Pith. sign in

REVIEW 3 major objections 4 minor 93 references

A neural-network ensemble finds 811 new strong lens candidates in the DESI Legacy Surveys DR10, most of them in sky already searched by earlier programs.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

A neural-network ensemble plus human grading yields 811 new strong gravitational lens candidates in DESI Legacy Surveys DR10.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A solid, incremental lens-catalog paper: the new DR10 footprint and 811 candidates are useful, but the Grade C majority has an unquantified false-positive rate and the abstract overstates the count. the 3 major comments →

arxiv 2508.20087 v1 pith:REZGSZVL submitted 2025-08-27 astro-ph.CO astro-ph.GA

Strong Lens Discoveries in DESI Legacy Imaging Surveys DR10 with Two Deep Learning Architectures

Jose Carlos Inchausti , Christopher J. Storfer , Xiaosheng Huang , Yuan-Ming Hsu , Brandt Kaufmann , Chaitanya Pasupala , S. Banka , A. Dey
show 6 more authors
D. Lang A. Meisner J. Moustakas A.D. Myers E. F. Schlafly D.J. Schlegel
This is my paper
classification astro-ph.CO astro-ph.GA
keywords strong gravitational lensinglens candidatesDESI Legacy SurveysDR10deep learningneural network ensembleResNetEfficientNet
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper claims that an ensemble of two deep-learning classifiers, a shielded ResNet and an EfficientNet, trained on observed images and combined by a meta-learner, can identify hundreds of new strong gravitational lens candidates across the nearly complete extragalactic sky of the DESI Legacy Surveys DR10. Applying the ensemble to about 43 million cutouts and inspecting the top 0.01% of recommendations by eye, the authors report 811 new candidates: 90 grade A, 104 grade B, and 617 grade C. Around 60% of these lie within the DR9 footprint that had already been searched multiple times, demonstrating that even well-mined imaging can yield a large number of previously missed candidates. The paper also introduces a visual-inspection portal that shows the individual g, r, z bands, which helps distinguish the red lens galaxy from bluer lensed arcs.

Core claim

The central discovery is a new catalog of 811 strong gravitational lens candidates, compiled by ranking neural-network recommendations and subjecting the top 5,680 images (after removing 1,102 known systems) to human inspection. The candidates include 90 grade A systems, 104 grade B, and 617 grade C. The search covers the DECam footprint of the Legacy Surveys DR10, about 14,000 square degrees, and uses a z-band magnitude cut of 20 for the central galaxy. The paper further finds that 484 of the new candidates fall inside the previously searched DR9 footprint and 327 in the newly added DR10 area. Combined with the previous three searches, the group reports a total of 3,868 new strong lens cand

What carries the argument

The key machinery is a two-model neural ensemble: a shielded residual network (ResNet) with 194,433 trainable parameters and an EfficientNetV2 with about 20.5 million parameters, both trained on the same 1372 lenses and high-grade candidates plus 134,182 nonlenses (a 100:1 nonlens-to-lens ratio). Their output probabilities are combined by a feature-weighted stacking meta-learner, a one-layer 300-node network that learns the optimal weighting of the two base models. This ensemble is deployed on cutouts centered on all non-PSF galaxies with z<20 mag; the top 0.01 percentile of ensemble scores is then visually inspected using a portal that displays the co-added image plus the separate g, r, and

Load-bearing premise

The headline count of 811 candidates rests on the assumption that the faint, small features seen in the 26-arcsecond cutouts at roughly 1.1 to 1.3 arcsecond seeing are real lensed arcs rather than aligned background galaxies or asymmetric structure, and this is least secure for the 617 Grade C systems.

What would settle it

Take a random sample of the Grade C candidates (and a smaller sample of Grade A and B) and obtain higher-resolution imaging with HST or JWST or integral-field spectroscopy. If a substantial fraction of Grade C systems show no lensed source, no counter-image, and no additional arc features at the higher resolution, the 811 count overestimates the true yield, and the paper's conclusion that the searched footprint still holds hundreds of new lenses would be weakened.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • If the catalog holds up, it provides more than 800 new targets for spectroscopy and high-resolution imaging, several hundred of which can be used to study galaxy dark matter halos and substructure.
  • The 484 candidates found inside the well-searched DR9 footprint imply that prior searches systematically missed a population of smaller, fainter, or bluer arcs; a complete census of strong lenses in this footprint is not yet complete.
  • The demonstration that a two-architecture ensemble with a meta-learner outperforms either model alone suggests a reusable recipe for future wide-field surveys such as LSST, Euclid, and Roman.
  • The increased nonlens-to-lens training ratio and the use of separate bands for visual inspection improve the purity of the candidate list relative to earlier searches in the series, as reported by the grade-by-type purity numbers.
  • The paper's claim that it is the first catalog covering nearly the entire extragalactic sky south of declination +32 degrees establishes a reference sample for studies of lens statistics and the selection function of strong lenses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If Grade C candidates are heavily contaminated by aligned background galaxies or asymmetric structure, the headline count of 811 substantially overstates the true number of strong lenses; the paper itself notes that Grade C systems need deeper or higher-resolution data to reach higher certainty, so the safe interpretable yield is closer to the 194 A and B grades.
  • The success of the ensemble in re-finding lenses in previously searched regions hints that other catalogs compiled from the same imaging may contain a comparable hidden population, and that cross-search comparisons of selection functions could recover more lenses without new observations.
  • A testable extension is to measure the contamination rate of the Grade C sample by obtaining Hubble or JWST imaging or spectroscopy for a random subset; the fraction that resolve into genuine lensed arcs would directly calibrate the false-positive rate of the entire visual-inspection pipeline.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper, the fourth in the authors' series of strong-lens searches in the DESI Legacy Surveys, applies a ResNet and an EfficientNet (combined by a meta-learner) to ~43 million non-PSF galaxy cutouts in the DR10 DECaLS footprint with z < 20 mag. The top 0.01% of ensemble predictions are visually inspected with a new portal that shows co-added and individual g/r/z bands. After removing known lenses and candidates, the authors report 811 new lens candidates: 90 Grade A, 104 Grade B, and 617 Grade C, of which 484 lie in the previously searched DR9 footprint. They also combine the new candidates with Papers I-III to claim a total of 3,868 new candidates. The training set is a compilation of known lenses and previous high-grade candidates plus ~134,000 nonlenses; the new candidates are not in the training set, so I see no circularity in the ML pipeline itself.

