938,720 Giants from LAMOST I: Determination of Stellar Parameters and α, C, N Abundances with Deep Learning

X. Zhang; G. Zhao; C. Q. Yang; Q. X. Wang; W. B. Zuo

doi:10.1088/1538-3873/ab2687

1. Introduction

To further study Galactic evolution, it is crucial to accurately estimate stellar atmospheric parameters and elemental abundances from a large sample of modern spectroscopic surveys, such as the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Zhao et al. 2006, 2012; Cui et al. 2012), the Sloan Extension for Galactic Understanding and Exploration (SEGUE; Yanny et al. 2009), the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017), the RAdial Velocity Experiment (RAVE; Steinmetz et al. 2006), the GALAH Survey (De Silva et al. 2015), Gaia (Gaia Collaboration et al. 2016), and Gaia-ESO (Gilmore et al. 2012). A variety of techniques and methods have been developed to estimate stellar parameters from large spectroscopic survey databases, ranging from a χ² related algorithm to a multivariable analysis.

Each survey has established its own stellar parameter pipeline: the LAMOST Stellar Parameter Pipeline (LASP; Wu et al. 2011; Luo et al. 2015), the LAMOST Stellar Parameter Pipeline at PKU (LSP3; Xiang et al. 2014, 2015; Ren et al. 2016), the APOGEE Stellar Parameter and Chemical Abundances Pipeline (ASPCAP; García Pérez et al. 2016), the SEGUE Stellar Parameter Pipeline (SSPP; Lee et al. 2008), and the RAVE pipeline (Steinmetz et al. 2006).

In the case of low-resolution survey, e.g., LAMOST, the accuracy of parameters derived by template matching remains to be improved, especially for log g. There are good reasons to trust that parameters from APOGEE which has higher spectral resolution and higher signal-to-noise ratio (S/N) are more accurate than those of LAMOST. Chen et al. (2015) compared stellar parameters T_eff, log g and [Fe/H] for common stars in LAMOST DR2 (Wu et al. 2011) and SDSS DR12 (Alam et al. 2015; Holtzman et al. 2015) and found systematic biases in log g and [Fe/H]. Systematic offsets are normal for two surveys with different wavelength coverage and different spectral resolutions, but parameters and abundances used to describe the properties of same stars should be consistent between surveys. That is to say, techniques must be developed to bring different surveys onto the same label scale. Ho et al. (2017a) have explained how we can transfer labels between two different surveys in details and transferred labels from APOGEE to LAMOST with The Cannon (Ho et al. 2016; Ness et al. 2015). Ho et al. (2017a) predicted precise stellar parameters and [α/M] for 450,000 LAMOST giants, and cross-validation of the model yielded uncertainties of 70 K in T_eff, 0.1 dex in log g, 0.1 dex in [Fe/H] and 0.04 dex in [α/M] for spectra with S/N larger than 50. Ho et al. (2017b) further measured C, N abundances for these stars. Xiang et al. (2014) estimated accurate stellar atmospheric parameters, absolute magnitudes and C, N elemental abundances from LAMOST spectra with KPCA, using stars in common with some other surveys (Hipparcos, Kepler, APOGEE) as training set. Given spectral S/N better than 50, the method can deliver stellar parameters with a precision of ∼100 K for T_eff, ∼0.1 dex for log g, 0.1 dex for [Fe/H], [C/H] and [N/H], and better than 0.05 dex for [α/M]. Ting et al. (2016, 2017) measured 14 elemental abundances from LAMOST spectra with ab initio models to argue low-resolution spectra enable precise measurements of many elemental abundances. Liu et al. (2015) set a Support Vector Regression (SVR) model for estimation of surface gravity supervised by LAMOST giants with the Kepler seismic surface gravity and reduced the uncertainty of the estimates down to about 0.1 dex.

