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arxiv: 2604.02730 · v1 · submitted 2026-04-03 · 🌌 astro-ph.GA · astro-ph.SR

Recognition: no theorem link

PhDLspec: physical-prior embedded deep learning method for spectroscopic determination of stellar labels in high-dimensional parameter space

Tianmin Wu , Maosheng Xiang , Jianrong Shi , Meng Zhang , Lanya Mou , Hong-Liang Yan , A-Li Luo
Authors on Pith no claims yet

Pith reviewed 2026-05-13 18:32 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.SR
keywords stellar spectradeep learningtransformerstellar labelselemental abundancesLAMOSTphysical priorshigh-dimensional modeling
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The pith

PhDLspec embeds differential spectra from ab initio models in a transformer to model stellar spectra with over 30 parameters at high speed.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces PhDLspec as a deep learning framework that incorporates physical priors from stellar atmospheric models into a transformer to analyze low-resolution stellar spectra. It shows that this embedding allows simultaneous and precise modeling of more than 30 physical parameters while operating hundreds of times faster than direct ab initio calculations. The method supports derivation of roughly 30 stellar labels, including elemental abundances, from spectra such as those in the LAMOST survey through affordable optimization. After calibration against wide binaries and high-resolution reference data, the abundance estimates align with results from high-resolution spectroscopic surveys. A catalog covering 25 elemental abundances for over 116,000 subgiant stars with age estimates is produced as a demonstration.

Core claim

PhDLspec imposes differential spectra derived from ab initio stellar atmospheric model calculations on a transformer framework to rigorously and precisely model stellar spectra by simultaneously taking into account more than 30 physical parameters at a computational speed hundreds of times faster than ab initio model calculation, allowing effective derivation of ~30 stellar labels from low-resolution spectra.

What carries the argument

Imposition of differential spectra from ab initio stellar atmospheric models onto a transformer framework, enabling high-dimensional parameter estimation from blended spectral features.

Load-bearing premise

Differential spectra from ab initio stellar atmospheric models can be imposed on the transformer without introducing uncalibrated systematic biases in the high-dimensional parameter estimates.

What would settle it

A large-sample comparison with independent high-resolution spectroscopic measurements that reveals substantial residual systematic offsets in elemental abundances after the described calibrations would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2604.02730 by A-Li Luo, Hong-Liang Yan, Jianrong Shi, Lanya Mou, Maosheng Xiang, Meng Zhang, Tianmin Wu.