Significance. If the candidate catalog is reliable, this is a substantial contribution to the strong-lens search literature: it extends the searched footprint to nearly the full DECaLS area, demonstrates that new high-grade candidates can still be found in previously mined regions, and introduces a useful two-model ensemble plus per-band visual inspection. The paper is transparent about its Grade definitions and acknowledges the need for follow-up for Grade C objects. However, the quantitative value of the paper is currently limited by three issues: the headline count is dominated by Grade C candidates with no false-positive calibration; the purity numbers in Table 5 rest on an unverified scaling assumption and lack uncertainties; and the catalog itself is not provided in machine-readable form. These are fixable, and the underlying search methodology is sound, so the contribution would be valuable after revision.

major comments (3)
  1. [§3.3.1 / §4.1 / Table 4] The headline '811 new lens candidates' is dominated by 617 Grade C objects (76%). By the paper's own definition, Grade C features are 'even fainter and/or smaller' than Grade B, often lack a discernible counter-image, and can have angular scales comparable to or only slightly larger than the seeing. The only evidence for these objects is the visual grading of 26" cutouts by two graders. The text says 'we report the average and difference of the results of these two graders' (§3.3.1), but no such statistics appear anywhere in the manuscript. There is also no blind control sample of nonlenses and no external validation. Because Grade C dominates the count, the unquantified false-positive rate of this class is load-bearing for the abstract's unqualified '811'. Please either calibrate the Grade C false-positive rate (e.g., by re-grading a subsample with higher-resolution data or spectroscopy
  2. [§5 / Table 5] The purity values in Table 5 are not measured purities. The authors inspected only 4,578 threshold-passing recommendations after removing 1,102 known systems, so the '1 in 5 SER' etc. numbers are derived by 'scaling the grade distribution of new candidates to known ones' under the assumption that new and rediscovered candidates share the same grade distribution. This assumption is unverified, and the known systems come from heterogeneous literature searches with different selection functions. No uncertainties are shown, and the conclusion (§6) repeats these as an 'increase in purity' relative to Paper III. Please report the actual inspected-set yields with error bars, state the scaling assumption explicitly, or remove the quantitative purity claims.
  3. [§4.1] The paper's main deliverable is the catalog of 811 candidates, but the manuscript contains only counts and figures; the coordinates and properties of the candidates are not given in a table. Only a small number of examples (Figures 8 and 9) have coordinates in their labels. A catalog paper should include a machine-readable table of all candidates (at minimum RA, Dec, grade, Tractor type, and redshift) either in the paper or as a journal ancillary file. As written, the central contribution is not accessible from the paper itself.
minor comments (4)
  1. [§4.2 / Figure 11] The total number of candidates from the four searches is given as 4,869 in §4.2 and in the Figure 11 caption, while the abstract and Section 6 state 3,868. Since 335 + 1,210 + 1,512 + 811 = 3,868, the 4,869 figure appears to be a typo and should be corrected consistently.
  2. [§3.3.1] The deployment threshold is described as 'the top 0.01 percentile', but 5,680 / 43,000,000 ≈ 0.013%, not 0.01%. Please make the percentile statement consistent with the actual number of recommendations.
  3. [§5] The meta-learner is described as advancing the ensemble method, but Figure 6 shows identical AUC for the meta-learner and simple averaging. This is acknowledged later in §5, but the earlier framing ('provides a more systematic approach') is somewhat overstated; consider tempering the language or showing a metric where the meta-learner helps.
  4. [§3.3.1] The grading scheme is subjective, but the procedure for resolving disagreements between CS and XH is not described. Please state how disagreements were settled (e.g., lower grade, discussion, or average) and report the number of disagreements or the inter-rater agreement.