Neural network (NN) has long been used in astrophysical applications. Bailer-Jones et al. (1997) and Bailer-Jones (2000) applied NN on synthetic stellar spectra to predict T_eff, log g, and [Fe/H]. Two NN were trained in the SEGUE pipeline (Lee et al. 2008): one on synthetic spectra and the other on previous SEGUE parameters. Recently, with the increase in computing power and the availability of large data sets, the successful implementation of more complex NN architectures have led to dramatic improvements in performances of algorithms (Fabbro et al. 2018). Fabbro et al. (2018) and Leung & Bovy (2018) applied Convolutional Neural Networks (CNN) to the APOGEE data set, and both methods yielded excellent performance. Wang et al. (2019) analyzed stellar spectra from LAMOST DR5 with Generative Spectrum Networks (GSN) and yielded a precision of 80 K for T_eff, 0.14 dex for log g, 0.07 dex for [Fe/H] and 0.168 dex for [α/Fe]. These methods benefit from the effectiveness of artificial neural networks in fitting complex nonlinear relations. In this work, a deep learning method named StarNet (Fabbro et al. 2018) is applied on LAMOST spectra to transfer labels from APOGEE to LAMOST by training common stars between two surveys. We trained a model to bring LAMOST onto APOGEE's label scale. Parameters which are consistent with those measured by the APOGEE pipeline can be directly inferred from LAMOST spectra ultimately.

The paper is organized as follows: in Section 2, LAMOST spectra and APOGEE labels which were used to train the deep learning model (StarNet) are introduced. In Section 3, the method used for determination of stellar parameters, the training step and the test step are described. In Section 4, the trained model is applied on spectra of 938,720 giants from LAMOST DR5 and parameters are predicted for these stars. The results are also compared with high-precision measurements. Finally, Error analysis and considerations of deep learning are discussed in Section 5, followed by a conclusion in Section 6.

2. Data Sets

The Large sky Area Multi-Object Spectroscopic Telescope (LAMOST) is a low-resolution (R ≈ 1800) optical (3700–9000 Å) spectroscopic survey. It can collect 4000 fiber spectra in a wild field (5°) simultaneously. The two-dimension data are processed with the LAMOST 2D pipeline for spectral extraction, wavelength calibration, flat-fielding, background subtraction and flux calibration to produce 1D spectra (Luo et al. 2015). Each of the final stellar spectra is a combination of three single-exposure spectra which consist of two sub-spectra obtained in the blue (3700–5900 Å) and red (5700–9000 Å) arms. All released spectra are wavelength calibrated at a vacuum wavelength based on lamp spectra. And the spectra are relative flux calibrated based on standard stars (Luo et al. 2015) or statistical response curve (Du et al. 2016). LAMOST DR5 includes a total of 9027,634 spectra, in which 832,886 are classified as stars. The LASP (Luo et al. 2015; Wu et al. 2011) used the Correlation Function Initial method to guess the initial values of the parameters and used the UlySS method (Koleva et al. 2009; Wu et al. 2011) to generate the final parameters.

The Apache Point Observatory for Galactic Evolution Experiment (APOGEE; Majewski et al. 2017) is a high-resolution (R ≈ 22,500), high S/N (≈100) spectroscopic survey in the near-infrared spectral range (15100–17000 Å). APOGEE spectra are obtained from the Sloan Foundation 2.5 m telescope at Apache Point Observatory (Gunn et al. 2006) and the 2.5 m du Pont Telescope at Las Campanas Observatory. APOGEE DR14 (Abolfathi et al. 2018; Holtzman et al. 2018; Jönsson et al. 2018) has already collected spectra of ∼277,000 giant stars. The stellar parameters and abundances including T_eff, log g, [M/H], [α/M], [C/M], [N/M], and microturbulence are derived by the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP; García Pérez et al. 2016) which is based on comparison between the observed and theoretical spectra with the FERRE code (Allende Prieto et al. 2006, 2014).

