A Model RRNet for Spectral Information Exploitation and LAMOST Medium-resolution Spectrum Parameter Estimation

LAMOST provides a large number of precious spectra for researchers. LAMOST began its Phase II medium-resolution survey in July 2017 and released 5.6 million medium-resolution spectra in LAMOST DR7, with a total of 2.4 million spectra with a signal-to-noise ratio (S/N) greater than 10 (Rui et al., 2019). During the survey, two spectra are obtained for each exposure, one is the blue part and the other is the red part, and their wavelength coverages are [4950, 5350] \textÅ and [6300, 6800] \textÅ respectively.

Ting et al. (2019) analyzed the spectra from APOGEE DR14 based on the Kurucz theoretical model, obtained a high-precision APOGEE-Payne catalog. The catalog gives stellar parameters for 222,702 stars, including $T_{\rm eff}$, $\log\,g$, and 15 elemental abundances. The coverages of the stellar atmospheric parameters in the APOGEE-Payne catalog are $\rm[3050,7950]$ K on $T_{\rm eff}$, $\rm[0,5]$ dex on $\log\,g$, and $\rm[-1.45,0.45]$ dex on $\rm[Fe/H]$. The accuracies of the three parameters are 30 K, 0.05 dex and 0.05 dex respectively.

Following Wang et al. (2020), we cross-matched the LAMOST DR7 medium-resolution spectra with the APOGEE-Payne catalog, obtained 161,447 LAMOST DR7 spectra from 34,372 common stars. To ensure the reliability of the dataset, the LAMOST spectra with $\rm S/N<10$ are eliminated from the cross-matched data set. In addition, some LAMOST spectra are affected by cosmic rays and other influences, which result in a large number of outliers (bad pixels) in them. Therefore, the spectra with more than 100 outliers or more than 30 consecutive outliers are rejected in this work. In the APOGEE-Payne catalog, we kept the information from the spectra with $\rm quality\_flag=good$ and $T_{\rm eff}\in\rm[4000,6500]$ K. Through the above processing, we finally obtained 28,523 common stars and 114,853 medium-resolution spectra of the common stars from LAMOST DR7. These spectra are used as the reference data for our model.

To facilitate the optimization of the model, we pre-process the LAMOST spectra as follows:

Wavelength correction: The Radial Velocity (RV) can broaden or narrow down the spectral lines in the observed spectrum. To account for this kind of broadening and narrowing down effects, a much large reference set should be used in training a machine learning parameter estimation scheme for a similar accuracy. To simplify the spectral parameter estimation problem based on the available reference set, we perform wavelength correction on each spectrum by shifting it to its rest frame using the RV provided by the LAMOST catalog:

where $\lambda^{\prime}$ is the corrected spectral wavelength in the rest frame, $\lambda$ is the observed spectral wavelength, RV is the radial velocity of the corresponding spectrum, and $c$ is the speed of light. (For more discussion see appendix C.)

Spectral resampling: According to the distribution of the spectral wavelength ranges from the reference set, the common part of the corrected spectral wavelength ranges are computed. The common wavelength ranges on blue part and red part are respectively [4968, 5328] \textÅ, and [6339, 6699] \textÅ. On the common wavelength range, each spectrum is resampled using a linear interpolation procedure with a step 0.1 \textÅ. Finally, 7200 fluxes (3600 in the blue part and 3600 in the red part) are obtained for each observed spectrum.

Spectral normalization: Consistent with Wang et al. (2020), each resampled spectrum is divided by its pseudo-continuum, which is computed using a 5-order polynomial fit. The normalized spectra are used as input values into the RRNet model.

Earlier works Bailer-Jones et al. (1997) and Manteiga et al. (2010) applied neural networks to atmospheric parameter estimation on synthetic stellar spectra. However, the effects of both works are limited by the data and hardware resources at that era. Fabbro et al. (2017) proposed a convolutional neural network (StarNet), consisting of two convolutional layers and three fully-connected layers. The StarNet is trained by ASSET (Koesterke et al., 2008) synthetic spectra and APOGEE observed spectra, and then used in estimating stellar parameters from APOGEE observed spectra. Subsequently, Bialek et al. (2020) improved StarNet using deep ensembling to give StarNet the ability to predict parameter uncertainty. Wang et al. (2020) developed a residual-like network (SPCANet) consisting of three convolutional layers and three fully-connected layers, and applied it to LAMOST DR7 medium-resolution spectra for stellar parameter and chemical abundance estimation.

