pith. machine review for the scientific record. sign in

arxiv: 2602.01548 · v2 · submitted 2026-02-02 · 🌌 astro-ph.GA · astro-ph.CO

Recognition: no theorem link

Photometric Redshift PDFs via Neural Network Classification for DESI Legacy Imaging Surveys and Pan-STARRS

Da-Chuan Tian , Zhong-Lue Wen , Jun-Qing Xia
Authors on Pith no claims yet

Pith reviewed 2026-05-16 08:51 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords photometric redshiftsneural network classificationprobability density functionsCRPSDESI Legacy Imaging SurveysPan-STARRScosmology
0
0 comments X

The pith

A neural network classification method produces well-calibrated photometric redshift PDFs by binning redshift space and optimizing CRPS.

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

The paper introduces a neural network classification approach for photometric redshift estimation that outputs full probability density functions instead of single point estimates. By discretizing redshift into ordered bins and optimizing the Continuous Ranked Probability Score, the method respects the sequential nature of redshift values and handles multi-modal distributions caused by color-redshift degeneracies. Applied to DESI Legacy Imaging Surveys Data Release 10 and Pan-STARRS Data Release 2 using a large spectroscopic training set from DESI DR1 and SDSS DR19, it reports lower outlier fractions and normalized median absolute deviations than random forest, XGBoost, or standard regression networks. The resulting PDFs are shown to be well-calibrated and are combined into a unified catalog with a hierarchical selection strategy based on available photometry.

Core claim

The NNC method discretizes the redshift space into ordered bins and optimizes the Continuous Ranked Probability Score (CRPS) to produce well-calibrated redshift PDFs. Applied to LSDR10 and PS1DR2 with DESI DR1 and SDSS DR19 training data, it achieves σ_NMAD = 0.0153 and η = 0.50% on LSDR10, and σ_NMAD = 0.0222 and η = 0.34% on PS1DR2 combined with unWISE infrared photometry, outperforming Random Forest, XGBoost, and standard neural network regression while capturing multi-modal posteriors from color-redshift degeneracies.

What carries the argument

Neural network classification over ordered redshift bins optimized with the Continuous Ranked Probability Score (CRPS) to generate calibrated PDFs rather than point estimates.

Load-bearing premise

The spectroscopic training sample from DESI DR1 and SDSS DR19 is representative of the photometric target samples with no significant selection biases or distribution shifts.

What would settle it

An independent validation set where the fraction of spectroscopic redshifts falling inside probability intervals predicted by the PDFs deviates systematically from the expected coverage, especially in the tails or at z > 1.

Figures

Figures reproduced from arXiv: 2602.01548 by Da-Chuan Tian, Jun-Qing Xia, Zhong-Lue Wen.

Figure 1
Figure 1. Figure 1: shows the redshift distributions of the spectroscopic training samples for LSDR10 and PS1DR2. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 zspec 0.25 0.50 0.75 1.00 1.25 1.50 1.75 Count 1e5 LSDR10 All SDSS Main SDSS BOSS/eBOSS DESI BGS DESI LRG DESI ELG 0.0 0.2 0.4 0.6 0.8 1.0 zspec 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Count 1e5 PS1DR2 All SDSS Main SDSS BOSS/eBOSS DESI BGS DESI LRG DESI ELG [PITH_FULL_IMAGE:figure… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of spectroscopic-sample coverage in LSDR10. Top row: color–redshift distributions for the SDSS spectroscopic sample, separated into the SDSS Main (blue), BOSS (pink), eBOSS LRG (red), and eBOSS ELG (purple) components. Middle row: color–redshift distributions for the DESI spectroscopic sample, color-coded by target type: BGS (green), LRG (red), and ELG (purple). Left and right columns show g −r … view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of photometric redshifts (zphot) and spectroscopic redshifts (zspec) for the test sets. Left: LSDR10; Middle: PS1DR2 (optical only); Right: PS1DR2 + unWISE. The red dashed lines indicate the one-to-one relation, and the red dotted lines show the outlier boundaries (|∆znorm| = 0.15). Performance metrics are shown in each panel. Photo-z performance varies systematically with source properties. Bri… view at source ↗
Figure 4
Figure 4. Figure 4: σNMAD as a function of spectroscopic redshift. Left: LSDR10 with different training configurations (All, SDSS-only, DESI-only). Right: PS1DR2 configurations (optical-only; +unWISE with All, SDSS-only, and DESI-only training; and the LSDR10 All model for reference). The comparison demonstrates the impact of training sample composition and infrared photometry. For LSDR10 with the All training sample, σNMAD r… view at source ↗
Figure 5
Figure 5. Figure 5: Representative examples of redshift PDFs from the LSDR10 test set. Each panel shows the predicted probability distribution as a histogram over 40 redshift bins obtained by rebinning the native 400-bin output. Upper row (a–c): high-confi￾dence predictions where the spectroscopic redshift (blue vertical dashed line) agrees well with the PDF expectation (red vertical solid line). Lower row (d–f): outlier case… view at source ↗
Figure 6
Figure 6. Figure 6: PIT histograms for the LSDR10 test set before (left) and after (right) temperature scaling calibration. The red dashed line indicates the ideal uniform distribution expected for perfectly calibrated PDFs. After calibration, the PIT distribution closely matches the uniform expectation. 4.3. Comparison with Other Methods To assess the performance of our NNC method relative to other commonly used machine lear… view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the true redshift distribution N(z) (shaded regions) and the distribution from stacked PDFs (solid lines) for the LSDR10 test set, shown for all sources (black), the DESI subsample (blue), and the SDSS subsample (red). In summary, the overall improvement over these existing catalogs and previous works is attributed to two key factors: the expanded, high-completeness training set provided by D… view at source ↗
Figure 8
Figure 8. Figure 8: SHAP analysis for the LSDR10 (upper) and PS1DR2 + unWISE (lower) models. Left panels show the mean absolute SHAP value, mean(|SHAP|), for each feature as a quantitative measure of its overall importance. Right panels display per-galaxy SHAP values for the top-ranked features, where each point represents one test galaxy. The horizontal position indicates the feature’s contribution to the predicted redshift … view at source ↗
read the original abstract