2.1. Preprocessing for the Input Spectra

Because LAMOST spectra has low resolution, low S/N, different wavelength region, large uncertainties of flux calibration and unknown extinction values for most of survey targets, it is necessary to normalize the LAMOST spectra to derive reliable stellar parameters (Xiang et al. 2014). To remove overall flux and large shape changes from the spectra, we normalized the spectra with The Cannon as Ho et al. (2017a). A continuum-normalized spectrum is generated by an error-weighted, broad Gaussian smoothing:

$\begin{eqnarray*}&&\bar{f}({\lambda }_{0})=\tfrac{{\displaystyle \sum }_{i}({f}_{i}{\sigma }_{i}^{-2}{\omega }_{i}({\lambda }_{0}))}{{\sum }_{i}({\sigma }_{i}^{-2}{\omega }_{i}({\lambda }_{0}))},\end{eqnarray*}$

where f_i is the flux at pixel i, σ_i is the uncertainty at pixel i, and the weight ω_i is drawn from a Gaussian:

$\begin{eqnarray*}&&{\omega }_{i}({\lambda }_{0})={e}^{-\tfrac{{\left({\lambda }_{0}-{\lambda }_{i}\right)}^{2}}{{L}^{2}}},\end{eqnarray*}$

L was chosen to be 50 Å, because 50 Å is much broader than typical atomic lines (Ho et al. 2017a for details).

Each spectrum was normalized through dividing the flux by $\bar{f}({\lambda }_{0})$ . We opted to use 3900–8800 Å segment to avoid the low instrument efficiency near the edges of wavelength. Figure 1 shows the raw and normalized LAMOST spectrum.

**Figure 1.** Sample of normalized LAMOST spectrum. Upper panel shows a LAMOST spectrum and the bottom panel shows the final "normalized" spectrum.
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3. The Method

Supervised machine learning has been widely applied to variable regression problems. Given a training set, that is, input spectrum with known stellar parameters, a supervised learning model can generate a function that transforms the input spectra to the output parameters. Then the learned function can be used to predict parameters for another data set of spectra (Fabbro et al. 2018). The form of this function depends on the NN architecture which can be arranged in layers of artificial neurons: an input layer, number of hidden layers, and an output layer. The more hidden layers used, the deeper the model is. LAMOST which provides a large database of stellar spectra is ideal for deep learning application.

3.1. The StarNet CNN

StarNet is a convolutional neural network (CNN) that Fabbro et al. (2018) implemented on APOGEE stellar spectra and synthetic stellar spectra. When it is trained on APOGEE data, the stellar parameters have similar precision as the APOGEE pipeline, and when it is trained on synthetic data, it can also predict accurate stellar parameters for both APOGEE spectra and synthetic spectra. StarNet is a deep neural network which is composed of seven layers. The first layer is input data, followed by two convolutional layers with four and 16 filters. Then it is a max pooling layer with window length of four units, followed by two fully connected layers with 256 and 128 nodes. The final layer is output layer. The detailed architecture can be referred to Figure 1 in Fabbro et al. (2018). The combination of convolutional layers and fully connected layers in StarNet means that the output parameters are affected not only by individual feature in the input spectrum, but also by features in different areas of the spectrum. This technique enhances the capabilities of StarNet to predict for spectra with a wide range of S/N (Fabbro et al. 2018). Therefore, we decided to apply it on the LAMOST spectral survey.

3.2. Training Step

In the training step, stars observed in common between LAMOST and APOGEE will be used to train the StarNet model. StarNet uses spectra from LAMOST and corresponding labels from APOGEE to fit a predictive model.