The above-mentioned models only employ a few layers of convolutional computations and fully-connected computations to approximate the mapping from spectra to stellar parameters. Unfortunately, there is much space to increase the quality of the extracted features based on the experiments in section 3.4. To this end, we develop a Residual Recurrent Neural Network (RRNet) specifically for extracting spectral features and used it for estimating stellar parameters from the medium-resolution spectra in LAMOST. The RRNet mainly consists of three kinds of modules: residual module, recurrent module and uncertainty prediction module. The structure of RRNet is shown in Figure 1.

Residual module: The residual module is to explore the correlation between the spectral features and the reference labels (the parameters to be estimated). Based on this correlation, not only the features sensitive to the parameters are enhanced, but also the negative effects from noises or irrelevant components are restrained. The residual module contains $N_{r}$ residual blocks (He et al., 2016) with the same structure. A typical configuration in residual module is the use of batch normalization (BN) to accelerate the training procedure by reducing internal covariate shift (He et al., 2016; Ioffe & Szegedy, 2015). However, our experiments on stellar parameter estimation show much more fluctuations in the training procedure on the implementation with BN than that without BN. As a result, the training time is increased approximately 127%, and there is some reduction on the accuracy of the spectral parameters from the learned model. These phenomena possibly come from the existences of a certain number of bad pixels in many of the LAMOST spectra. The fluxes of the bad pixels are usually enormously deviated from the normal pixels and have evident negative influences on the estimations of mean and variance in BN (Ioffe & Szegedy, 2015). Therefore, this work removed the BN from the traditional residual blocks. In addition, our stellar parameter estimation experiments show better performance on the implementation with an Average-pooling layer than that with a Max-pooling layer. Therefore, the proposed residual module used an average-pooling layer in each residual block.

Recurrent module: The recurrent module is to extract the features of various subbands from the spectrum and analyze the correlation between them. This correlation enables maximum information recovery and noise suppression. Since neither convolutional networks nor fully-connected networks can achieve this kind of information extraction across subbands. For this reason, the spectral vectors are reshaped into sequence data $S=\{S_{1},S_{2},\cdots,S_{N_{s}-1},S_{N_{s}}\}$ of length $N_{s}$, and then $S$ is processed cross wavelength by a recurrent layer to obtain $S^{\prime}$. Through this processing, RRNet can achieve information recovery and noise suppression from the spectral features on different wavelength.

Uncertainty prediction module: Following Bialek et al. (2020), we used three fully-connected layers to predict the Probability Density Function (PDF) of stellar parameters and chemical abundances. The PDF is approximated using a Gaussian distribution. Therefore, RRNet just needs to output the estimation of the mean $\mu$ and variance $\sigma^{2}$. In addition, we added Dropout layers (Hinton et al., 2012) into the Uncertainty prediction module to avoid overfitting in the model training process. The Dropout deals with overfitting by reducing co-adaptations between neurons (especially in the same layer) and restraining the relying of a neuron on the presence of particular other neurons. It should be noted that to ensure the stability of the model output, Dropout is only enabled in the training phase and is disabled in the inference phase.

The reference set is randomly divided into a training set, a validation set and a test set at the ratio of 7:1:2. The three data sets respectively consist of 80,812 spectra from 19,996 stars, 11,473 spectra from 2,852 stars, and 23,198 spectra from 5,705 stars. The training set is used for the training of the RRNet model (see section 3.2), the validation set is used for the selection of the model hyperparameters (see section 3.3), and the test set is used for the evaluation of the model (see section 3.4). In LAMOST observations, some spectra are from the same sources. If the spectra from the same source simultaneously appear in the training set, validation set and test set, there is the possibility of reducing the objectivity of the model evaluation. Therefore, this work divides the reference set based on the sources instead of the spectra.

In order to enable the RRNet model to predict the PDF of physical parameters, consistent with Bialek et al. (2020), we use the negative log-likelihood of the normal distribution as the loss function of the model, as follows:

where $\mathbf{x},y$ are the input spectra and the corresponding reference labels, $\mu_{\theta}(\mathbf{x}),\sigma^{2}_{\theta}(\mathbf{x})$ are the mean and variance of the Gaussian distribution predicted by the model, and $\theta$ is the parameter of the RRNet model to be optimized. To learn the model parameter $\theta$, the Adam (Kingma & Ba, 2014) is used as the optimizer to speed up the convergence of the learning procedures. And during the training process, a data augmentation by disturbing a reference spectrum with Gaussian noise can improve the robustness of the model.