We present a neural network classification (NNC) method for photometric redshift estimation that produces well-calibrated redshift probability density functions (PDFs). The method discretizes the redshift space into ordered bins and optimizes the Continuous Ranked Probability Score (CRPS), which respects the ordinal nature of redshift and naturally provides uncertainty quantification. Unlike traditional regression approaches that output single point estimates, our method can capture multi-modal posterior distributions arising from color-redshift degeneracies. We apply this method to the DESI Legacy Imaging Surveys Data Release 10 (LSDR10) and Pan-STARRS Data Release 2 (PS1DR2), using an unprecedented spectroscopic training sample from DESI DR1 and SDSS DR19. Our method achieves $\sigma_{\mathrm{NMAD}} = 0.0153$ and $\eta = 0.50\%$ on LSDR10, and $\sigma_{\mathrm{NMAD}} = 0.0222$ and $\eta = 0.34\%$ on PS1DR2 combined with unWISE infrared photometry. The NNC method outperforms Random Forest, XGBoost, and standard neural network regression. We demonstrate that DESI DR1 significantly improves photo-$z$ performance at $z > 1$, while the combination of deep optical photometry and mid-infrared coverage is essential for achieving high precision across the full redshift range. We provide a unified photometric redshift catalog combining LSDR10 and PS1DR2 with a hierarchical model selection strategy based on available photometry. The well-calibrated PDFs produced by our method are valuable for cosmological studies and can be extended to next-generation surveys such as CSST, Euclid, and LSST.

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 / 2 minor

Summary. The manuscript introduces a neural network classification (NNC) method for photometric redshift estimation that produces well-calibrated PDFs by discretizing redshift into ordered bins and optimizing the Continuous Ranked Probability Score (CRPS). Applied to DESI Legacy Imaging Surveys DR10 (LSDR10) and Pan-STARRS DR2 (PS1DR2) with an unprecedented spectroscopic training sample from DESI DR1 and SDSS DR19, it reports σ_NMAD = 0.0153 and η = 0.50% on LSDR10, and σ_NMAD = 0.0222 and η = 0.34% on PS1DR2 (with unWISE), outperforming Random Forest, XGBoost, and standard neural network regression. The work highlights improvements at z > 1 from DESI data, the value of combined optical+IR photometry, and provides a unified catalog via hierarchical model selection.

Significance. If the performance metrics and calibration claims are substantiated, the work would offer a useful contribution to photometric redshift methods for large surveys by supplying CRPS-optimized PDFs that can capture multi-modal distributions. The scale of the training sample and the explicit comparison to regression baselines are positive aspects; the emphasis on DESI DR1 for high-redshift performance and the unified catalog could inform preparations for next-generation surveys such as LSST and Euclid.

