: An Enhanced Stellar Age Determination Method Based on TabNet. Appl. Sci. 2024, 14, 1203. https://doi.org/10.3390/app14031203
Zhang H, Wu Y, Zhang W, Zhang Y. FFNN–TabNet: An Enhanced Stellar Age Determination Method Based on TabNet. Applied Sciences. 2024; 14(3):1203. https://doi.org/10.3390/app14031203
Chicago/Turabian StyleZhang, Han, Yadong Wu, Weihan Zhang, and Yuling Zhang. 2024. "FFNN–TabNet: An Enhanced Stellar Age Determination Method Based on TabNet" Applied Sciences 14, no. 3: 1203. https://doi.org/10.3390/app14031203
APA StyleZhang, H., Wu, Y., Zhang, W., & Zhang, Y. (2024). FFNN–TabNet: An Enhanced Stellar Age Determination Method Based on TabNet. Applied Sciences, 14(3), 1203. https://doi.org/10.3390/app14031203