Finally, in order to accurately estimate the PDF of the physical parameters, $M$ instances of the RRNet are trained with different random initializations ($M=6$ in this paper). The mean of ensembling $\hat{\mu}(\mathbf{x})$ is obtained by averaging the predicted mean of $M$ RRNet instance models. The variance of ensembling $\hat{\sigma}^{2}(\mathbf{x})$ is determined by the following equation:

In the application of machine learning, the choice of model hyperparameters have strong influences on model performance. The depth of the RRNet is determined by the number of residual blocks. After the residual blocks, the information of a spectrum is represented using a vector $v$ and further processed by the recurrent module in RRNet (Fig. 1). In the recurrent module, the $v$ is divided into a series of wavelength sub-bands (Fig. 1). The numbers of residual blocks and the wavelength sub-bands are represented by $N_{r}$ and $N_{s}$ respectively. They are the hyperparameters of RRNet. To explore the effects of the hyperparameters $N_{r}$ and $N_{s}$ on model performance, we compared the RRNet with its variants. Various variants of the RRNet are designed using different configurations of $N_{r}$ and $N_{s}$. In these experiments, the performance measures are computed on the validation set for determining the model hyperparameters $N_{r}$ and $N_{s}$. This work used the Mean Absolute Error (MAE) to evaluate the performance of a stellar atmospheric parameter estimation model as follows:

where $\hat{y_{i}}$ and $y_{i}$ denote the predicted value by RRNet and the corresponding reference value from a spectrum $\mathbf{x}_{i}$ respectively, and $n$ denotes the number of samples. The experimental results are presented in Table 1.

It is shown that the model performance is improved with the increases of $N_{r}$ and $N_{s}$. However, after these hyperparameters reach certain thresholds, the performance improvement will be trivial or even degrade. The above-mentioned phenomena indicate that more residual blocks and more wavelength sub-bands in an RRNet model help to improve the spectral information extraction capability and increase the parameter estimation performance to a certain degree. More residual blocks result in an RRNet with more complexity and more model parameters to be optimized. This kind of models need a training data set with more reference spectra. However, the scale of the training set is difficult to be expanded without any limitations in a real application. Therefore, the performance of the RRNet firstly is improved gradually with the increase of $N_{r}$, and then decreases in case that the complexity of the RRNet exceeds that supporting from the available training data. Therefore, the performance of the RRNet can be improved further by adding more residual blocks if a training set with a larger scale can be obtained.

Another characteristic of the RRNet is that the model can exploit spectral features and restrain the negative influences from noise based on CBE between the observations on different wavelengths (Fig. 1). Two non-directly adjacent sub-bands can indirectly communicate with each other through a series of directly adjacent sub-bands between them, and conduct belief enhancement. In the recurrent module, a series of sub-bands can be numbered and indexed by integers from 1 to $N_{s}$ from left to right, and the distance between each two sub-bands can be measured by the difference between their indexes (Fig. 1). The further the distance between two non-direct adjacent sub-bands, the weaker the communication and information fusion ability between them. In the case of the number of sub-bands changing from 1, to 2, to 3, similarly to more, the amount of sub-band pairs with a directly adjacent relationship or small distance from each other increases gradually. Therefore, the CBE ability and prediction effect of RRNet are improved gradually in this procedure. At the same time, with the increase of $N_{s}$, more and more long-distance sub-band pairs appear. This kind of sub-band pairs results in poor communication between them and unsatisfactory belief enhancement. Therefore, the performance of the RRNet increases firstly and then decreases in the case of $N_{s}$ gradually increasing. Ultimately, this work utilized the configuration $N_{r}=3$ and $N_{s}=40$ based on the experimental investigations.

After determining the optimal hyperparameters of the model, we demonstrate the performance of RRNet on the test set and compare it with other models. Figure 3 shows the distribution of the inconsistencies, and the dependence of the $1\sigma$ uncertainty predicted by RRNet on S/N and inconsistencies. The inconsistency refers to the difference between the RRNet predictions and the APOGEE-Payne catalog on the test set. On the whole, the RRNet predictions have high accuracy and precision. The precision of the stellar parameters ($T_{\rm eff}$ and $\log\,g$) are 88 K and 0.13 dex respectively, elements C, Mg, Al, Si, Ca, Fe, Ni are 0.05 dex to 0.08 dex, and N, O, S, K, Ti, Cr, Mn are 0.09dex to 0.14 dex, while that of Cu is 0.19 dex. In addition, although the quality of a spectrum helps improve the parameter estimation performance (small bias and standard deviation) on the whole, the standard deviation of the RRNet prediction varies in a small range. Therefore, the RRNet are robust against noises and disturbances. The robustness benefits from the CBE of the recurrent module, which enables the RRNet model to fuse the feature information from different wavelength sub-bands and restrain the negative influences from noise and disturbances based on the correlation between different sub-bands.