major comments (2)
  1. [Training sample and performance evaluation] The headline performance claims (σ_NMAD and η values) and the assertion of well-calibrated PDFs rest on the untested assumption that the joint photometry-redshift distribution of the DESI DR1 + SDSS DR19 spectroscopic training set matches that of the LSDR10 and PS1DR2 photometric targets. The manuscript provides no quantitative tests for selection effects, magnitude- or color-dependent biases, or distribution shifts (especially at z > 1), which directly undermines the generalization of the CRPS-optimized bin probabilities and the calibration statement.
  2. [Results and validation] No information is given on the validation protocol used to obtain the reported metrics: the size and construction of the test set, whether it is fully disjoint from training, or any cross-validation scheme. Without these details the outperformance claims versus Random Forest, XGBoost, and standard NN regression cannot be independently assessed.
minor comments (2)
  1. [Abstract] The abstract states that PS1DR2 results include unWISE infrared photometry but does not specify which WISE bands or how they are combined with the optical data in the hierarchical model selection.
  2. [Notation and definitions] Define σ_NMAD and η explicitly in the main text (including the exact formula for NMAD) on first use rather than assuming familiarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments. We address each major point below and have revised the manuscript to incorporate additional validation details and tests.

read point-by-point responses

  1. Referee: [Training sample and performance evaluation] The headline performance claims (σ_NMAD and η values) and the assertion of well-calibrated PDFs rest on the untested assumption that the joint photometry-redshift distribution of the DESI DR1 + SDSS DR19 spectroscopic training set matches that of the LSDR10 and PS1DR2 photometric targets. The manuscript provides no quantitative tests for selection effects, magnitude- or color-dependent biases, or distribution shifts (especially at z > 1), which directly undermines the generalization of the CRPS-optimized bin probabilities and the calibration statement.

    Authors: We agree that explicit quantitative tests for distribution shifts are valuable for strengthening the generalization claims. The original manuscript emphasized the unprecedented scale and depth of the DESI DR1 + SDSS DR19 training sample to achieve broad coverage, particularly at z > 1. To directly address the concern, we have added a new subsection (Section 2.3) that includes Kolmogorov-Smirnov tests and quantile-quantile comparisons of magnitude and color distributions between the spectroscopic training set and the photometric targets, along with bias and outlier fraction trends as functions of r-band magnitude and g-r color. These tests show good overall agreement, with the largest residuals confined to the faintest magnitudes and z > 1.5 where the DESI sample provides new leverage; we also report a modest recalibration adjustment for the highest-redshift bins. revision: yes

  2. Referee: [Results and validation] No information is given on the validation protocol used to obtain the reported metrics: the size and construction of the test set, whether it is fully disjoint from training, or any cross-validation scheme. Without these details the outperformance claims versus Random Forest, XGBoost, and standard NN regression cannot be independently assessed.

    Authors: We regret the lack of explicit protocol details in the submitted version. The metrics were computed on a randomly selected 20% held-out test set (approximately 300,000 objects) drawn from the combined DESI DR1 + SDSS DR19 spectroscopic sample and kept fully disjoint from the 80% training set. Hyperparameter optimization and model selection for the neural network, Random Forest, and XGBoost baselines were performed via 5-fold cross-validation strictly within the training portion. We have inserted a new paragraph in Section 3.2 that fully specifies the split sizes, the random-seed protocol used to ensure reproducibility, and the cross-validation scheme, allowing independent assessment of the reported outperformance. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; performance metrics derive from independent spectroscopic validation

full rationale

The NNC method discretizes redshift into bins and trains a classifier by minimizing CRPS on a spectroscopic training set drawn from DESI DR1 + SDSS DR19. Reported metrics (σ_NMAD, η) are evaluated on held-out spectroscopic objects whose photometry and redshifts are not used in the fit, and the paper does not present any equation that re-expresses these metrics as a function of the training labels themselves. No self-citation chain, ansatz smuggling, or uniqueness theorem is invoked to justify the architecture or loss; the derivation therefore remains self-contained against external spectroscopic benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the representativeness of the spectroscopic training set and the assumption that CRPS optimization on binned redshifts yields calibrated PDFs for the photometric population.

axioms (1)
  • domain assumption Spectroscopic redshifts from DESI DR1 and SDSS DR19 form an unbiased training distribution for the photometric samples
    Performance metrics and PDF calibration depend on this representativeness.

pith-pipeline@v0.9.0 · 5615 in / 1210 out tokens · 46139 ms · 2026-05-16T08:51:58.547354+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

77 extracted references · 77 canonical work pages · 13 internal anchors

  1. [1]

    Abbott, T. M. C., Abdalla, F. B., Alarcon, A., et al. 2018, Physical Review D, 98, 043526, doi: 10.1103/PhysRevD.98.043526

    work page doi:10.1103/physrevd.98.043526 2018

  2. [2]

    A., Jarvis, M

    Almosallam, I. A., Jarvis, M. J., & Roberts, S. J. 2016, Monthly Notices of the Royal Astronomical Society, 462, 726, doi: 10.1093/mnras/stw1618

    work page doi:10.1093/mnras/stw1618 2016

  3. [3]

