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REVIEW 3 major objections 6 minor 118 references

Predicting Halo Formation Time Using Machine Learning

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Galaxy observables, not merger trees, reveal when a dark matter halo formed.

desk verdict A useful set of linear fits for halo formation time from magnitude gaps, with a real but fixable validation flaw in the ML part. read the letter →

arxiv 2504.14426 v1 pith:G77W4Q7R submitted 2025-04-19 astro-ph.CO

Atulit Srivastava , Weiguang Cui , Daniel de Andres , Jesse B. Golden-Marx , Elena Rasia , Ying Zu This is my paper · ORCID
classification astro-ph.CO
keywords haloformationtimeassemblyhistorymachinelearningrandomforestconvolutionalneuralnetworkbrightestclustergalaxyintraclusterlightmagnitudegap
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the formation time of a dark matter halo—when it has acquired half of its current mass—can be predicted from observable galaxy properties rather than from its invisible merger history. Using cluster simulations, the authors train random forest, convolutional neural network, and simple linear models on halo, brightest-cluster-galaxy, and intracluster-light properties. Random forests recover formation time with median biases of 4% to 9% and scatter near 20%, while convolutional networks reduce median bias below 4% at the cost of slightly larger scatter. Strikingly, linear models using only two magnitude gaps and a BCG-to-satellite mass ratio perform about as well as the full random forest.

What carries the argument

The load-bearing object is t1/2 itself, defined through AHF merger trees as the epoch when the main progenitor has accreted half the halo's current mass. The predictive machinery has three tiers: random forests over the full set of halo, BCG, and intracluster-light features, with permutation importance identifying com_offset and the magnitude gaps M12 and M14 as dominant; convolutional networks trained on 6×40 radial property maps of stellar and gas mass, metallicity, age, and temperature, interpreted afterwards with saliency maps; and three explicit least-squares formulas in M12, M14, and MBCG/Msat that observers can apply directly.

What would settle it

Take the linear model of Eq. (4), apply it to halos from a different hydrodynamical simulation with different feedback physics, or to field and group-mass halos in the same simulation, and compare the predicted t1/2 with that simulation's merger-tree half-mass times. If the median relative bias exceeds about 10% or the scatter grows well beyond 0.27, the claim of transferable prediction is falsified. A sharper test removes dynamically disturbed halos and checks whether M12 still predicts t1/2; if the predictive power largely vanishes, the apparent signal is mainly dynamical state rather than formation epoch.

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Extended reading notes

Core claim

The central claim is that t1/2 is imprinted in baryonic observables, particularly the magnitude gaps between the brightest cluster galaxy and the second and fourth brightest substructures, the ratio of BCG stellar mass to satellite stellar mass, and the dynamical-state indicator com_offset. A random forest trained on all available halo and baryonic features reaches median relative errors between 4% and 9% with standard deviations of about 19% to 23%, while convolutional networks fed only six radially binned baryonic properties reach median biases of 0.4% to 4.1% with slightly larger scatter. Explicit linear relations—Eqs. 3, 4, and 5—give 3.5% to 5.3% bias and scatter of 0.25 to 0.27, matching random forest performance. The predicted formation times also reproduce the known correlations with halo mass and concentration.

Load-bearing premise

The load-bearing premise is that the relation between baryonic observables such as magnitude gaps and BCG-to-satellite mass ratio and halo assembly time is universal enough to survive outside the specific cluster zoom-in sample and baryonic feedback implementation on which the models were trained.