Figure 1
Figure 1. Figure 1: Schematic diagram of the PhDLspec method. The transformer-based spectral model employs an embedding layer that combines wavelength encoding and parameter embedding, followed by multiple encoder blocks with multi-head attention, layer normalization, and feed-forward layers. The output spectra are generated through a fully connected output layer. The model training is regularized with physical gradient spect… view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of the Kurucz spectra training set in the Teff -log g diagram, color-coded by their [Fe/H]. model using the Pytorch framework on an NVIDIA GeForce RTX 4090 machine. To fit the memory, we di￾vided the full spectrum into 11 segments, and trained the model segment by segment. Each segment was trained for 3000 epochs, utilizing a batch size of 256 and a cosine-annealing adjustable learning rate st… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between the Kurucz spectrum (black squares) and the PhDLspec prediction (red line) for a test star with Teff = 5930 K, log g = 4.48, and [Fe/H]=0.00 (left panel). The top subpanel shows the flux, and the bottom subpanel shows the residual (∆f(λ) = fPhDLspec − fKurucz). The right panel displays histograms of the overall residuals for a test set of 623 spectra, each with 3800 pixels in wavelength.… view at source ↗
Figure 4
Figure 4. Figure 4: The partial derivatives of the normalized fluxes to elemental abundance ratios [Co/Fe] and [La/Fe] for a representative set of stars with different stellar atmospheric parameters (Teff , log g, [Fe/H]). For each case, the upper subpanel shows the reference gradients from the Kurucz model (black) alongside the predictions from PhDLspec (red) and the Transformer model (green). The lower subpanel shows the re… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the stellar labels derived with PhDLspec and the true labels for the test spectra set. Each panel shows one parameter ratio, with the one-to-one black dashed line indicating perfect agreement. The color represents the [Fe/H] value of the test spectra. The standard deviation of the residuals is presented both for the entire test set (σa) and for metal-rich stars ([Fe/H] > −1) with 4500 K … view at source ↗
Figure 6
Figure 6. Figure 6: Correlation matrix between stellar atmospheric parameters (Teff , log g, and [Fe/H]) and abundances of 25 elements, derived by computing the Pearson correlation coefficient of their gradient spectra. Strong correlations are seen between [Fe/H] and many elemental abundances, as well as among the light elements (e.g., O and N) [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the atmospheric parameters de￾rived with PhDLspec and those from the DD-Payne estimates of Zhang et al. (2025a). From top to bottom, the residuals of Teff , log g, and [Fe/H] as a function of Teff from PhDLspec are presented, respectively. Triangles and circles denote dwarf and giant stars, respectively, with colors representing their log g values. Red and blue dashed lines show cubic spline … view at source ↗
Figure 8
Figure 8. Figure 8: Abundance differences between the primary and secondary stars of wide binary systems as a function of the primary’s effective temperature. Each panel shows [X/Fe]Primary−[X/Fe]Secondary for a given element. The color bar represents the effective temperature difference between the primary and secondary. Median and standard deviation of the differences are marked in each panel [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 9
Figure 9. Figure 9: Elemental abundance ratios [X/Fe] as a function of surface gravity. Gray dots represent PhDLspec abundance estimates from LAMOST spectra for our sample stars with [Fe/H] > −0.5, while orange dots are high-resolution spectroscopic measurements compiled in the Hypatia Catalog (Hinkel et al. 2014) for stars with [Fe/H] > −0.2. Black and red lines indicate cubic spline fits to the binned medians for our sample… view at source ↗
Figure 10
Figure 10. Figure 10: Abundance ratios [X/Fe] as a function of surface gravity log g for M67 member stars. Each panel corresponds to a different element, as indicated. The dots are color-coded by effective temperature Teff . The mean abundance (µ) and dispersion (σ) are marked in the bottom-right corner of each panel. imply that some extra, underestimated systematic er￾rors exist in the survey datasets. Stars with rela￾tively … view at source ↗
Figure 11
Figure 11. Figure 11: Comparison between the elemental abundances of M67 member stars derived with PhDLspec from LAMOST spectra and those from the GALAH DR3. The X- and Y-axes have the same scale unit, but are arbitrarily shifted for different elements. The scatter points represent individual stars, and error bars (when visible) indicate the measurement uncertainties [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: One-to-one comparison of the atmospheric parameters and elemental abundances ([X/Fe]) derived with PhDLspec from LAMOST spectra with those from APOGEE DR17 (Abdurro’uf et al. 2022) for stars in common. Each panel shows the comparison for a label, with the dashed line indicating the 1:1 relation. Points are color-coded by Teff derived with PhDLspec. The standard deviation (σ) of the label differences is ma… view at source ↗
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Density scatter plot of elemental abundances derived with PhDLspec from LAMOST spectra for a sample of 116,611 subgiant stars. The red dashed line in each panel indicates the median abundance trend from high-resolution spectroscopy for stars compiled in the Hypatia catalog (Hinkel et al. 2014) [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Differences in elemental abundances between the two components of wide binaries, plotted against the effective temperature of the primary star. Each panel shows ∆[X/Fe] = [X/Fe]Primary − [X/Fe]Secondary for a given element. The color scale indicates the effective temperature difference between the binary components. Systematic trends with Teff are apparent for several elements, particularly Na, Mg, Sr, Pr… view at source ↗
read the original abstract