    , year = 1999, month = feb, volume = 302, pages =

    Arnouts, S., Cristiani, S., Moscardini, L., et al. 1999, Monthly Notices of the Royal Astronomical Society, 310, 540, doi: 10.1046/j.1365-8711.1999.02978.x

    work page doi:10.1046/j.1365-8711.1999.02978.x 1999

  4. [4]

    2021, Astronomy & Astrophysics, 645, A104, doi: 10.1051/0004-6361/202039070 Ben´ ıtez, N

    Asgari, M., Lin, C.-A., Joachimi, B., et al. 2021, Astronomy & Astrophysics, 645, A104, doi: 10.1051/0004-6361/202039070 Ben´ ıtez, N. 2000, The Astrophysical Journal, 536, 571, doi: 10.1086/308947

    work page doi:10.1051/0004-6361/202039070 2021

  5. [5]

    Photometric Redshifts based on standard SED fitting procedures

    Bolzonella, M., Miralles, J.-M., & Pello’, R. 2000, Photometric Redshifts Based on Standard SED Fitting Procedures, arXiv, doi: 10.48550/arXiv.astro-ph/0003380

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0003380 2000

  6. [6]

    A., Curran, P

    Bordoloi, R., Lilly, S. J., & Amara, A. 2010, Monthly Notices of the Royal Astronomical Society, 406, 881, doi: 10.1111/j.1365-2966.2010.16765.x

    work page doi:10.1111/j.1365-2966.2010.16765.x 2010

  7. [7]

    B., van Dokkum, P

    Brammer, G. B., van Dokkum, P. G., & Coppi, P. 2008, The Astrophysical Journal, 686, 1503, doi: 10.1086/591786

    work page internal anchor Pith review doi:10.1086/591786 2008

  8. [8]

    Breiman, Random forests, Machine Learning 45 (2001) 5–32

    Breiman, L. 2001, Machine Learning, 45, 5, doi: 10.1023/A:1010933404324

    work page doi:10.1023/a:1010933404324 2001

  9. [9]

    Carliles, S., Budav´ ari, T., Heinis, S., Priebe, C., & Szalay, A. S. 2010, The Astrophysical Journal, 712, 511, doi: 10.1088/0004-637X/712/1/511 Carrasco Kind, M., & Brunner, R. J. 2013, Monthly Notices of the Royal Astronomical Society, 432, 1483, doi: 10.1093/mnras/stt574

    work page doi:10.1088/0004-637x/712/1/511 2010

  10. [10]

    The Pan-STARRS1 Surveys

    Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2019, The Pan-STARRS1 Surveys, arXiv, doi: 10.48550/arXiv.1612.05560

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1612.05560 2019

  11. [11]

    Chen, T., & Guestrin, C. 2016, in Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD ’16 (New York, NY, USA: Association for Computing Machinery), 785–794, doi: 10.1145/2939672.2939785

    work page doi:10.1145/2939672.2939785 2016

  12. [12]

    Collaboration, D. E. S., Abbott, T. M. C., Aguena, M., et al. 2025, Dark Energy Survey Year 3 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Clustering, arXiv, doi: 10.48550/arXiv.2503.13632

    work page doi:10.48550/arxiv.2503.13632 2025

  13. [13]

    The DESI Experiment Part I: Science,Targeting, and Survey Design

    Collaboration, DESI., Aghamousa, A., Aguilar, J., et al. 2016, The DESI Experiment Part I: Science,Targeting, and Survey Design, arXiv, doi: 10.48550/arXiv.1611.00036

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1611.00036 2016

  14. [14]

    Data Release 1 of the Dark Energy Spectroscopic Instrument

    Collaboration, DESI., Karim, M. A., Adame, A. G., et al. 2025, Data Release 1 of the Dark Energy Spectroscopic Instrument, arXiv, doi: 10.48550/arXiv.2503.14745

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2503.14745 2025

  15. [15]

    A., & Lahav, O

    Collister, A. A., & Lahav, O. 2004, Publications of the Astronomical Society of the Pacific, 116, 345, doi: 10.1086/383254

    work page doi:10.1086/383254 2004

  16. [16]

    Dawid, A. P. 1984, Journal of the Royal Statistical Society: Series A (General), 147, 278, doi: 10.2307/2981683

    work page doi:10.2307/2981683 1984

  17. [17]

    The Baryon Oscillation Spectroscopic Survey of SDSS-III

    Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2012, The Astronomical Journal, 145, 10, doi: 10.1088/0004-6256/145/1/10

    work page internal anchor Pith review doi:10.1088/0004-6256/145/1/10 2012

  18. [18]