Circularity Check

0 steps flagged

No significant circularity: catalog is generated by human inspection of model recommendations, not by a fitted parameter.

full rationale

The paper's central claim is a catalog of 811 visually-graded lens candidates, not a fitted physical quantity. The candidate count is produced by (i) training ResNet/EfficientNet on a fixed set of known lenses/nonlenses, (ii) applying the ensemble to ~43 million unseen cutouts, (iii) thresholding at the top 0.01% of meta-learner probabilities, and (iv) human grading of the 4578 images not matching known systems. None of these steps defines the output in terms of the input: the reported candidates were not in the training set, and the network's probability is not later reinterpreted as a lens confirmation. The AUC values (0.9984/0.9987/0.9989) are computed on a held-out split of the training labels and do not feed back into the candidate catalog. The purity estimates in Table 5 rest on an explicit assumption that new and rediscovered candidates share the same grade distribution; this is a modeling assumption rather than a derivation, and it is not the basis for the main '811' result. The paper does cite Papers I-III for the ResNet architecture and for 869 training lenses, but these are methodology/data reuse, not a self-citation used to prove the new candidates. Therefore, no circular step is exhibited.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The paper relies on standard assumptions in survey astronomy and machine learning: the Tractor galaxy typing, the reliability of literature training labels, and the validity of human visual grading. The free parameters are the selection thresholds and training-class balance, all chosen by hand. No new physical entities are introduced.

free parameters (3)
  • probability threshold for deployment = 0.9867 (meta-learner)
    Chosen to select the top 0.01% of recommendations (5680 images) for visual inspection; directly determines the yield and purity.
  • nonlens-to-lens ratio in training = 100:1
    Chosen by hand to better reflect the expected deployment ratio, up from 33:1 in Paper III; affects model calibration and precision.
  • z-band magnitude cut = 20.0 AB mag
    Selection criterion for candidate lens galaxies; initially tested in Paper I; affects survey volume and completeness.
axioms (3)
  • domain assumption The Tractor's morphological classification (SER, DEV, REX, EXP) correctly identifies galaxies suitable for lensing.
    The search is restricted to non-PSF objects classified by The Tractor; systematic misclassification would bias the candidate sample. Invoked in Section 2.1 and Section 4.1.
  • domain assumption Known lens catalogs used for training and cross-matching are reliable enough to serve as positive labels.
    Training labels come from a compilation of literature lenses and the authors' own candidates (Section 3.1); label noise directly propagates to the model.
  • domain assumption Visual inspection of ground-based cutouts is a valid ground truth for identifying strong lens candidates.
    The 811 candidates are classified by humans from 26 arcsecond cutouts at roughly 1.1 to 1.3 arcsecond seeing; this is the actual evidence for the central claim, cited in Sections 3.3 and 4.1.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Strong Lens Discoveries in DESI Legacy Imaging Surveys DR10 with Two Deep Learning Architectures." pith.science (2026). https://pith.science/paper/REZGSZVL

@misc{pith2026250820087,
  author       = {Pith},
  title        = {Pith review of: Strong Lens Discoveries in DESI Legacy Imaging Surveys DR10 with Two Deep Learning Architectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/REZGSZVL}},
  note         = {Machine review of arXiv:2508.20087}
}
Share X Bluesky LinkedIn Reddit HN
abstract

We have conducted a search for strong gravitational lensing systems in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 10 (DR10). This paper is the fourth in a series of searches (following Huang et al. 2020; Huang et al. 2021; Storfer et al. 2024, Paper I, II, & III respectively). This is the first catalog of lens candidates covering nearly the entirety of the extragalactic sky south of declination $\delta\approx +32$ deg, all of it observed by the DECam, covering $\sim$14,000 $deg^2$. We impose a $z$-band magnitude cut of < 20 in AB magnitude. We deploy a Residual Neural Network and EfficientNet as an ensemble trained on a compilation of known lensing systems and high-grade candidates as well as nonlenses in the same footprint. The predictions from these two base models are aggregated using a meta-learner. After applying our ensemble to the survey data, we exclude known candidates and systems, and use our own visual inspection portal to rank images in the top 0.01 percentile of all neural network recommendations. We have found 811 new lens candidates. These include 484 new candidates in the Legacy Surveys DR9 footprint, all parts of which have been searched for strong lenses at least once before, either by our group or others. Combining the discoveries from this work with those from Paper I (335), II (1210), and III (1512), we have discovered a total of 3868 new candidates in the DESI Legacy Surveys.

Figures

Figures reproduced from arXiv: 2508.20087 by A. Dey, A.D. Myers, A. Meisner, Brandt Kaufmann, Chaitanya Pasupala, Christopher J. Storfer, D.J. Schlegel, D. Lang, E. F. Schlafly, J. Moustakas, Jose Carlos Inchausti, S. Banka, Xiaosheng Huang, Yuan-Ming Hsu.