Unlocking the full physical information encoded in low-resolution spectra poses a significant challenge for astronomical survey analysis. Such a task demands modeling spectra and optimizing astrophysical parameters in high-dimensional space, as a consequence of line blending. Here we present PhDLspec -- a deep learning framework embedded with physical priors for stellar spectra modeling and analysis. By imposing differential spectra derived from ab initio stellar atmospheric model calculation on a transformer framework, PhDLspec can rigorously and precisely model stellar spectra by simultaneously taking into account more than 30 physical parameters, at a computational speed hundreds of times faster than ab initio model calculation. With such a flexible stellar modeling approach, PhDLspec can effectively derive ~30 stellar labels from a low-resolution spectrum using affordable optimization techniques. Application to LAMOST spectra (R~1800) yields stellar elemental abundances in good agreement with high-resolution spectroscopic surveys, following essential calibrations to correct systematic biases in elemental abundance estimates using wide binaries and reference high-resolution datasets. We provide a catalog of 25 elemental abundances for 116,611 subgiant stars with precise age estimates. The successful application of PhDLspec to LAMOST spectra for high-dimensional parameter determination sheds light on similar challenges faced by other surveys and disciplines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces PhDLspec, a transformer-based deep learning framework that embeds physical priors by imposing differential spectra derived from ab initio stellar atmospheric models. This enables simultaneous determination of more than 30 stellar labels from low-resolution spectra at speeds hundreds of times faster than traditional calculations. Application to LAMOST spectra (R~1800) produces elemental abundances for 116,611 subgiant stars that agree with high-resolution surveys after essential post-hoc calibrations using wide binaries and reference datasets.

Significance. If the physical-prior embedding can be shown to produce accurate high-dimensional labels with quantified and minimal residual systematics, the method would offer a substantial advance for large-scale spectroscopic surveys by enabling efficient modeling of blended lines and many parameters simultaneously, with potential applicability beyond astronomy.

major comments (2)
  1. Abstract: The central claim that PhDLspec 'rigorously and precisely model[s] stellar spectra' via differential spectra imposition is load-bearing but weakened by the explicit requirement for 'essential calibrations to correct systematic biases in elemental abundance estimates'. The magnitude, origin, and pre-calibration size of these offsets are not reported, leaving open whether the transformer framework fully incorporates the physical priors without uncalibrated errors.
  2. LAMOST application section: The post-hoc corrections using wide binaries and high-resolution reference datasets indicate residual systematics in the raw outputs. This dependency must be addressed by quantifying the differential impact of the calibrations on the derived abundances and demonstrating that the method's accuracy does not rely on empirical adjustments external to the differential-spectra prior.
minor comments (1)
  1. Abstract: The speed claim ('hundreds of times faster') would benefit from a specific benchmark (e.g., wall-time per spectrum versus a standard ab initio code) to allow direct comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which help clarify the presentation of PhDLspec's physical-prior embedding and its application to LAMOST data. We address each major comment below and will incorporate revisions to provide the requested quantifications while preserving the manuscript's core claims.

read point-by-point responses

  1. Referee: Abstract: The central claim that PhDLspec 'rigorously and precisely model[s] stellar spectra' via differential spectra imposition is load-bearing but weakened by the explicit requirement for 'essential calibrations to correct systematic biases in elemental abundance estimates'. The magnitude, origin, and pre-calibration size of these offsets are not reported, leaving open whether the transformer framework fully incorporates the physical priors without uncalibrated errors.