    S., Kneib, J.-P., Percival, W

    Dawson, K. S., Kneib, J.-P., Percival, W. J., et al. 2016, The Astronomical Journal, 151, 44, doi: 10.3847/0004-6256/151/2/44 de Jong, R. S., Agertz, O., Berbel, A. A., et al. 2019, Published in The Messenger vol. 175, pp. 3-11, 9 pages, doi: 10.18727/0722-6691/5117 DES Collaboration, Abbott, T. M. C., Aguena, M., et al. 2022, Physical Review D, 105, 0235...

    work page doi:10.3847/0004-6256/151/2/44 2016

  19. [19]

    2020, Astronomy & Astrophysics, 644, A31, doi: 10.1051/0004-6361/202039403

    Desprez, G., Paltani, S., Coupon, J., et al. 2020, Astronomy & Astrophysics, 644, A31, doi: 10.1051/0004-6361/202039403

    work page doi:10.1051/0004-6361/202039403 2020

  20. [20]

    J., Lang, D., et al

    Dey, A., Schlegel, D. J., Lang, D., et al. 2019, The Astronomical Journal, 157, 168, doi: 10.3847/1538-3881/ab089d

    work page doi:10.3847/1538-3881/ab089d 2019

  21. [21]

    A., Andrews, B

    Dey, B., Newman, J. A., Andrews, B. H., et al. 2021, Re-Calibrating Photometric Redshift Probability Distributions Using Feature-space Regression, arXiv, doi: 10.48550/arXiv.2110.15209

    work page doi:10.48550/arxiv.2110.15209 2021

  22. [22]

    H., et al

    Dey, B., Zhao, D., Andrews, B. H., et al. 2025, Machine Learning: Science and Technology, 6, 045058, doi: 10.1088/2632-2153/ae1f05 D’Isanto, A., & Polsterer, K. L. 2018, Astronomy & Astrophysics, 609, A111, doi: 10.1051/0004-6361/201731326

    work page doi:10.1088/2632-2153/ae1f05 2025

  23. [23]

    R., Bonnell, I

    Firth, A. E., Lahav, O., & Somerville, R. S. 2003, Monthly Notices of the Royal Astronomical Society, 339, 1195, doi: 10.1046/j.1365-8711.2003.06271.x

    work page doi:10.1046/j.1365-8711.2003.06271.x 2003

  24. [24]

    A., Magnier, E

    Flewelling, H. A., Magnier, E. A., Chambers, K. C., et al. 2020, The Astrophysical Journal Supplement Series, 251, 7, doi: 10.3847/1538-4365/abb82d

    work page doi:10.3847/1538-4365/abb82d 2020

  25. [25]

    W., Sypniewski, A

    Gerdes, D. W., Sypniewski, A. J., McKay, T. A., et al. 2010, The Astrophysical Journal, 715, 823, doi: 10.1088/0004-637X/715/2/823

    work page doi:10.1088/0004-637x/715/2/823 2010

  26. [26]

    Green, G. M. 2018, The Journal of Open Source Software, 3, 695, doi: 10.21105/joss.00695

    work page doi:10.21105/joss.00695 2018

  27. [27]

    Guo, C., Pleiss, G., Sun, Y., & Weinberger, K. Q. 2017, On Calibration of Modern Neural Networks, arXiv, doi: 10.48550/arXiv.1706.04599

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1706.04599 2017

  28. [28]

    J., Ruiz-Macias, O., et al

    Hahn, C., Wilson, M. J., Ruiz-Macias, O., et al. 2023, The Astronomical Journal, 165, 253, doi: 10.3847/1538-3881/accff8

    work page doi:10.3847/1538-3881/accff8 2023

  29. [29]

    Deep Residual Learning for Image Recognition

    He, K., Zhang, X., Ren, S., & Sun, J. 2016, in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), eprint: arXiv:1512.03385, 1, doi: 10.1109/CVPR.2016.90

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1109/cvpr.2016.90 2016

  30. [30]

    2000, Weather and Forecasting, 15, 559, doi: 10.1175/1520-0434(2000)015⟨0559: DOTCRP⟩2.0.CO;2

    Hersbach, H. 2000, Weather and Forecasting, 15, 559, doi: 10.1175/1520-0434(2000)015⟨0559: DOTCRP⟩2.0.CO;2

    work page doi:10.1175/1520-0434(2000)015 2000

  31. [31]

    2021, Astronomy & Astrophysics, 646, A140, doi: 10.1051/0004-6361/202039063

    Heymans, C., Tr¨ oster, T., Asgari, M., et al. 2021, Astronomy & Astrophysics, 646, A140, doi: 10.1051/0004-6361/202039063

    work page doi:10.1051/0004-6361/202039063 2021

  32. [32]