In APOGEE DR14 (Holtzman et al. 2018), calibration relations have been applied to the ASPCAP measurements. APOGEE DR14 catalog totally contains 277,371 stars with their empirically calibrated parameters. Here, T_eff, log g, [M/H], [α/M], [C/M] and [N/M] which are stored under the header PARAM in the fits file are utilized for training. A, F, G, and K type stars catalog provided by LAMOST DR5 v1 version includes 5344,058 stars with spectra. We identified stars in common between two catalogs based on spatial position (i.e., R.A. and decl.) within 1'' and finally found 63,887 common objects. To select reliable objects, we made a number of quality cuts to this set. First, it is necessary to remove objects with missing values which is represented by −9999 in APOGEE. Then, we select reliable stars with 4000 K < T_eff(APOGEE) < 5300 K and 0 dex < log g(APOGEE) <3.8 dex, STARFLAG == 0, ASPCAPFLAG == 0, as described in Holtzman et al. (2015, 2018), which yields 19,137 common stars. In order to extract reliable spectral features, we only use stars with LAMOST spectral S/N_g larger than 10 for training. In the end, there were a total of 18,557 stars left in the set.

We divided the 18,557 stars into reference set and test set randomly in the proportion of 8:2. There were 14,845 stars in the reference set which was used for training and cross-validation, and 3712 stars in the test set which was used for testing the performance of the model we trained. To exclude interference among different labels (e.g., [M/H] to [C/M], [N/M]), we transferred [X/M] to [X/H] with the formula [X/H] = [X/M] + [M/H] where X was α, C, N. Figure 2 shows the relative number distributions of labels for stars in the reference set and the test set. In each panel, distributions between the reference set and the test set are similar. This is because we selected the reference sample and the test sample from common stars randomly. There are few stars with [M/H] < −1.0 dex. The reference samples were then divided into training set and cross-validation set in the proportion of 8:2. Finally, 11,876 stars were used for training and 2969 stars were used to cross-validate the model following each "Epoch" during the training process.

**Figure 2.** Distributions of labels for 14,845 stars in the reference set and for 3712 stars in the test set. The reference set is shown in blue and the test set in yellow.
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StarNet used training samples to fit a model which characterized the normalized spectra as a function of labels. The input data is normalized spectral fluxes and the output data is six stellar parameters. The training set was used for training and the cross-validation set was used to cross-validate the model during the training stage. A mean-squared-error (MSE) loss function is used as the metric between targets and predicted parameters. Early-stopping is employed to prevent overfitting, which means that the model will stop training when the performance (i.e., MSE) of the model on the cross-validation set begins to decline. Considering the fact that LAMOST spectra has low S/N, low resolution, a different rectification and continuum normalization scheme and is in a different wavelength region, we added more layers based on the original StarNet architecture to expect better results. Fabbro et al. (2018) have introduced the process of model selection. In the first stage, the number of convolutional and fully connected layers were set up randomly to select optimal model architecture. In the second stage, fixing the number of convolutional and fully connected layers, the hyper-parameters were optimized. We tried to combine different numbers of convolutional layers and fully connected layers and found that increasing the number of layers can improve the MSE. Figure 3 shows the changes of MSE in the training process with different combinations of convolutional and fully connected layers. When four convolutional layers and four fully connected layers were combined, the convergence process was more stable. The adjustment in hyper-parameter had no significant improvement for prediction. The cross-validation set which was not used for training validated the model at the end of each epoch. When the performance (MSE) of the model on the cross-validation set declined to ∼0.056, the training process stopped.

**Figure 3.** Changes of loss values and validation loss values in the training process. Loss is MSE between StarNet predictions and target parameters for stars in the training set, and validation loss is MSE for stars in the cross-validation set. Different colors indicate the combination of different numbers of convolutional layers and fully connected layers.
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3.3. Test Step