Editorial extensions

If this is right

  • If the linear relations hold beyond this training sample, observers can estimate cluster formation times from photometric magnitude gaps and BCG-to-satellite mass ratios alone, with no spectral or dynamical data.
  • The best random forest scatter of about 20% in t1/2 is enough to separate clusters into early- and late-forming samples for studies of environmental and assembly effects.
  • Reproducing the M200c-t1/2 and cNFW-t1/2 correlations with predicted values means the models can assign formation-time labels without tracing merger trees.
  • The low ranking of the ICL fraction in feature importance suggests surveys should prioritize magnitude gaps over intracluster-light fractions when targeting formation time.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The strong correlations of com_offset and M12 with t1/2 suggest the models may be reading dynamical state rather than assembly epoch per se; a control experiment that holds dynamical state fixed would isolate how much true assembly signal remains.
  • The linear calibration may be mass-dependent, so extending Eqs. 3-5 to group-mass halos below the cluster range would probably require refitting; this is testable on field or group simulations.
  • The CNN saliency ranges lying largely outside the BCG/ICL transition radius hint that outer stellar envelopes carry assembly information, which could be checked by measuring ICL colours and ages at roughly 60 to 100 kpc in real clusters.
  • Because only one baryonic feedback implementation was used, agreement of these relations with a different feedback model would be the strongest sign that the baryonic-to-assembly link is physical rather than simulation-specific.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper trains random forest (RF), convolutional neural network (CNN), and simple linear models to predict dark matter halo formation time t1/2 (the epoch when a halo has assembled half of its final mass) for 1,918 halos from the The300 Gizmo-Simba cluster zoom-in simulations. The RF models use six feature sets built from halo properties, BCG+ICL properties, and aperture-based baryonic properties; the CNNs take 2D radial maps of stellar and gas properties under three binning schemes; the linear models use the magnitude gaps M12 and M14 plus the mass ratio MBCG/Msat (Eqs. 3-5). Using a fixed 85/15 halo-level train/test split, the paper reports RF median relative biases of 4%-9% with ~20% scatter, CNN biases below 4% with somewhat larger scatter, and linear-model performance comparable to the RFs. The predictions are also shown to reproduce the M200c-t1/2 and cNFW-t1/2 trends and are compared with the Correa et al. (2015) EPS-based analytical relation.

Significance. If the reported accuracy is robust, the paper offers a practical, observationally motivated route to estimating halo formation time at cluster scales, and the simple linear relations in Eqs. 3-5 are directly usable by observers. The work is honest about its limitations: the results are explicitly stated to be specific to Gizmo-Simba physics (Section 7), the CNN saliency maps are acknowledged to be noisy and weakly correlated with t1/2 (Appendix B), and the ML pipeline is standard and well described. The main significance hinges on the credibility of the headline error metrics, which currently rest on a single halo-level split with no cluster-grouped validation and no quantitative baseline comparison; both issues are testable within the existing simulation suite and should be fixable in revision.

major comments (3)
  1. [Sec. 2, Sec. 3.1, Figs. 3 and 8] This is the most load-bearing issue because the central quantitative claims are the reported test-set accuracies, and the data structure makes the halo-independence assumption untenable.
  2. [Abstract, Sec. 5, Sec. 6, Eqs. 3-5] This is load-bearing because without a baseline the reported absolute scatter cannot be judged; the 'surpass' claim in the abstract is not quantitatively supported.
  3. [Sec. 3.1, Figs. 3, 8, and 12] This is a separate but related issue: even if the cluster-grouped split shows no leakage, the lack of error bars prevents any claim about which model is best.
minor comments (6)
  1. [Sec. 4.1] The handling of NaN values in the property maps is unclear: bins with absent gas particles are said to be 'excluded' from the maps, but the maps are then 'resized later on to have the same dimensions'; please specify whether the excluded bins are masked, imputed, or dropped before the resize, since this affects the CNN input data.
  2. [Sec. 4.1] The half-stellar-mass radius Rhalf from the CAESAR catalog is replaced by the linear-fit proxy Rhalf,fit because of a scatter of approximately 8.78 kpc, but the scatter is not characterized or propagated; please state whether this replacement biases the Binning Method 3 maps and whether the CNN results are sensitive to this choice.
  3. [Sec. 6] The brute-force selection of MBCG/Msat and M14 as additional linear-model features is described only qualitatively; please list the full set of candidate features tested and the specific scoring metric used to select each additional term.
  4. [Sec. 7 and Appendix B.2] The Conclusions quote biases of 7.3%-9.7% for the saliency-range RF models, but these results appear only in Appendix B.2 (Figure B.4); consider adding a one-line summary of these numbers in the main text so that the main-body conclusions are self-contained.
  5. [Figure B.4 caption] In the caption for the middle panel, 'as detailed in the first column of Table B.1' appears to be a typo; it should refer to the second column of Table B.1, since the panel corresponds to CNN Model 2.
  6. [Sec. 5] The Pearson correlation between M200c and predicted t1/2 is reported as ~0.52 for RF and ~0.46 for CNN, higher than the true correlation of 0.39; this regression-to-the-mean effect deserves a brief comment, as it indicates the models are somewhat more mass-driven than the actual t1/2 values.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: test-set predictions are learned from independent features and held-out evaluation.