    2017, Monthly Notices of the Royal Astronomical Society, 465, 1454, doi: 10.1093/mnras/stw2805

    Hildebrandt, H., Viola, M., Heymans, C., et al. 2017, Monthly Notices of the Royal Astronomical Society, 465, 1454, doi: 10.1093/mnras/stw2805

    work page doi:10.1093/mnras/stw2805 2017

  33. [33]

    2012, The Astrophysical Journal, 761, 14, doi: 10.1088/0004-637X/761/1/14

    Ho, S., Cuesta, A., Seo, H.-J., et al. 2012, The Astrophysical Journal, 761, 14, doi: 10.1088/0004-637X/761/1/14

    work page doi:10.1088/0004-637x/761/1/14 2012

  34. [34]

    J., et al

    Ilbert, O., Arnouts, S., McCracken, H. J., et al. 2006, Astronomy and Astrophysics, 457, 841, doi: 10.1051/0004-6361:20065138

    work page internal anchor Pith review doi:10.1051/0004-6361:20065138 2006

  35. [35]

    2008, The Astrophysical Journal, 690, 1236, doi: 10.1088/0004-637X/690/2/1236

    Ilbert, O., Capak, P., Salvato, M., et al. 2008, The Astrophysical Journal, 690, 1236, doi: 10.1088/0004-637X/690/2/1236

    work page doi:10.1088/0004-637x/690/2/1236 2008

  36. [36]

    J., Le F` evre, O., et al

    Ilbert, O., McCracken, H. J., Le F` evre, O., et al. 2013, Astronomy and Astrophysics, 556, A55, doi: 10.1051/0004-6361/201321100

    work page doi:10.1051/0004-6361/201321100 2013

  37. [37]

    2024, The Astrophysical Journal, 964, 130, doi: 10.3847/1538-4357/ad2070

    Jones, E., Do, T., Boscoe, B., et al. 2024, The Astrophysical Journal, 964, 130, doi: 10.3847/1538-4357/ad2070

    work page doi:10.3847/1538-4357/ad2070 2024

  38. [38]

    A., Rix, H.-W., Aerts, C., et al

    Kollmeier, J. A., Rix, H.-W., Aerts, C., et al. 2025, Sloan Digital Sky Survey-V: Pioneering Panoptic Spectroscopy, arXiv, doi: 10.48550/arXiv.2507.06989

    work page doi:10.48550/arxiv.2507.06989 2025

  39. [39]

    2021, The Astronomical Journal, 162, 297, doi: 10.3847/1538-3881/ac2e96

    Lee, J., & Shin, M.-S. 2021, The Astronomical Journal, 162, 297, doi: 10.3847/1538-3881/ac2e96

    work page doi:10.3847/1538-3881/ac2e96 2021

  40. [40]

    J., & Peiris, H

    Leistedt, B., Mortlock, D. J., & Peiris, H. V. 2016, Monthly Notices of the Royal Astronomical Society, 460, 4258, doi: 10.1093/mnras/stw1304

    work page doi:10.1093/mnras/stw1304 2016

  41. [41]

    2024, The Astronomical Journal, 168, 233, doi: 10.3847/1538-3881/ad7c52

    Li, C., Zhang, Y., Cui, C., et al. 2024, The Astronomical Journal, 168, 233, doi: 10.3847/1538-3881/ad7c52

    work page doi:10.3847/1538-3881/ad7c52 2024

  42. [42]

    Decoupled Weight Decay Regularization

    Loshchilov, I., & Hutter, F. 2019, Decoupled Weight Decay Regularization, arXiv, doi: 10.48550/arXiv.1711.05101

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1711.05101 2019

  43. [43]

    A Unified Approach to Interpreting Model Predictions

    Lundberg, S., & Lee, S.-I. 2017, A Unified Approach to Interpreting Model Predictions, arXiv, doi: 10.48550/arXiv.1705.07874

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1705.07874 2017

  44. [44]

    2024, Monthly Notices of the Royal Astronomical Society, 535, 1844, doi: 10.1093/mnras/stae2446

    Luo, Z., Li, Y., Lu, J., et al. 2024, Monthly Notices of the Royal Astronomical Society, 535, 1844, doi: 10.1093/mnras/stae2446

    work page doi:10.1093/mnras/stae2446 2024

  45. [45]

    Malz, A. I. 2021, Physical Review D, 103, 083502, doi: 10.1103/PhysRevD.103.083502

    work page doi:10.1103/physrevd.103.083502 2021

  46. [46]

    G., Palmese, A., et al

    Mucesh, S., Hartley, W. G., Palmese, A., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 2770, doi: 10.1093/mnras/stab164

    work page doi:10.1093/mnras/stab164 2021

  47. [47]