With completion of the training step, our model is evaluated on the test set containing 3712 stars. T_eff, log g, [M/H], [α/H], [C/H] and [N/H] were predicted by the model from the test LAMOST spectra, and compared with parameters from APOGEE. The test results are shown in Figure 4. "Bias" represents mean value of residuals and "scatter" represents standard deviation of residuals. There is no significant bias for these parameters except for T_eff with a bias of 11.85 K. The scatter is 45.53 K for T_eff, 0.10 dex for log g, 0.05 dex for [M/H], 0.05 dex for [α/H], 0.08 dex for [C/H] and 0.08 dex for [N/H], respectively. Thanks to the large training data set, StarNet shows an outstanding performance on spectral predictions. The low bias and low scatter between StarNet predictions and APOGEE values indicate that the model we trained has powerful ability in estimating accurate parameters from LAMOST spectra. We converted [X/H] back to [X/M] (i.e., [α/M], [C/M], [N/M]) with formula [X/M] = [X/H] − [M/H] and compared with the corresponding APOGEE values. There is no significant bias for these three parameters, and scatter is 0.03 dex for [α/M], 0.058 dex for [C/M] and 0.073 dex for [N/M]. The predictions still keep high consistency with APOGEE values. It is noted that the training set includes few stars with [M/H] < −1.0 dex, thus the scatter is dominated by stars with [M/H] > −1.0 dex.

**Figure 4.** Predictions from StarNet and values from APOGEE are compared to test the capability of the model. The specific bias and scatter of the residuals for each parameter are marked in the corresponding panel.
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Figure 5 plots the differences between model predicted values and APOGEE values with the increasing LAMOST spectral S/N in the g band (S/N_g) which is measured by the LAMOST pipeline for the test samples. The differences have clear dependencies on the spectral S/N_g. The dispersions of residuals decrease significantly with increasing S/N_g when S/N_g is less than 70 and it becomes flat when S/N_g is larger than 70. The mean uncertainties are 47.55 K for T_eff, 0.10 dex for log g, 0.05 dex for [M/H], 0.03 dex for [α/M], 0.06 dex for [C/M] and 0.07 dex for [N/M] with S/N_g larger than 10. For high S/N_g spectra, StarNet predictions indicate high agreement with the APOGEE values, while for low S/N_g spectra, deviations becomes larger. Such trends of dispersions are expected. For stars with low spectral S/N_g, the errors mainly come from spectral imperfections. The dispersions are small enough at low S/N_g end, which proves deep learning has an outstanding performance for low S/N_g spectra due to the combination of convolutional layer and fully connected layers. Differences and dispersions between LAMOST measurements and APOGEE measurements for stellar parameters are also shown in the plots, and the dispersions also reduce with the increasing S/N_g. The dispersions between StarNet predictions and APOGEE measurements are overall lower than those between LAMOST and APOGEE, which indicates deep learning shows an improvement than the LAMOST pipeline.

4. 938,720 Giants from LAMOST DR5

Within the range of 4000 K < T_eff (LAMOST) < 5300 K and 0 dex < log g (LAMOST) < 3.8 dex, we selected 938,720 giant stars from A, F, G, and K type stars catalog provided by LAMOST DR5. We applied our trained model on spectra of these giants and predicted T_eff, log g, [M/H], [α/M], [C/M], [N/M] for them.

4.1. Comparison with Stellar Isochrones

Stellar atmospheric parameters provided by LAMOST, StarNet and APOGEE were compared to stellar isochrones in Figure 6 (in this work, metallicity provided by StarNet and APOGEE is represented by "[M/H]," while for other surveys it is still represented by "[Fe/H]"). Four isochrones with different metallicities ([Fe/H] = 0.25, −0.25, −0.75, and −1.75) were generated from Dartmouth Stellar Evolution Database (Dotter et al. 2008) using age of 5 Gyr and [α/Fe] = 0. Stars with parameters provided by LAMOST present a wide distribution and some scattered points. But from the panel which shows distribution of the same stars with estimates from StarNet, the distribution is more consistent with the stellar evolution isochrones. It is interesting that horizontal branch stars can be seen in our parameters space while they almost have no trace in original LAMOST parameters. Compared with distribution of stars with APOGEE values in the isochrones, our result is similar to the APOGEE distribution, which reflects deep learning method is reliable and our estimates are robust.