Figure 1
Figure 1. Figure 1: displays the z-band depth map of objects classified as SER with z < 20.0 mag in the Legacy Survey DR10. The figure also outlines the coverage of the DECaLS footprint in DR9, illustrating the overlapping regions as well as the additional areas newly observed in DR10. SER is the most common galaxy type in this magnitude regime [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The 1372 lenses included in the training sample over the depth map of the Legacy Surveys DR10 shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Left: Cross-entropy loss for the training and validation sets (left y-axis) and validation AUC (right y-axis) vs. training epochs. The vertical dashed black line at epoch 126 marks the point where the model achieved its highest AUC at 0.9984. This trained model was selected for deployment. Right: ROC curve for the validation set using the best-performing model from epoch 126. 3.2.2. EfficientNet Model For … view at source ↗
Figure 4
Figure 4. Figure 4: Left: Cross-entropy loss for the training and validation sets (left y-axis) and validation AUC (right y-axis) vs. the training epochs. The vertical dashed black line at epoch 50 marks the point where the model achieved its highest AUC. This trained model was selected for deployment. Right: ROC curve for the validation set using the best-performing model from epoch 50. The divergent behavior of the loss and… view at source ↗
Figure 5
Figure 5. Figure 5: Upper panel: The probability distributions on the validation set from the EfficientNet at the 50th epoch (clear blue) and at the 160th epoch (maroon outline), where the counts are shown in logarithmic scale. Lower panel: differences between counts at the 160th and 50th epoch (160th epoch - 50th epoch counts) in linear scale. The histogram shows a noticeable drop in the bins between the first and last in th… view at source ↗
Figure 6
Figure 6. Figure 6: ROCs for the base models individually (ResNet and EfficientNet), the meta-learner, and simple averaging of the base models’ predictions. The legend displays the AUC for each of these ROCs. Given that the two base models are trained on the same dataset, their predictions are inherently correlated. This correlation constrains the meta-learner’s ability to substantially outperform simple averaging of the base… view at source ↗
Figure 7
Figure 7. Figure 7: User interface of the visual inspection portal, displaying images from left to right: co-added image, and the g, r, and z bands. The candidate system DESI-316.3086-07.3386, identified for the first time on this paper, is shown as an example. In this case, the arc, and especially the counter-arc are more clearly visible in the g-band without the putative lens (the red galaxy at the center of the cutout, hig… view at source ↗
Figure 8
Figure 8. Figure 8: Twelve of the 811 new candidates found in this work, categorized into four groups: doubles, quads, arc-counterarc systems, and cluster/group lenses. The naming convention follows R.A. and decl. in decimal format. All images have north up and east to the left. The grade is shown at the top-right corner of each image, while the bottom-left corner indicates The Tractor type and the photometric redshift of the… view at source ↗
Figure 9
Figure 9. Figure 9: All 21 newly identified A-grade strong lens candidates located within the DR10 data but falling inside the previously mined DR9 footprint. The purity of systems by type is shown in [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The 811 new candidate lensing systems discovered in this work by grades over the depth map of the Legacy Surveys DR10 shown in [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Declination Right Ascension Papers I, II & III This work 330° 300° 270° 240° 210° 180° 150° 120° 90° 60° 30° -60° -60° -30° 0° 30° 30° 60° 60° 21.0 21.5 22.0 22.5 23.0 23.5 24.0 Magnitude Limit [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Left: lens spectroscopic redshift, zd,spec, stacked distributions of the candidates found in this work (SDSS Data Release 17 in dark red and DESI DR1 DESI Collaboration et al. (2025) in cyan), and photometric redshift, zd,phot, distribution from Zhou et al. (2021) in light red. When DR1 redshift is not available, SDSS redshift is reported. In the absence of DR1 and SDSS redshifts, photometric redshift is … view at source ↗
Figure 13
Figure 13. Figure 13: compares the output probabilities assigned by the ResNet and the EfficientNet for new candidates graded A, B, and C. Although both models achieve similar AUCs, they exhibit slight differences in their probability distributions. The EfficientNet assigns a broader range of probabilities, extending down to ∼ 0.86, whereas the ResNet probabilities only drop to ∼ 0.92. This suggests that the ResNet is more con… view at source ↗

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

93 extracted references · 18 canonical work pages · 3 internal anchors

  1. [1]

    F., Gladders, M

    Anguita, T., Barrientos, L. F., Gladders, M. D., et al. 2012, ApJ, 748, 129, doi: 10.1088/0004-637X/748/2/129

    work page doi:10.1088/0004-637x/748/2/129 2012

  2. [2]

    J., Galan, A., et al

    Birrer, S., Shajib, A. J., Galan, A., et al. 2020, arXiv e-prints, arXiv:2007.02941. https://arxiv.org/abs/2007.02941

    Pith/arXiv arXiv 2020

  3. [3]

    Moustakas, L. A. 2006, ApJ, 638, 703, doi: 10.1086/498884

    doi:10.1086/498884 2006

  4. [4]

    2000, ApJL, 534, L15, doi: 10.1086/312651

    Broadhurst, T., Huang, X., Frye, B., & Ellis, R. 2000, ApJL, 534, L15, doi: 10.1086/312651

    doi:10.1086/312651 2000

  5. [5]

    R., Bolton, A

    Brownstein, J. R., Bolton, A. S., Schlegel, D. J., et al. 2012, ApJ, 744, 41, doi: 10.1088/0004-637X/744/1/41 Ca˜ nameras, R., Schuldt, S., Suyu, S. H., et al. 2020, arXiv e-prints, arXiv:2004.13048. https://arxiv.org/abs/2004.13048 Ca˜ nameras, R., Schuldt, S., Shu, Y., et al. 2021, A&A, 653, L6, doi: 10.1051/0004-6361/202141758

    Pith/arXiv arXiv 2012

  6. [6]

    B., Suyu, S

    Caminha, G. B., Suyu, S. H., Grillo, C., & Rosati, P. 2022, A&A, 657, A83, doi: 10.1051/0004-6361/202141994

    doi:10.1051/0004-6361/202141994 2022

  7. [7]

    F., Anguita, T., et al

    Carrasco, M., Barrientos, L. F., Anguita, T., et al. 2017, ApJ, 834, 210, doi: 10.3847/1538-4357/834/2/210 C ¸ a˘ gan S ¸eng¨ ul, A., Dvorkin, C., Ostdiek, B., & Tsang, A. 2021, arXiv e-prints, arXiv:2112.00749. https://arxiv.org/abs/2112.00749