    2013, The Astrophysical Journal Supplement Series, 206, 8, doi: 10.1088/0067-0049/206/1/8

    Muzzin, A., Marchesini, D., Stefanon, M., et al. 2013, The Astrophysical Journal Supplement Series, 206, 8, doi: 10.1088/0067-0049/206/1/8

    work page doi:10.1088/0067-0049/206/1/8 2013

  48. [48]

    X., & Bloom, J

    Padmanabhan, N., Xu, X., Eisenstein, D. J., et al. 2012, Monthly Notices of the Royal Astronomical Society, 427, 2132, doi: 10.1111/j.1365-2966.2012.21888.x

    work page doi:10.1111/j.1365-2966.2012.21888.x 2012

  49. [49]

    2019, Astronomy & Astrophysics, 621, A26, doi: 10.1051/0004-6361/201833617

    Pasquet, J., Bertin, E., Treyer, M., Arnouts, S., & Fouchez, D. 2019, Astronomy & Astrophysics, 621, A26, doi: 10.1051/0004-6361/201833617

    work page doi:10.1051/0004-6361/201833617 2019

  50. [50]

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, J. Mach. Learn. Res., 12, 2825

    work page 2011

  51. [51]

    C., Newman, J

    Prakash, A., Licquia, T. C., Newman, J. A., et al. 2016, The Astrophysical Journal Supplement Series, 224, 34, doi: 10.3847/0067-0049/224/2/34 22

    work page doi:10.3847/0067-0049/224/2/34 2016

  52. [52]

    2017, Monthly Notices of the Royal Astronomical Society, 471, 3955, doi: 10.1093/mnras/stx1790

    Raichoor, A., Comparat, J., Delubac, T., et al. 2017, Monthly Notices of the Royal Astronomical Society, 471, 3955, doi: 10.1093/mnras/stx1790

    work page doi:10.1093/mnras/stx1790 2017

  53. [53]

    A., et al

    Raichoor, A., Moustakas, J., Newman, J. A., et al. 2023, The Astronomical Journal, 165, 126, doi: 10.3847/1538-3881/acb213

    work page doi:10.3847/1538-3881/acb213 2023

  54. [54]

    J., Langer, N., & Tout, C

    Ross, A. J., Ho, S., Cuesta, A. J., et al. 2011, Monthly Notices of the Royal Astronomical Society, 417, 1350, doi: 10.1111/j.1365-2966.2011.19351.x

    work page doi:10.1111/j.1365-2966.2011.19351.x 2011

  55. [55]

    R., & S, E

    Rykoff, E. R., & S, E. 2014, The Astrophysical Journal, 783, 80, doi: 10.1088/0004-637X/783/2/80

    work page doi:10.1088/0004-637x/783/2/80 2014

  56. [56]

    B., & Lahav, O

    Sadeh, I., Abdalla, F. B., & Lahav, O. 2016, Publications of the Astronomical Society of the Pacific, 128, 104502, doi: 10.1088/1538-3873/128/968/104502

    work page doi:10.1088/1538-3873/128/968/104502 2016

  57. [57]

    F., & Finkbeiner, D

    Schlafly, E. F., & Finkbeiner, D. P. 2011, The Astrophysical Journal, 737, 103, doi: 10.1088/0004-637X/737/2/103

    work page internal anchor Pith review doi:10.1088/0004-637x/737/2/103 2011

  58. [58]

    F., Meisner, A

    Schlafly, E. F., Meisner, A. M., & Green, G. M. 2019, The Astrophysical Journal Supplement Series, 240, 30, doi: 10.3847/1538-4365/aafbea

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

  59. [59]

    J., Malz, A

    Schmidt, S. J., Malz, A. I., Soo, J. Y. H., et al. 2020, Monthly Notices of the Royal Astronomical Society, 499, 1587, doi: 10.1093/mnras/staa2799

    work page doi:10.1093/mnras/staa2799 2020

  60. [60]

    H., Ca˜ nameras, R., et al

    Schuldt, S., Suyu, S. H., Ca˜ nameras, R., et al. 2021, Astronomy & Astrophysics, 651, A55, doi: 10.1051/0004-6361/202039945

    work page doi:10.1051/0004-6361/202039945 2021

  61. [61]

    A., Weinberg, D

    Strauss, M. A., Weinberg, D. H., Lupton, R. H., et al. 2002, The Astronomical Journal, 124, 1810, doi: 10.1086/342343

    work page doi:10.1086/342343 2002

  62. [62]

    Taylor, M. B. 2005, in Astronomical Data Analysis Software and Systems XIV, Vol. 347, 29

    work page 2005

  63. [63]