4.2. Comparison with PASTEL Catalog and Asteroseismic log g

The PASTEL catalog (Soubiran et al. 2010, 2016) collects stellar parameters (T_eff, log g, [Fe/H]) which were derived from high-resolution and high S/N spectra. Stellar parameters from PASTEL catalog can be used to test the reliability of our results. The updated PASTEL catalog (Soubiran et al. 2016) includes 64,082 determinations of T_eff, log g, [Fe/H] for 31,401 stars. The PASTEL catalog includes 181 stars in common with the LAMOST giants sample. Three stellar parameters (T_eff, log g, [Fe/H]) are compared between our estimates and those provided by the PASTEL catalog in Figure 7.

From upper panel of Figure 7, T_eff has −12.20 K bias and 100.36 K scatter. From middle panel of Figure 7, a slight trend is found in log g comparison. Some discrete points exists where residual is greater than 0.3 dex or less than −0.3 dex. To detect the origin of the trend, common stars between APOGEE DR14 and the PASTEL catalog were selected, and we found a similar distribution using 516 common stars. Thus we considered the trend caused by propagation of the APOGEE values. To further test log g we had predicted, we used log g determined by astroseismology to test our results because of the high precision of the asteroseismic measurements. Huber et al. (2014) have collected stellar parameters for 196,468 stars in the Kepler field from literatures published in recent years. Most parameters of Huber et al. (2014) are more precise than those provided by the Kepler Input Catalog (KIC; Brown et al. 2011), but T_eff and [Fe/H] are still inaccurate. We found 8960 giant stars which had asteroseismic surface gravity. The comparison shows there is no obvious trend between our values and asteroseismic surface gravities. There are 8851 stars (98.7%) in the range of residual less than 0.3 dex. The small 0.03 dex bias and 0.10 dex scatter indicate log g we measured is consistent with that of Huber. From lower panel, [Fe/H] has −0.06 bias and 0.12 scatter with no trend. It is noted that three outliers are located at [Fe/H] < −2.5 dex. There are little training samples in the range of [Fe/H] < −2.5 dex so that metallicities of stars are calculated to be richer. Therefore, we think metallicity is reliable in the range of −2.5 dex < [Fe/H] < 0.5 dex.

4.3. Comparison with [α/M] from The Cannon

Ho et al. (2017a) estimated [α/M] for 450,000 giants from LAMOST DR2 (Wu et al. 2011) with The Cannon which is a data-driven method by training LAMOST DR2-APOGEE DR12 common stars. So we compared [α/M] determined by APOGEE, StarNet, and The Cannon. There are 15,380 stars which have [α/M] determined by these three methods. From upper panel of Figure 8, histograms of [α/M] for these stars are compared and the histograms have similar distributions with two peaks, which indicates values from StarNet and The Cannon are reliable. Both StarNet and The Cannon are trained using APOGEE labels, so estimates from StarNet and from The Cannon are compared with APOGEE values in the lower panel of Figure 8. Estimates from StarNet and from The Cannon are correlated with APOGEE values while different scatters can be found. [α/M] estimated by StarNet have smaller bias and scatter (bias_StarNet = 0.015, scatter_StarNet = 0.039) relative to APOGEE measurements than those estimated by The Cannon (bias_Cannon = 0.031, scatter_Cannon = 0.052). Therefore, we consider [α/M] from StarNet is acceptable and accurate.

**Figure 8.** Comparison of [α/M] measured by APOGEE, StarNet, and *The Cannon* for 15,380 stars. Upper panel: histograms of [α/M] from different measurements. Black line show measurements from APOGEE, red line show measurements from StarNet, and green line show measurements from *The Cannon*. Lower panel: StarNet and *The Cannon* measurements against APOGEE measurements. Red points represent comparison between StarNet and APOGEE, and green points show comparison between *The Cannon* and APOGEE. Bias and Scatter were calculated and shown in the panel.
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4.4. [α/M] Map of the Milky Way from LAMOST and APOGEE

Here, we give the initial astrophysical exploitation of the new parameters, by showing distribution of 938,720 LAMOST giants with measured [α/M] in the galactic longitude and latitude, as well as 224,257 giant stars from APOGEE DR14 with [α/M] measurements.