To further demonstrate the performance of RRNet, we compared RRNet with models such as StarNet. Fabbro et al. (2017) mentions that StarNet can be tried to apply to other spectral studies. Therefore, this work investigated its application on LAMOST DR7 by training the StarNet using the training set same with RRNet, and compared its results with our model. In addition, to verify the effectiveness of the combination of residual module and recurrent module, we constructed a model StarNet-R by adding the recurrent module same with RRNet into the StarNet, and compared the RRNet with ResNet and StarNet-R. Figure 3 shows the MAE (equation 4) of parameter prediction for RRNet, ResNet, StarNet and StarNet-R on the test set.

It is shown that RRNet has significant advantages over the other three models (Figure 3). The performance of ResNet is lower than that of RRNet because ResNet only extracts flux features longitudinally from the spectrum based on the correlation between the fluxes and the parameter to be estimated, and lacks the capability of CBE. The StarNet consists of several convolutional layers and fully-connected layers. It is shown that this method does not work as well as RRNet on LAMOST spectra. After adding a recurrent module, a variant of StarNet is obtained and referred to as StarNet-R. Therefore, the StarNet-R has the capability of CBE and shows a performance superior to the original StarNet (Figure 3). In RRNet, there are both the residual module and recurrent module. Therefore, the RRNet has better performance on 1) feature extraction for the residual module than StarNet and StarNet-R; 2) information recovery and noise & disturbances abatement for CBE from recurrent module than StarNet and ResNet. Therefore, it is shown that the RRNet is more accurate and stable compared with other models.

To visualize why the RRNet modules are effective, Figure 4 shows the average partial derivatives of the stellar parameters by the StarNet, StarNet-R, and RRNet. The upper and lower panels of the figure represent the spectral average partial derivatives from 1000 randomly selected cool stars ($T_{\rm eff}\in\rm[4000,4300]$ K) and 1000 hot stars ($T_{\rm eff}\in\rm[6000,6300]$ K) in the test set, respectively. The results show that, on the whole, three models are consistent with each other very well on their average partial derivatives.

The comparisons on (RRNet, StarNet, StarNet-R) and their visualizations are further summarized. 1) Both StarNet-R and RRNet have a recurrent module which enhances some hidden sub-band features compared to StarNet without the recurrent module (See Figure 4 for the sub-bands shaded in red). These phenomena indicate that the recurrent module does help recover the spectral features through CBE and thus improve the performance of the model. 2) Both StarNet-R and RRNet have recurrent modules, the difference is that StarNet-R uses a traditional convolutional neural network to extract spectral features while RRNet uses the superposition of multiple residual blocks to extract features. The results show that the residual module reinforces more dense features than the traditional convolutional neural network (See Figure 4 for the sub-bands with borders shaded in green). These phenomena indicate that the residual module does provide stronger feature extraction performance than the traditional convolutional neural network.

After training and testing the RRNet model (sections 3.2 and 3.4), the stellar parameters and elemental abundances are derived for medium-resolution spectra from LAMOST DR7 by RRNet. Based on the distribution range of the stellar parameters in the reference set, we kept only the LAMOST DR7 spectra with LASP (Luo et al., 2015; Wu et al., 2011) estimation $T_{\rm eff}\in\rm[3500,7000]$ K, and processed these spectra using the pre-processing procedures in section 2.2. Ultimately, the LAMOST-RRNet catalog is obtained by RRNet. This catalog contains stellar atmospheric parameters, chemical abundances, and corresponding $1\sigma$ uncertainties for 2,377,510 medium-resolution spectra in LAMOST DR7 estimated by RRNet.