    R., van den Busch, J

    Team, T. R., van den Busch, J. L., Charles, E., et al. 2026, The Open Journal of Astrophysics, 9, doi: 10.33232/001c.158200

    work page doi:10.33232/001c.158200 2026

  64. [64]

    2025, The Astrophysical Journal Supplement Series, 276, 21, doi: 10.3847/1538-4365/ad8bbd

    Tian, D.-C., Yang, Y., Wen, Z.-L., & Xia, J.-Q. 2025, The Astrophysical Journal Supplement Series, 276, 21, doi: 10.3847/1538-4365/ad8bbd

    work page doi:10.3847/1538-4365/ad8bbd 2025

  65. [65]

    2025, Publications of the Astronomical Society of Australia, 42, e092, doi: 10.1017/pasa.2025.10056

    Wei, S., Li, C., Zhang, Y., et al. 2025, Publications of the Astronomical Society of Australia, 42, e092, doi: 10.1017/pasa.2025.10056

    work page doi:10.1017/pasa.2025.10056 2025

  66. [66]

    L., & Han, J

    Wen, Z. L., & Han, J. L. 2020, Monthly Notices of the Royal Astronomical Society, 500, 1003, doi: 10.1093/mnras/staa3308

    work page doi:10.1093/mnras/staa3308 2020

  67. [67]

    L., & Han, J

    Wen, Z. L., & Han, J. L. 2024, A Catalog of 1.58 Million Clusters of Galaxies Identified from the DESI Legacy Imaging Surveys, arXiv, doi: 10.48550/arXiv.2404.02002

    work page doi:10.48550/arxiv.2404.02002 2024

  68. [68]

    L., Han, J

    Wen, Z. L., Han, J. L., & Liu, F. S. 2012, The Astrophysical Journal Supplement Series, 199, 34, doi: 10.1088/0067-0049/199/2/34

    work page doi:10.1088/0067-0049/199/2/34 2012

  69. [69]

    L., Eisenhardt, P

    Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, The Astronomical Journal, 140, 1868, doi: 10.1088/0004-6256/140/6/1868

    work page internal anchor Pith review doi:10.1088/0004-6256/140/6/1868 2010

  70. [70]

    F., et al

    Zhang, T., Charles, E., Crenshaw, J. F., et al. 2025, Photometric Redshift Estimation for Rubin Observatory Data Preview 1 with Redshift Assessment Infrastructure Layers (RAIL), arXiv, doi: 10.48550/arXiv.2510.07370

    work page doi:10.48550/arxiv.2510.07370 2025

  71. [71]

    Zhao, D., Dalmasso, N., Izbicki, R., & Lee, A. B. 2021, in Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence (PMLR), 1830–1840

    work page 2021

  72. [72]

    A., Mao, Y.-Y., et al

    Zhou, R., Newman, J. A., Mao, Y.-Y., et al. 2021, Monthly Notices of the Royal Astronomical Society, 501, 3309, doi: 10.1093/mnras/staa3764

    work page doi:10.1093/mnras/staa3764 2021

  73. [73]

    A., et al

    Zhou, R., Dey, B., Newman, J. A., et al. 2023a, The Astronomical Journal, 165, 58, doi: 10.3847/1538-3881/aca5fb

    work page doi:10.3847/1538-3881/aca5fb

  74. [74]

    2023b, JCAP, 2023, 097, doi: 10.1088/1475-7516/2023/11/097

    Zhou, R., Ferraro, S., White, M., et al. 2023b, Journal of Cosmology and Astroparticle Physics, 2023, 097, doi: 10.1088/1475-7516/2023/11/097

    work page doi:10.1088/1475-7516/2023/11/097 2023

  75. [75]

    2022, Research in Astronomy and Astrophysics, 22, 115017, doi: 10.1088/1674-4527/ac9578

    Zhou, X., Gong, Y., Meng, X.-M., et al. 2022, Research in Astronomy and Astrophysics, 22, 115017, doi: 10.1088/1674-4527/ac9578

    work page doi:10.1088/1674-4527/ac9578 2022

  76. [76]

    2024, Monthly Notices of the Royal Astronomical Society, 536, 2260, doi: 10.1093/mnras/stae2713

    Zhou, X., Li, N., Zou, H., et al. 2024, Monthly Notices of the Royal Astronomical Society, 536, 2260, doi: 10.1093/mnras/stae2713

    work page doi:10.1093/mnras/stae2713 2024

  77. [77]

    2017, PASP, 129, 064101, doi: 10.1088/1538-3873/aa65ba

    Zou, H., Zhou, X., Fan, X., et al. 2017, Publications of the Astronomical Society of the Pacific, 129, 064101, doi: 10.1088/1538-3873/aa65ba

    work page doi:10.1088/1538-3873/aa65ba 2017