As Figure 9 shows, The extensive coverage of LAMOST is obvious. The combination of LAMOST survey and APOGEE survey will overcome the limitation of previous studies of the Galactic disk: most large surveys have either extensive coverage at high Galactic latitudes and sparse sampling in the Galactic plane or vice versa (Ho et al. 2017a). One can clearly see that the low-α stars are concentrated on the mid-plane and α-enhanced stars are found in the high latitudes (thick disk and halo) as well as in the Galactic bulge (Longitude = 0°, Latitude = 0°). The [α/M] distribution is the same as Figure 14 in Ho et al. (2017a). The combination of LAMOST survey and APOGEE survey through label transfer will draw a more complete stellar picture of the Galaxy.

5. Discussion

5.1. Error Analysis

From the test result in Figure 4, we can estimate error for each parameter. In this part, we discuss the causes of error. Fabbro et al. (2018) trained and tested StarNet on the ASPCAP stellar parameters and corresponding spectra with S/N > 200 from APOGEE DR13. The scatter from their test is 35.95 K for T_eff, 0.075 dex for log g, 0.025 dex for [Fe/H], which is mainly caused by the technique and S/N of the APOGEE spectra. From our test, scatter is 45.53 K for T_eff, 0.10 dex for log g, 0.05 dex for [M/H]. Our scatters are larger than those from Fabbro et al. (2018). There are many differences between LAMOST spectra and APOGEE spectra, such as different resolution, different S/N, different wavelength region, different rectification, and continuum normalization scheme. So the LAMOST spectra trained on different stellar features. Therefore, we think the increased scatter (∼10 K for T_eff, 0.025 for log g, 0.025 for [M/H]) for each parameter is caused by these reasons. The spectral features that contribute to the StarNet will be explored in the future using Jacobian for the different stellar labels. The uncertainties propagating the error spectrum are also estimated from the covariance matrix. It will be attached to the value-added catalog as formal uncertainties. At present, StarNet can not take errors of APOGEE labels into account during training. From our measurement, We found scatter is uncorrelated with errors of APOGEE labels.

Ho et al. (2017a) and Xiang et al. (2014) have proved the effectiveness of data-driven method in transferring labels between two different surveys. Here, we compare our estimations with parameters from LAMOST pipeline to validate the effectiveness of deep learning in label transformation. In Figure 10, the left three panels show the comparison of stellar parameters (T_eff, log g, [Fe/H]) provided by LAMOST and APOGEE of common stars in the reference set. With a limitation of S/N_g > 10, 14,845 stars are left for comparison. Obvious bias and scatter can be seen from the panels, especially for log g and [Fe/H], which indicates systematic offsets between two surveys. Right three panels show the comparison of parameters provided by StarNet and APOGEE for the same reference set. The scatter is kept at 47.19 K for T_eff, 0.11 dex for log g and 0.05 dex for [Fe/H], with little bias. Compared with left panels, bias and scatter are reduced. It is proved that our method is useful to eliminate differences between two surveys. The precision of three stellar parameters is improved compared with original LAMOST parameters. The promotion in log g further prove our method is effective in extracting parameters those occupying a small proportion in spectrum.

**Figure 10.** Left panels: systematic offsets in T_eff, log g, [Fe/H] derived by LAMOST and APOGEE. There are obvious biases and scatter in these parameters. Detailed bias and scatter are marked in the corresponding panel. Right panels: offsets in T_eff, log g, [Fe/H] which were derived by StarNet and APOGEE. Biases and scatter have been eliminated effectively.
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5.2. Considerations of Deep Learning

The combination of convolutional layers and fully connected layers in deep learning strengthens the ability of deep learning to predict for spectra with a wide range of spectral S/N. A limitation of deep learning is the demand for large training samples. The distributions of stars with different S/N_g in the reference set and the test set are shown in Figure 11. LAMOST spectra with S/N_g > 0, S/N_g > 10, S/N_g > 30, and S/N_g > 50 were used to train the StarNet, respectively. When we use LAMOST spectra with S/N_g > 10 for training, the test yields better result than other selections. So a cut of S/N_g > 10 not only ensures enough spectra used for training but also the accuracy of predictions.