full rationale

The paper's derivation chain is not circular. The target t1/2 is computed independently from AHF MERGERTREE mass-accretion histories (Sec. 2.2) and is never used as an input feature. RF features (Tables 1-3) and CNN map rows (Z*, t_age, M*, M_gas, Z_gas, T_gas) are independent halo and baryonic properties. RF and CNN test metrics are evaluated on a held-out 15% split (Sec. 3.1) after fitting on the 85% training set, so the reported errors are not fitted-input predictions. The linear models (Eqs. 3-5) are least-squares fits to the training sample and are then assessed on the same held-out test set; their coefficients are not derived from t1/2. Self-citations to The300, Gizmo-Simba, and Golden-Marx et al. serve as data provenance and prior motivation, not as load-bearing derivations. The paper explicitly acknowledges the Gizmo-Simba-specific scope in Sec. 7, which is a generalizability caveat rather than circularity. The remaining concerns—Z-score normalization computed over train and test combined, saliency-range selection that includes test maps, and the random halo-level rather than cluster-grouped split—are validation or leakage issues that could affect the reliability of the reported errors, but they do not make any prediction equivalent to its input by construction.

Assumptions & free parameters 10 free parameters · 6 assumptions · 0 invented entities

The central claim depends on fitted linear coefficients (Eqs. 3-5) and on several domain assumptions about simulation fidelity, sample representativeness, and the aperture-based definitions of BCG/ICL. No new physical entities are introduced.

free parameters (10)
  • Linear model 1: M12 slope = -4.26 Gyr per dex
    Least-squares fit to training data (Eq. 3).
  • Linear model 1: intercept = 8.91 Gyr
    Least-squares intercept in Eq. 3.
  • Linear model 2: M12 coefficient = -4.58 Gyr per dex
    Fitted in Eq. 4.
  • Linear model 2: MBCG/Msat coefficient = 0.12 Gyr
    Fitted in Eq. 4.
  • Linear model 2: intercept = 8.86 Gyr
    Fitted in Eq. 4.
  • Linear model 3: M12 coefficient = -3.53 Gyr per dex
    Fitted in Eq. 5.
  • Linear model 3: MBCG/Msat coefficient = 0.19 Gyr
    Fitted in Eq. 5.
  • Linear model 3: M14 coefficient = -1.48 Gyr per dex
    Fitted in Eq. 5.
  • Linear model 3: intercept = 9.91 Gyr
    Fitted in Eq. 5.
  • Rhalf-fit coefficients from CAESAR catalog
    Used in Binning Method 3 (Section 4.1) to estimate half-mass radii from stellar mass; derived from the CAESAR catalog, not from this paper, but the CNN Model 3 depends on it.
assumptions (6)
  • domain assumption The Gizmo-Simba baryonic physics implementation in The300 simulations provides a realistic mapping between baryonic properties and halo assembly history.
    The models are trained on these simulations and the results are only applicable to this physics (Section 2, Section 7).
  • domain assumption The AHF merger tree construction with the merit function N2ab/(NaNb) yields reliable main progenitor tracks for computing t1/2.
    t1/2 is the target variable and is computed from these merger trees (Section 2.2).
  • domain assumption The fixed aperture radii (30, 50, 100 kpc) and the particle selection for BCG and ICL provide physically meaningful features.
    Section 2.3; if the apertures exclude relevant stellar components, the feature-target correlations could be spurious or diluted.
  • domain assumption The selected sample of 1,918 halos from cluster zoom-in regions is sufficiently representative for learning the mass range without significant environmental bias.
    Section 2, Figure 2 shows a completeness bump; the sample is not volume-limited.
  • standard math Standard supervised learning assumption: the training and test split is independent and identically distributed.
    The ML performance metrics assume that test halos are drawn from the same distribution as training halos.
  • domain assumption The CAESAR catalog's half-mass radius estimates and the linear fit used for Rhalf,fit are accurate enough for Binning Method 3.
    Section 4.1; scatter in Rhalf values motivated the linear fit.