    Pith/arXiv arXiv 2017

  8. [8]

    Chan, J. H. H., Suyu, S. H., Sonnenfeld, A., et al. 2020, A&A, 636, A87, doi: 10.1051/0004-6361/201937030

    doi:10.1051/0004-6361/201937030 2020

  9. [9]

    L., Oguri, M., et al

    Chen, W., Kelly, P. L., Oguri, M., et al. 2022, Nature, 611, 256, doi: 10.1038/s41586-022-05252-5

    doi:10.1038/s41586-022-05252-5 2022

  10. [10]

    E., & Auger, M

    Collett, T. E., & Auger, M. W. 2014, MNRAS, 443, 969, doi: 10.1093/mnras/stu1190

    doi:10.1093/mnras/stu1190 2014

  11. [11]

    H., & Izbicki, R

    Coscrato, V., de Almeida In´ acio, M. H., & Izbicki, R. 2020, Neurocomputing, 399, 141, doi: https://doi.org/10.1016/j.neucom.2020.02.073 Strong Lenses in DESI Legacy Surveys DR10 19 Dark Energy Survey Collaboration, Abbott, T., Abdalla, F. B., et al. 2016, MNRAS, 460, 1270, doi: 10.1093/mnras/stw641

    work page doi:10.1016/j.neucom.2020.02.073 2020

  12. [12]

    2023, ApJS, 269, 61, doi: 10.3847/1538-4365/ad015a DESI Collaboration, Abdul-Karim, M., Adame, A

    Dawes, C., Storfer, C., Huang, X., et al. 2023, ApJS, 269, 61, doi: 10.3847/1538-4365/ad015a DESI Collaboration, Abdul-Karim, M., Adame, A. G., et al. 2025, arXiv e-prints, arXiv:2503.14745, doi: 10.48550/arXiv.2503.14745

    Pith/arXiv arXiv doi:10.48550/arxiv.2503.14745 2023

  13. [13]

    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

    doi:10.3847/1538-3881/ab089d 2019

  14. [14]

    T., Buckley-Geer, E

    Diehl, H. T., Buckley-Geer, E. J., Lindgren, K. A., et al. 2017, ApJS, 232, 15, doi: 10.3847/1538-4365/aa8667

    doi:10.3847/1538-4365/aa8667 2017

  15. [15]

    2021, MNRAS, 504, 5621, doi: 10.1093/mnras/stab1240

    Ding, X., Liao, K., Birrer, S., et al. 2021, MNRAS, 504, 5621, doi: 10.1093/mnras/stab1240

    doi:10.1093/mnras/stab1240 2021

  16. [16]

    L., Nidever, D

    Drlica-Wagner, A., Carlin, J. L., Nidever, D. L., et al. 2021, ApJS, 256, 2, doi: 10.3847/1538-4365/ac079d

    doi:10.3847/1538-4365/ac079d 2021

  17. [17]

    Measuring the Substructure Mass Power Spectrum of 23 SLACS Strong Galaxy-Galaxy Lenses with Convolutional Neural Networks

    Fagin, J., Vernardos, G., Tsagkatakis, G., et al. 2024, arXiv e-prints, arXiv:2403.13881, doi: 10.48550/arXiv.2403.13881

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2403.13881 2024

  18. [18]

    T., Honscheid, K., et al

    Flaugher, B., Diehl, H. T., Honscheid, K., et al. 2015, AJ, 150, 150, doi: 10.1088/0004-6256/150/5/150

    doi:10.1088/0004-6256/150/5/150 2015

  19. [19]

    L., Madore, B

    Freedman, W. L., Madore, B. F., Hoyt, T., et al. 2020, ApJ, 891, 57, doi: 10.3847/1538-4357/ab7339

    doi:10.3847/1538-4357/ab7339 2020

  20. [20]

    J., Treu, T., & Sonnenfeld, A

    Gavazzi, R., Marshall, P. J., Treu, T., & Sonnenfeld, A. 2014, ApJ, 785, 144, doi: 10.1088/0004-637X/785/2/144 Gonz´ alez, J., Holloway, P., Collett, T., et al. 2025, arXiv e-prints, arXiv:2501.15679, doi: 10.48550/arXiv.2501.15679

    Pith/arXiv arXiv doi:10.48550/arxiv.2501.15679 2014

  21. [21]

    H., Rosati, P., et al

    Grillo, C., Suyu, S. H., Rosati, P., et al. 2015, ApJ, 800, 38, doi: 10.1088/0004-637X/800/1/38

    doi:10.1088/0004-637x/800/1/38 2015

  22. [22]

    2023, A&A, 672, A123, doi: 10.1051/0004-6361/202245484

    He, Z., Li, N., Cao, X., et al. 2023, A&A, 672, A123, doi: 10.1051/0004-6361/202245484

    doi:10.1051/0004-6361/202245484 2023

  23. [23]

    2025, spherimatch: Cross-matching and self-matching in spherical coordinates, Astrophysics Source Code Library, ascl:2507.022

    Hsu, Y.-M. 2025, spherimatch: Cross-matching and self-matching in spherical coordinates, Astrophysics Source Code Library, ascl:2507.022

    2025

  24. [24]