    Authors: We agree the abstract would benefit from greater precision on this point. The differential spectra derived from ab initio models are imposed directly on the transformer to embed the physical priors, enabling rigorous high-dimensional modeling without uncalibrated errors in the spectral synthesis itself. The mentioned calibrations address only small residual zero-point offsets arising from survey-specific factors such as resolution differences and reference scale mismatches, not from shortcomings in the prior embedding. In revision we will rephrase the abstract to state that the core modeling is physically grounded, and we will add a dedicated paragraph (with accompanying table) in the results section that reports the pre-calibration offsets, their origins (quantified via wide-binary and APOGEE comparisons), and typical magnitudes (0.05–0.15 dex for most elements). This will demonstrate that the framework incorporates the priors effectively. revision: yes

  2. Referee: LAMOST application section: The post-hoc corrections using wide binaries and high-resolution reference datasets indicate residual systematics in the raw outputs. This dependency must be addressed by quantifying the differential impact of the calibrations on the derived abundances and demonstrating that the method's accuracy does not rely on empirical adjustments external to the differential-spectra prior.

    Authors: The referee is correct that post-hoc calibrations are applied to the LAMOST outputs. These adjustments align absolute scales but do not drive the method's accuracy; the differential-spectra priors already capture the physical dependencies and relative trends. In the revised manuscript we will expand the LAMOST section with new quantitative material: (i) tables listing raw versus calibrated abundances for each element, (ii) figures showing the differential impact on means, scatters, and [X/Fe] trends, and (iii) explicit demonstrations that key physical correlations (e.g., abundance ratios versus metallicity and stellar parameters) are already present in the raw outputs. This will confirm that the core performance originates from the embedded priors rather than external empirical adjustments. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper derives its framework by taking differential spectra computed from external ab initio stellar atmospheric models and imposing them as physical priors within a transformer architecture. Training targets and model spectra originate from the same external grid, but this is standard supervised learning on synthetic data rather than self-definition or a fitted input renamed as prediction. Application to LAMOST spectra produces raw labels that are then corrected via post-hoc empirical calibrations against independent wide-binary and high-resolution reference sets; the need for these calibrations is explicitly stated and does not reduce the core modeling step to its own inputs by construction. No load-bearing self-citations, uniqueness theorems imported from the authors, or ansatzes smuggled via prior work are present in the abstract or described method. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of pre-existing ab initio stellar atmosphere calculations and on the assumption that their differential spectra form effective, bias-free priors for the transformer.

free parameters (1)
  • transformer architecture hyperparameters
    Number of layers, attention heads, embedding dimensions, and learning-rate schedule chosen during training on model spectra.
axioms (1)
  • domain assumption Ab initio stellar atmospheric models produce differential spectra that faithfully capture the physical response of real stellar spectra to changes in more than 30 parameters.
    Invoked when the abstract states that these differentials are imposed on the transformer framework.

pith-pipeline@v0.9.0 · 5544 in / 1237 out tokens · 44652 ms · 2026-05-13T18:32:58.668785+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages · 6 internal anchors

  1. [1]

    , keywords =

    Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35, doi: 10.3847/1538-4365/ac4414

    work page doi:10.3847/1538-4365/ac4414 2022

  2. [2]

    Layer Normalization

    Ba, J. L., Kiros, J. R., & Hinton, G. E. 2016, Layer Normalization. https://arxiv.org/abs/1607.06450

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  3. [3]

    2021, MNRAS, 506, 150, doi: 10.1093/mnras/stab1242

    Buder, S., Sharma, S., Kos, J., et al. 2021, MNRAS, 506, 150, doi: 10.1093/mnras/stab1242

    work page doi:10.1093/mnras/stab1242 2021

  4. [4]

    Publications of the Astronomical Society of Australia , author =

    Buder, S., Kos, J., Wang, X. E., et al. 2025, PASA, 42, e051, doi: 10.1017/pasa.2025.26

    work page doi:10.1017/pasa.2025.26 2025

  5. [5]

    2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 25

    Castelli, F. 2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 25

    work page 2005

  6. [6]

    2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102

    Choi, J., Dotter, A., Conroy, C., et al. 2016, ApJ, 823, 102, doi: 10.3847/0004-637X/823/2/102

    work page internal anchor Pith review doi:10.3847/0004-637x/823/2/102 2016

  7. [7]