The $T_{\rm eff}-\log\,g$ distributions for the spectra with S/N in multiple intervals are shown in Fig. 5, and three MIST stellar isochrones (Dotter, 2016; Choi et al., 2016) with stellar ages of 7 Gyr are added to the figure for reference. The stellar parameters estimated by RRNet are consistent with the three MIST stellar isochrones, and the distribution of $T_{\rm eff}-\log\,g$ becomes “cleaner” as $\rm S/N$ increases. The density distributions of [X/Fe] relative to [Fe/H] for giant and dwarf stars are shown in Figure 6. In general, the elemental abundances estimated by RRNet are more dense, especially for Si, S, Ca, and Ni. In addition, the $\alpha$ elements (O, Mg, Si, S, Ca, Ti) show a more obvious bimodal structure on the giant star samples.

To verify the accuracy and precision of LAMOST-RRNet catalog, we investigated the consistency of LAMOST-RRNet catalog with the SPCANet catalog, the APOGEE-ASPCAP DR16 catalog, and the GALAH DR3 catalog on the spectra from the common stars between them.

Wang et al. (2020) proposed a residual-like neural network model (SPCANet) to estimate stellar parameters and elemental abundances for 1,472,211 medium-resolution spectra from LAMOST DR7. Both SPCANet catalog (Wang et al., 2020) and LAMOST-RRNet catalog are computed from parameter estimation models learned from the the spectra of the common stars between APOGEE-Payne catalog and LAMOST observations. Therefore, the comparability between these two catalogs are very well. The comparing tests are performed on the LAMOST observations from 24,347 common stars. It should be noted that there are three kinds of estimations from the spectra of these common stars: the estimation of the SPCANet model, the estimation of the RRNet model, and the reference values of the APOGEE-Payne catalog.

APOGEE (Majewski et al., 2017) is a medium-high resolution (R $\thicksim$ 22500) spectroscopic survey, which uses the Sloan telescope at Apache Point Observatory in New Mexico City, USA, to achieve observations of stellar spectra. The APOGEE spectral band covers the near-infrared 1.51-1.70 µm, and the stellar parameters and elemental abundances for most of their stellar spectra are mainly calculated by the ASPCAP (Pérez et al., 2016). We cross-matched LAMOST-RRNet with the APOGEE-ASPCAP DR16 catalog, and excluded stars with STARFLAG, ASPCAPFLAG, and PARAMFLAG flags. Finally, 127,574 LAMOST DR7 spectra from 31,356 common stars are obtained.

GALAH (De Silva et al., 2015) is a large-scale high-resolution (R $\thicksim$ 28000) spectroscopic survey, which uses the Anglo-Australian Telescope and the HERMES spectrograph at the Australian Observatory to observe stellar spectra. The GALAH spectral coverage are [4713, 4903] \textÅ, [5648, 5873] \textÅ, [6478, 6737] \textÅ and [7585, 7887] \textÅ. GALAH DR3 (Buder et al., 2021) presented stellar parameters and elemental abundances for a total of 588,571 stars, including 383,088 dwarfs, 200,927 giants, and 4,556 unclassified stars. We cross-matched LAMOST-RRNet with the Galah DR3 catalog, and removed the observations with $\rm flag\_sp\neq 0$ and $\rm snr\_c3\_iraf\leq 30$ as suggested by Buder et al. (2021). Finally, 74,090 LAMOST DR7 spectra from 16,582 common stars are obtained.

Compared with the SPCANet catalog (see Table 2 (SPCANet-Payne, RRNet-Payne)), LAMOST-RRNet adds the estimations for [K/H] and [Mn/H], and reduces the overall MAE by 14% on their common parameters. In addition, LAMOST-RRNet has smaller bias and standard deviation compared to the SPCANet catalog. Therefore, RRNet has better estimation performance. For elements Ti and Cu, the precision improvement of the RRNet model are not significant, which may be caused by the lack of stronger metal lines in the blue part from the LAMOST spectra. In addition, the SPCANet input spectrum has 8000 data points (fluxes), while the RRNet input spectrum has only 7200 data points (fluxes). The less inputs result in less feature space that can be extracted by RRNet than SPCANet. Compared to the GALAH and APOGEE-ASPCAP catalogs (see Table 2 (RRNet-GALAH, RRNet-ASPCAP)), LAMOST-RRNet shows good consistencies with APOGEE-ASPCAP and GALAH with smaller bias. Similar with the findings by Wang et al. (2020), for $T_{\rm eff}$, [C/H], [K/H], [Mn/H] and [Cu/H], the LAMOST-RRNet have different levels of underestimation compared to APOGEE-ASPCAP and GALAH. The same phenomenon is shown between APOGEE-Payne and APOGEE-ASPCAP (see Table 2 Payne-ASPCAP). This indicates that the inconsistency between RRNet and APOGEE-ASPCAP, in addition to the inconsistency in RRNet model estimation, may partly originate from the APOGEE-Payne label.