    K., et al

    Huang, X., Morokuma, T., Fakhouri, H. K., et al. 2009, ApJ, 707, L12, doi: 10.1088/0004-637X/707/1/L12

    doi:10.1088/0004-637x/707/1/l12 2009

  25. [25]

    2020, The Astrophysical Journal, 894, 78, doi: 10.3847/1538-4357/ab7ffb

    Huang, X., Storfer, C., Ravi, V., et al. 2020, The Astrophysical Journal, 894, 78, doi: 10.3847/1538-4357/ab7ffb

    doi:10.3847/1538-4357/ab7ffb 2020

  26. [26]

    2021, ApJ, 909, 27, doi: 10.3847/1538-4357/abd62b

    Huang, X., Storfer, C., Gu, A., et al. 2021, ApJ, 909, 27, doi: 10.3847/1538-4357/abd62b

    doi:10.3847/1538-4357/abd62b 2021

  27. [27]

    H., Noebauer, U

    Huber, S., Suyu, S. H., Noebauer, U. M., et al. 2021, A&A, 646, A110, doi: 10.1051/0004-6361/202039218

    doi:10.1051/0004-6361/202039218 2021

  28. [28]

    2017, MNRAS, 471, 167, doi: 10.1093/mnras/stx1492

    McCarthy, C. 2017, MNRAS, 471, 167, doi: 10.1093/mnras/stx1492

    doi:10.1093/mnras/stx1492 2017

  29. [29]

    2019a, MNRAS, 484, 5330, doi: 10.1093/mnras/stz272 —

    Jacobs, C., Collett, T., Glazebrook, K., et al. 2019a, MNRAS, 484, 5330, doi: 10.1093/mnras/stz272 —. 2019b, ApJS, 243, 17, doi: 10.3847/1538-4365/ab26b6

    doi:10.1093/mnras/stz272

  30. [30]

    T., More, A., Oguri, M., et al

    Jaelani, A. T., More, A., Oguri, M., et al. 2020, MNRAS, 495, 1291, doi: 10.1093/mnras/staa1062

    doi:10.1093/mnras/staa1062 2020

  31. [31]

    T., Rusu, C

    Jaelani, A. T., Rusu, C. E., Kayo, I., et al. 2021, Monthly Notices of the Royal Astronomical Society, 502, 1487, doi: 10.1093/mnras/stab145

    doi:10.1093/mnras/stab145 2021

  32. [32]

    E., Irwin, J

    Johnson, L. E., Irwin, J. A., White, III, R. E., et al. 2018, ApJ, 856, 131, doi: 10.3847/1538-4357/aab430

    work page doi:10.3847/1538-4357/aab430 2018

  33. [33]

    P., et al

    Jullo, E., Natarajan, P., Kneib, J. P., et al. 2010, Science, 329, 924, doi: 10.1126/science.1185759

    doi:10.1126/science.1185759 2010

  34. [34]

    L., Holwerda, B

    Knabel, S., Steele, R. L., Holwerda, B. W., et al. 2020, AJ, 160, 223, doi: 10.3847/1538-3881/abb612

    work page doi:10.3847/1538-3881/abb612 2020

  35. [35]

    Kochanek, C. S. 1991, ApJ, 373, 354, doi: 10.1086/170057

    doi:10.1086/170057 1991

  36. [36]

    Koopmans, L. V. E., & Treu, T. 2002, ApJL, 568, L5, doi: 10.1086/340143

    doi:10.1086/340143 2002

  37. [37]

    Moustakas, L. A. 2006, ApJ, 649, 599, doi: 10.1086/505696

    doi:10.1086/505696 2006

  38. [38]

    W., & Mykytyn, D

    Lang, D., Hogg, D. W., & Mykytyn, D. 2016, The Tractor: Probabilistic astronomical source detection and measurement, Astrophysics Source Code Library. http://ascl.net/1604.008

    2016

  39. [39]

    2018, MNRAS, 473, 3895, doi: 10.1093/mnras/stx1665

    Lanusse, F., Ma, Q., Li, N., et al. 2018, MNRAS, 473, 3895, doi: 10.1093/mnras/stx1665

    doi:10.1093/mnras/stx1665 2018

  40. [40]

    R., Spiniello, C., et al

    Li, R., Napolitano, N. R., Spiniello, C., et al. 2021, ApJ, 923, 16, doi: 10.3847/1538-4357/ac2df0

    work page doi:10.3847/1538-4357/ac2df0 2021

  41. [41]

    E., Krawczyk, C

    Li, T., Collett, T. E., Krawczyk, C. M., & Enzi, W. 2024, MNRAS, 527, 5311, doi: 10.1093/mnras/stad3514

    doi:10.1093/mnras/stad3514 2024

  42. [42]

    Linder, E. V. 2016, PhRvD, 94, 083510, doi: 10.1103/PhysRevD.94.083510

    work page doi:10.1103/physrevd.94.083510 2016

  43. [43]

    2010, Reports on Progress in Physics, 73, 086901, doi: 10.1088/0034-4885/73/8/086901

    Massey, R., Kitching, T., & Richard, J. 2010, Reports on Progress in Physics, 73, 086901, doi: 10.1088/0034-4885/73/8/086901

    doi:10.1088/0034-4885/73/8/086901 2010

  44. [44]