    P., Koposov, S

    Cooper, A. P., Koposov, S. E., Allende Prieto, C., et al. 2023, ApJ, 947, 37, doi: 10.3847/1538-4357/acb3c0

    work page doi:10.3847/1538-4357/acb3c0 2023

  8. [8]

    2012, Research in Astronomy and Astrophysics, 12, 1197, doi: 10.1088/1674-4527/12/9/003

    Cui, X.-Q., Zhao, Y.-H., Chu, Y.-Q., et al. 2012, Research in Astronomy and Astrophysics, 12, 1197, doi: 10.1088/1674-4527/12/9/003 De Silva, G. M., Freeman, K. C., Bland-Hawthorn, J., et al. 2015, MNRAS, 449, 2604, doi: 10.1093/mnras/stv327

    work page doi:10.1088/1674-4527/12/9/003 2012

  9. [9]

    El-Badry, K., Rix, H.-W., & Heintz, T. M. 2021, MNRAS, 506, 2269, doi: 10.1093/mnras/stab323

    work page doi:10.1093/mnras/stab323 2021

  10. [10]

    W., Lang, D., & Goodman, J

    Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306, doi: 10.1086/670067

    work page doi:10.1086/670067 2013

  11. [11]

    2011, in International Conference on Artificial Intelligence and Statistics

    Glorot, X., Bordes, A., & Bengio, Y. 2011, in International Conference on Artificial Intelligence and Statistics. https://api.semanticscholar.org/CorpusID:2239473 Gonz´ alez Hern´ andez, J. I., & Bonifacio, P. 2009, A&A, 497, 497, doi: 10.1051/0004-6361/200810904 26

    work page doi:10.1051/0004-6361/200810904 2011

  12. [12]

    2016, arXiv e-prints, arXiv:1604.00772, doi: 10.48550/arXiv.1604.00772

    Hansen, N. 2016, arXiv e-prints, arXiv:1604.00772, doi: 10.48550/arXiv.1604.00772

    work page doi:10.48550/arxiv.1604.00772 2016

  13. [13]

    2019, CMA-ES/pycma on Github, Zenodo, DOI:10.5281/zenodo.2559634, doi: 10.5281/zenodo.2559634

    Hansen, N., Akimoto, Y., & Baudis, P. 2019, CMA-ES/pycma on Github, Zenodo, DOI:10.5281/zenodo.2559634, doi: 10.5281/zenodo.2559634

    work page doi:10.5281/zenodo.2559634 2019

  14. [14]

    Completely derandomized self-adaptation in evolution strategies

    Hansen, N., & Ostermeier, A. 2001, Evolutionary Computation, 9, 159, doi: 10.1162/106365601750190398

    work page doi:10.1162/106365601750190398 2001

  15. [15]

    Deep Residual Learning for Image Recognition

    He, K., Zhang, X., Ren, S., & Sun, J. 2015, Deep Residual Learning for Image Recognition. https://arxiv.org/abs/1512.03385

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  16. [16]

    Gaussian Error Linear Units (GELUs)

    Hendrycks, D., & Gimpel, K. 2023, Gaussian Error Linear Units (GELUs). https://arxiv.org/abs/1606.08415

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  17. [17]

    R., Timmes, F

    Hinkel, N. R., Timmes, F. X., Young, P. A., Pagano, M. D., & Turnbull, M. C. 2014, AJ, 148, 54, doi: 10.1088/0004-6256/148/3/54

    work page doi:10.1088/0004-6256/148/3/54 2014

  18. [18]

    Adam: A Method for Stochastic Optimization

    Kingma, D. P., & Ba, J. 2014, arXiv e-prints, arXiv:1412.6980, doi: 10.48550/arXiv.1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1412.6980 2014

  19. [19]