**Figure 11.** Distributions of stars with different S/Ng in the reference set and the test set. The reference set is shown in blue and the test set is shown in yellow. Similar distributions can be found.
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From Figure 2, there is a small number of stars at high temperatures, low gravities, low metallicity and low elemental abundances. Fewer training sample in these regions of parameter space results in low accuracy of estimation for stars in these regions, as shown in Figure 3. Ho et al. (2017a) has proved the sparse coverage in parameter space has limited influence on training. From Figure 3, i.e., the test result, scatters which reflect the departures from the APOGEE values provide uncertainty estimates. The scatters are small enough from the test result so that this can be neglected. But one still needs to be cautious when using stars at the edges of parameter space. From the test result, we can estimate the range over which stellar parameters should be trusted. The range for T_eff is 4000 K < T_eff < 5300 K, for log g is 0.5 < log g < 3.7, for [M/H] is −2.5 < [M/H] < 0.5, for [α/H] is −1.5 < [α/H] < 0.7, for −2.5 < [C/H] < 0.7, for [N/H] is −2.5 < [N/H] < 1.2. The training set includes few stars with [M/H] < −1.0 dex, so stellar parameters are more reliable for stars with [M/H] >−1.0 dex than those with [M/H] < −1.0 dex. Furthermore, we lack dwarf star samples for training. So we only apply the method to giant stars from LAMOST and do not expend it to dwarf stars.

LAMOST provides us an unprecedentedly large number of spectra with low resolution. With a deep learning method, we can estimate accurate parameters close to high-resolution observations from low-resolution spectra. With this large data set of accurate stellar parameters, we can further explore the Galaxy evolution.

6. Conclusion

In this work, a deep learning method named StarNet is explored to estimate stellar atmospheric parameters and α, C, N elemental abundances from LAMOST spectra through training LAMOST spectra and APOGEE labels. With LAMOST spectral S/N_g larger than 10, the test shows scatter is 45 K for T_eff, 0.1 dex for log g, 0.05 dex for [M/H], 0.03 dex for [α/M], 0.06 dex for [C/M] and 0.07 dex for [N/M], which indicates deep learning presents an outstanding performance on LAMOST spectra. It is proved that the practicability of deep learning in transferring labels from a low-resolution survey to high-precision parameters.

Stellar parameters (T_eff, log g, [M/H]) and α, C, N abundances of 938,720 giants from LAMOST DR5 are predicted, and comparison with PASTEL catalog yields uncertainties of 100 K for T_eff, 0.12 dex for [M/H] and comparison with asteroseismic surface gravity yields uncertainties of 0.10 dex for log g. [α/M] determined by deep learning is similar to APOGEE values with a precision of 0.04 dex as well as previous data-driven method. A more complete stellar [α/M] map of the Milky Way through combining LAMOST survey with APOGEE survey is plotted. It is found that low-α stars are concentrated on the mid-plane and α-enhanced stars are found in the thick disk and halo as well as in the Galactic bulge.

LAMOST have collected millions of low-resolution spectra so far. Furthermore, Gaia will provide a billion low-resolution spectra. Depending on the deep learning technique, we can achieve accurate parameters close to high-resolution measurements for these stars through combining low-resolution spectra with high-resolution labels. Using the large samples with accurate stellar parameters and abundances, we can carried out more detailed researches about Galactic evolution in the future.

We thank the referee for the helpful comments which significantly improved the paper. We also thank XiangXiang Xue, Chao Liu, JingKun Zhao, and HuiGang Wei for their helpful discussion. This study is supported by the National Natural Science Foundation of China under grant No. 11890694. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.

938,720 Giants from LAMOST I: Determination of Stellar Parameters and α, C, N Abundances with Deep Learning

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Abstract

1. Introduction