    2020, Science, 369, 1347, doi: 10.1126/science.aax5164

    Meneghetti, M., Davoli, G., Bergamini, P., et al. 2020, Science, 369, 1347, doi: 10.1126/science.aax5164

    doi:10.1126/science.aax5164 2020

  45. [45]

    2023, A&A, 678, L2, doi: 10.1051/0004-6361/202346975

    Meneghetti, M., Cui, W., Rasia, E., et al. 2023, A&A, 678, L2, doi: 10.1051/0004-6361/202346975

    doi:10.1051/0004-6361/202346975 2023

  46. [46]

    B., Meneghetti, M., Avestruz, C., et al

    Metcalf, R. B., Meneghetti, M., Avestruz, C., et al. 2018, arXiv e-prints, arXiv:1802.03609. https://arxiv.org/abs/1802.03609

    Pith/arXiv arXiv 2018

  47. [47]

    2020, A&A, 639, A101, doi: 10.1051/0004-6361/201937351

    Millon, M., Galan, A., Courbin, F., et al. 2020, A&A, 639, A101, doi: 10.1051/0004-6361/201937351

    doi:10.1051/0004-6361/201937351 2020

  48. [48]

    2012, ApJ, 749, 38, doi: 10.1088/0004-637X/749/1/38

    More, A., Cabanac, R., More, S., et al. 2012, ApJ, 749, 38, doi: 10.1088/0004-637X/749/1/38

    work page doi:10.1088/0004-637x/749/1/38 2012

  49. [49]

    J., et al

    More, A., Verma, A., Marshall, P. J., et al. 2016, MNRAS, 455, 1191, doi: 10.1093/mnras/stv1965

    doi:10.1093/mnras/stv1965 2016

  50. [50]

    T., et al

    More, A., Ca˜ nameras, R., Jaelani, A. T., et al. 2024, MNRAS, 533, 525, doi: 10.1093/mnras/stae1597

    work page doi:10.1093/mnras/stae1597 2024

  51. [51]

    2014, MNRAS, 440, 2742, doi: 10.1093/mnras/stu376 20 Inchausti, Storfer, Huang et al

    Nordin, J., Rubin, D., Richard, J., et al. 2014, MNRAS, 440, 2742, doi: 10.1093/mnras/stu376 20 Inchausti, Storfer, Huang et al. O’Donnell, J. H., Wilkinson, R. D., Diehl, H. T., et al. 2022, ApJS, 259, 27, doi: 10.3847/1538-4365/ac470b

    work page doi:10.1093/mnras/stu376 2014

  52. [53]

    L., Pierel, J

    Pascale, M., Frye, B. L., Pierel, J. D. R., et al. 2024, arXiv e-prints, arXiv:2403.18902, doi: 10.48550/arXiv.2403.18902

    Pith/arXiv arXiv doi:10.48550/arxiv.2403.18902 2024

  53. [54]

    L., Pierel, J

    Pascale, M., Frye, B. L., Pierel, J. D. R., et al. 2025, The Astrophysical Journal, 979, 13, doi: 10.3847/1538-4357/ad9928

    doi:10.3847/1538-4357/ad9928 2025

  54. [55]

    W., et al

    Patel, B., McCully, C., Jha, S. W., et al. 2014, ApJ, 786, 9, doi: 10.1088/0004-637X/786/1/9

    work page doi:10.1088/0004-637x/786/1/9 2014

  55. [56]

    E., Tortora, C., Vernardos, G., et al

    Petrillo, C. E., Tortora, C., Vernardos, G., et al. 2019, MNRAS, 484, 3879, doi: 10.1093/mnras/stz189

    doi:10.1093/mnras/stz189 2019

  56. [57]

    Pierel, J. D. R., & Rodney, S. 2019, ApJ, 876, 107, doi: 10.3847/1538-4357/ab164a

    doi:10.3847/1538-4357/ab164a 2019

  57. [58]

    Pierel, J. D. R., Arendse, N., Ertl, S., et al. 2023, ApJ, 948, 115, doi: 10.3847/1538-4357/acc7a6

    doi:10.3847/1538-4357/acc7a6 2023

  58. [59]

    Pierel, J. D. R., Newman, A. B., Dhawan, S., et al. 2024, arXiv e-prints, arXiv:2404.02139, doi: 10.48550/arXiv.2404.02139 Planck Collaboration, Aghanim, N., Akrami, Y., et al. 2020, A&A, 641, A6, doi: 10.1051/0004-6361/201833910

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2404.02139 2024

  59. [60]

    1964, MNRAS, 128, 307, doi: 10.1093/mnras/128.4.307

    Refsdal, S. 1964, MNRAS, 128, 307, doi: 10.1093/mnras/128.4.307

    doi:10.1093/mnras/128.4.307 1964

  60. [61]

    G., Casertano, S., Yuan, W., et al

    Riess, A. G., Casertano, S., Yuan, W., et al. 2021, ApJL, 908, L6, doi: 10.3847/2041-8213/abdbaf

    doi:10.3847/2041-8213/abdbaf 2021

  61. [62]

    A., Strolger, L

    Rodney, S. A., Strolger, L. G., Kelly, P. L., et al. 2016, ApJ, 820, 50, doi: 10.3847/0004-637X/820/1/50

    work page doi:10.3847/0004-637x/820/1/50 2016

  62. [63]

    2021, Strong lens systems search in the Dark Energy Survey using Convolutional Neural Networks