    2009, A&A, 501, 1269, doi: 10.1051/0004-6361/200811467

    Koleva, M., Prugniel, P., Bouchard, A., & Wu, Y. 2009, A&A, 501, 1269, doi: 10.1051/0004-6361/200811467

    work page doi:10.1051/0004-6361/200811467 2009

  20. [20]

    Kurucz, R. L. 1970, SAO Special Report, 309 —. 1993, SYNTHE spectrum synthesis programs and line data —. 2005, Memorie della Societa Astronomica Italiana Supplementi, 8, 14

    work page 1970

  21. [21]

    S., Beers, T

    Lee, Y. S., Beers, T. C., Allende Prieto, C., et al. 2011, AJ, 141, 90, doi: 10.1088/0004-6256/141/3/90

    work page doi:10.1088/0004-6256/141/3/90 2011

  22. [22]

    2016, Research in Astronomy and Astrophysics, 16, 110, doi: 10.1088/1674-4527/16/7/110

    Li, J., Han, C., Xiang, M.-S., et al. 2016, Research in Astronomy and Astrophysics, 16, 110, doi: 10.1088/1674-4527/16/7/110

    work page doi:10.1088/1674-4527/16/7/110 2016

  23. [23]

    R., Schiavon , R

    Majewski, S. R., Schiavon, R. P., Frinchaboy, P. M., et al. 2017, AJ, 154, 94, doi: 10.3847/1538-3881/aa784d

    work page doi:10.3847/1538-3881/aa784d 2017

  24. [24]

    2015, ApJ, 808, 16, doi: 10.1088/0004-637X/808/1/16 O’Briain, T., Ting, Y.-S., Fabbro, S., et al

    Zasowski, G. 2015, ApJ, 808, 16, doi: 10.1088/0004-637X/808/1/16 O’Briain, T., Ting, Y.-S., Fabbro, S., et al. 2021, ApJ, 906, 130, doi: 10.3847/1538-4357/abca96

    work page doi:10.1088/0004-637x/808/1/16 2015

  25. [25]

    Rix, H.-W., Ting, Y.-S., Conroy, C., & Hogg, D. W. 2016, ApJL, 826, L25, doi: 10.3847/2041-8205/826/2/L25 R´ o˙ za´ nski, T., Ting, Y.-S., & Jab lo´ nska, M. 2024, arXiv e-prints, arXiv:2407.05751, doi: 10.48550/arXiv.2407.05751 —. 2025, ApJ, 980, 66, doi: 10.3847/1538-4357/ad9b99

    work page doi:10.3847/2041-8205/826/2/l25 2016

  26. [26]

    2018, ApJ, 860, 159, doi: 10.3847/1538-4357/aac6c9

    Ting, Y.-S., Conroy, C., Rix, H.-W., & Asplund, M. 2018, ApJ, 860, 159, doi: 10.3847/1538-4357/aac6c9

    work page doi:10.3847/1538-4357/aac6c9 2018

  27. [27]

    2019, ApJ, 879, 69, doi: 10.3847/1538-4357/ab2331

    Ting, Y.-S., Conroy, C., Rix, H.-W., & Cargile, P. 2019, ApJ, 879, 69, doi: 10.3847/1538-4357/ab2331

    work page doi:10.3847/1538-4357/ab2331 2019

  28. [28]

    Ting, Y.-S., Rix, H.-W., Conroy, C., Ho, A. Y. Q., & Lin, J. 2017, ApJL, 849, L9, doi: 10.3847/2041-8213/aa921c

    work page doi:10.3847/2041-8213/aa921c 2017

  29. [29]

    Attention Is All You Need

    Vaswani, A., Shazeer, N., Parmar, N., et al. 2017, arXiv e-prints, arXiv:1706.03762, doi: 10.48550/arXiv.1706.03762

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1706.03762 2017

  30. [30]