The RRNet is able to predict the PDF of parameters more accurately through deep ensembling. The uncertainty of the predicted parameters $\sigma_{pred}$ is obtained by the PDF of the parameter estimations. In addition, in the LAMOST sky survey, some stars are observed for multiple times at various time and under different observation conditions. Therefore, we can use this phenomenon to analyze the uncertainty caused by observation errors, this uncertainty is denoted by $\sigma_{obs}$. Suppose we have $n_{s}$ repeated observations $\{\mathbf{x}_{1},\cdots,\mathbf{x}_{n_{s}}\}$ from a source. From these observations, the RRNet gives $n_{s}$ estimations $\{y_{1},\cdots,y_{n_{s}}\}$ for any stellar parameter $X$. The standard deviation of $\{y_{1},\cdots,y_{n_{s}}\}$ is the corresponding uncertainty $\sigma_{obs}$.

Figure 7 shows the dependencies of the uncertainty of LAMOST-RRNet catalog on S/N. The dots indicate uncertainty $\sigma_{pred}$ predicted by RRNet and the length of the line segment centered on the dots indicates the uncertainty $\sigma_{obs}$. The lower uncertainty indicates the strong robustness and generalization ability of the RRNet model. When S/N $\geq 20$, the $\sigma_{pred}$ of the parameters $T_{\rm eff}$, $\log\,g$, [Fe/H], [Cu/H] are 146 K, 0.18 dex, 0.07 dex and 0.22 dex, respectively, and those of the remaining elements are 0.06 dex $\thicksim$ 0.17 dex. In addition, both $\sigma_{pred}$ and $\sigma_{obs}$ decrease with the increase of S/N. This phenomenon indicates that the $\sigma_{pred}$ and $\sigma_{obs}$ are rational indicators of uncertainty. At the same time, the changes of $\sigma_{pred}$ trend curve is mild. Therefore, the RRNet model is stable for estimating parameters from LAMOST spectra.

To further examine the accuracy of element abundance from LAMOST-RRNet, we performed more tests on open clusters. Since the stars in open clusters are produced almost simultaneously from gas clouds, open clusters are a stellar population of chemically homogeneous (Bovy, 2016; Ness et al., 2018). Therefore, we performed some tests using 8,811 cluster member stars published by Zhong et al. (2020). We selected the three open clusters (Melotte 22, NGC 2682, and NGC 2632) with the largest number of matches to LAMOST-RRNet and removed parameter estimations with large uncertainties $\sigma_{pred}$ (section 4.3).

Figure 7 shows the dependencies of the elemental abundances (from LAMOST-RRNet) on $T_{\rm eff}$ in the above-mentioned clusters. In agreement with Ting et al. (2019), the LAMOST-RRNet do not show any evident [X/H]-$T_{\rm eff}$ trend in all three aforementioned clusters, and the chemical abundances exhibit a low standard deviation. In addition, Figure 9 shows the comparison of the chemical abundances of LAMOST-RRNet and SPCANet catalogs in the above-mentioned clusters. Overall, the standard deviation of chemical abundances from LAMOST-RRNet is slightly lower than that of the SPCANet catalog. The overall chemical homogeneity from LAMOST-RRNet on the three clusters are $0.055\pm 0.017$ dex, $0.064\pm 0.022$ dex and $0.047\pm 0.016$ dex, respectively. These phenomena indicate that RRNet has higher accuracy compared to SPCANet.

Finally, the LAMOST-RRNet catalog of stellar atmospheric parameters and elemental abundances for 2,377,510 medium-resolution spectra from LAMOST DR7 is made publicly available online. This catalog contains the following information: the identifier for the observation spectrum (obsid), the fits file name corresponding to the observation spectrum (filename), coordinate information (ra, dec), the extension name of the spectrum (extname_blue, extname_red), the S/N of the spectrum (snr_blue, snr_red), effective temperature (Teff[K]), surface gravity (Logg), 15 elemental abundances (XH), $1\sigma$ uncertainty of parameters (X_err) and recommended flags (flag). The detailed catalog description information is shown in Table 3, and the complete parameter catalog can be downloaded from https://github.com/Chan-0312/RRNet/releases.