    Rojas, K., Savary, E., Cl´ ement, B., et al. 2021, Strong lens systems search in the Dark Energy Survey using Convolutional Neural Networks. https://arxiv.org/abs/2109.00014

    Pith/arXiv arXiv 2021

  63. [64]

    2022, A&A, 668, A73, doi: 10.1051/0004-6361/202142119

    Rojas, K., Savary, E., Cl´ ement, B., et al. 2022, A&A, 668, A73, doi: 10.1051/0004-6361/202142119

    doi:10.1051/0004-6361/202142119 2022

  64. [65]

    2018, ApJ, 866, 65, doi: 10.3847/1538-4357/aad565

    Rubin, D., Hayden, B., Huang, X., et al. 2018, ApJ, 866, 65, doi: 10.3847/1538-4357/aad565

    work page doi:10.3847/1538-4357/aad565 2018

  65. [66]

    2018, CoRR, abs/1801.04381

    Chen, L. 2018, CoRR, abs/1801.04381

    Pith/arXiv arXiv 2018

  66. [67]

    2022, A&A, 666, A1, doi: 10.1051/0004-6361/202142505

    Savary, E., Rojas, K., Maus, M., et al. 2022, A&A, 666, A1, doi: 10.1051/0004-6361/202142505

    doi:10.1051/0004-6361/202142505 2022

  67. [68]

    Sharma, D., & Linder, E. V. 2022, arXiv e-prints, arXiv:2204.03020. https://arxiv.org/abs/2204.03020

    Pith/arXiv arXiv 2022

  68. [69]

    Retrospective Search for Strongly Lensed Supernovae in the DESI Legacy Imaging Surveys

    Sheu, W., Huang, X., Cikota, A., et al. 2024, ApJ, 973, 24, doi: 10.3847/1538-4357/ad5dad —. 2023, arXiv e-prints, arXiv:2301.03578, doi: 10.48550/arXiv.2301.03578

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2301.03578 2024

  69. [70]

    2022, A&A, 662, A4, doi: 10.1051/0004-6361/202243203

    Shu, Y., Ca˜ nameras, R., Schuldt, S., et al. 2022, A&A, 662, A4, doi: 10.1051/0004-6361/202243203

    doi:10.1051/0004-6361/202243203 2022

  70. [71]

    R., Bolton, A

    Shu, Y., Brownstein, J. R., Bolton, A. S., et al. 2017, ApJ, 851, 48, doi: 10.3847/1538-4357/aa9794

    doi:10.3847/1538-4357/aa9794 2017

  71. [72]

    2019, A&A, 622, A30, doi: 10.1051/0004-6361/201834260

    Sonnenfeld, A., Wang, W., & Bahcall, N. 2019, A&A, 622, A30, doi: 10.1051/0004-6361/201834260

    doi:10.1051/0004-6361/201834260 2019

  72. [73]

    Sonnenfeld, A., Chan, J. H. H., Shu, Y., et al. 2018, PASJ, 70, S29, doi: 10.1093/pasj/psx062

    doi:10.1093/pasj/psx062 2018

  73. [74]

    2020, arXiv e-prints, arXiv:2004.00634

    Sonnenfeld, A., Verma, A., More, A., et al. 2020, arXiv e-prints, arXiv:2004.00634. https://arxiv.org/abs/2004.00634

    Pith/arXiv arXiv 2020

  74. [75]

    2022, ApJ, 932, 107, doi: 10.3847/1538-4357/ac6d63

    Stein, G., Blaum, J., Harrington, P., Medan, T., & Luki´ c, Z. 2022, ApJ, 932, 107, doi: 10.3847/1538-4357/ac6d63

    work page doi:10.3847/1538-4357/ac6d63 2022

  75. [76]

    2024, ApJS, 274, 16, doi: 10.3847/1538-4365/ad527e

    Storfer, C., Huang, X., Gu, A., et al. 2024, ApJS, 274, 16, doi: 10.3847/1538-4365/ad527e

    doi:10.3847/1538-4365/ad527e 2024

  76. [77]

    J., Magnier, E

    Storfer, C. J., Magnier, E. A., Huang, X., et al. 2025, arXiv e-prints, arXiv:2505.05032, doi: 10.48550/arXiv.2505.05032

    Pith/arXiv arXiv doi:10.48550/arxiv.2505.05032 2025

  77. [78]

    H., Huber, S., Ca˜ nameras, R., et al

    Suyu, S. H., Huber, S., Ca˜ nameras, R., et al. 2020, arXiv e-prints, arXiv:2002.08378. https://arxiv.org/abs/2002.08378

    Pith/arXiv arXiv 2020

  78. [79]

    2014, arXiv e-prints, arXiv:1409.4842

    Szegedy, C., Liu, W., Jia, Y., et al. 2014, arXiv e-prints, arXiv:1409.4842. https://arxiv.org/abs/1409.4842

    Pith/arXiv arXiv 2014

  79. [80]

    S., Brownstein, J

    Talbot, M. S., Brownstein, J. R., Dawson, K. S., Kneib, J.-P., & Bautista, J. 2021, MNRAS, 502, 4617, doi: 10.1093/mnras/stab267

    work page doi:10.1093/mnras/stab267 2021

  80. [81]

    Tan, M., & Le, Q. V. 2019, ArXiv, abs/1905.11946

    Pith/arXiv arXiv 2019

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.