    L., Zhang, S., et al

    Wang, R., Luo, A. L., Zhang, S., et al. 2023, ApJS, 266, 40, doi: 10.3847/1538-4365/acce36

    work page doi:10.3847/1538-4365/acce36 2023

  31. [31]

    L., Chen, J.-J., et al

    Wang, R., Luo, A. L., Chen, J.-J., et al. 2020, ApJ, 891, 23, doi: 10.3847/1538-4357/ab6dea

    work page doi:10.3847/1538-4357/ab6dea 2020

  32. [32]

    2020, ApJ, 898, 58, doi: 10.3847/1538-4357/ab9a46

    Wheeler, A., Ness, M., Buder, S., et al. 2020, ApJ, 898, 58, doi: 10.3847/1538-4357/ab9a46

    work page doi:10.3847/1538-4357/ab9a46 2020

  33. [33]

    2014, in IAU Symposium, Vol

    Wu, Y., Du, B., Luo, A., Zhao, Y., & Yuan, H. 2014, in Statistical Challenges in 21st Century Cosmology, ed. A. Heavens, J.-L. Starck, & A. Krone-Martins, Vol. 306, 340–342, doi: 10.1017/S1743921314010825

    work page doi:10.1017/s1743921314010825 2014

  34. [34]

    2022, Nature, 603, 599, doi: 10.1038/s41586-022-04496-5

    Xiang, M., & Rix, H.-W. 2022, Nature, 603, 599, doi: 10.1038/s41586-022-04496-5

    work page doi:10.1038/s41586-022-04496-5 2022

  35. [35]

    2019, ApJS, 245, 34, doi: 10.3847/1538-4365/ab5364

    Xiang, M., Ting, Y.-S., Rix, H.-W., et al. 2019, ApJS, 245, 34, doi: 10.3847/1538-4365/ab5364

    work page doi:10.3847/1538-4365/ab5364 2019

  36. [36]

    2022, A&A, 662, A66, doi: 10.1051/0004-6361/202141570

    Xiang, M., Rix, H.-W., Ting, Y.-S., et al. 2022, A&A, 662, A66, doi: 10.1051/0004-6361/202141570

    work page doi:10.1051/0004-6361/202141570 2022

  37. [37]

    S., Liu, X

    Xiang, M. S., Liu, X. W., Yuan, H. B., et al. 2015, MNRAS, 448, 822, doi: 10.1093/mnras/stu2692

    work page doi:10.1093/mnras/stu2692 2015

  38. [38]

    S., Liu, X

    Xiang, M. S., Liu, X. W., Shi, J. R., et al. 2017, MNRAS, 464, 3657, doi: 10.1093/mnras/stw2523

    work page doi:10.1093/mnras/stw2523 2017

  39. [39]

    2022, The Innovation, 3, 100224, doi: 10.1016/j.xinn.2022.100224

    Yan, H., Li, H., Wang, S., et al. 2022, The Innovation, 3, 100224, doi: 10.1016/j.xinn.2022.100224

    work page doi:10.1016/j.xinn.2022.100224 2022

  40. [40]

    2024, ApJS, 273, 19, doi: 10.3847/1538-4365/ad51dd —

    Zhang, M., Xiang, M., Ting, Y.-S., et al. 2024, ApJS, 273, 19, doi: 10.3847/1538-4365/ad51dd —. 2025a, ApJS, 279, 5, doi: 10.3847/1538-4365/add016

    work page doi:10.3847/1538-4365/ad51dd 2024

  41. [41]

    Zhang, S., Zhang, H.-W., Ting, Y.-S., et al. 2025b, ApJS, 277, 47, doi: 10.3847/1538-4365/adb614 27 APPENDIX While Figure 8 in the main text presents the difference in the calibrated elemental abundances between binary com- ponent stars, we show here in Figure 16 the corresponding results for the originalPhDLspecestimates–i.e., abundances prior to calibra...

    work page doi:10.3847/1538-4365/adb614