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Cite this review

Pith. "Pith review of Predicting Halo Formation Time Using Machine Learning." pith.science (2026). https://pith.science/paper/G77W4Q7R

@misc{pith2026250414426,
  author       = {Pith},
  title        = {Pith review of: Predicting Halo Formation Time Using Machine Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/G77W4Q7R}},
  note         = {Machine review of arXiv:2504.14426}
}
read the original abstract

Context:Halo formation time, which quantifies the mass assembly history of dark-matter halos, directly impacts galaxy properties and evolution. Although not directly observable, it can be inferred through proxies like star formation history or galaxy spatial distributions. Recent advances in machine learning enable more accurate predictions of halo formation time using galaxy and halo properties. Aims:This study aims to investigate a machine learning-based approach to predict halo formation time-defined as the epoch when a halo accretes half of its current mass-using both halo and baryonic properties derived from cosmological simulations. By incorporating properties associated with the brightest cluster galaxy located at the cluster center, its associated intracluster light component and satellite galaxies, we aim to surpass these analytical predictions, improve prediction accuracy and identify key properties that can provide the best proxy for the halo assembly history. Methods:Using The Three Hundred cosmological simulations, we train Random Forest (RF) and Convolutional Neural Network (CNN) models on halo and baryonic properties, such as mass, concentration, stellar and gas masses, and features of the brightest cluster galaxy and intracluster light. CNN models are trained on two-dimensional radial property maps. We also construct simple linear models using only observationally accessible features. Results:RF models show median biases of 4%-9% with standard deviations of 20%. CNN models reduce median bias to <4%, although they have higher scatter. Simple linear models using a limited number of observables achieve prediction accuracy comparable to RF models. Traditional relations between halo formation time and mass/concentration are preserved.

Figures

Figures reproduced from arXiv: 2504.14426 by the authors.

Figure 1
Figure 1. Scatter plot depicting the relationship between the logarithmic halo mass at z = 0 and t1/2 in Gyr for the selected sample of halos from The300. The red line represents the best-fit line that has been obtained by fitting a simple linear relation between the halo mass and the t1/2. We select all the gas, stars, black holes, and dark matter particles within the spheres defined by these three different aperture radii t… view at source ↗
Figure 2
Figure 2. The upper panel depicts the PDF of the t1/2 values denoted by t1/2 and the lower panel gives the histogram for the mass distribution for our selected halos sample used in this study. formly distributed datasets to avoid this source of bias. In our study, we implemented a weight to all the following ML training based on the distribution of the t1/2 in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Mean squared error (MSE) for the training, test, and out-of-bag samples for the six models trained using the RF algorithm to assess the model performance. Lastly, the importance of each feature for the six models we trained in our study was determined using the scikit-learn permutation_importance function Breiman (2001). The al￾gorithm works by first calculating the baseline performance of the model using a metric (… view at source ↗
Figures from the paper (9 more)
Figure 3
Figure 3. Figure 3: The left panel illustrates the relationship between the true and the predicted t1/2 values using the six trained RF models through a bi￾variate joint distribution or 2D probability density function. The black data points represent the scatter between the RF predictions…
Figure 5
Figure 5. Figure 5: Permutation importance of the features in the six different ran￾dom forest regressor models we considered in this study. However, the feature importance plot in [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Property maps for a halo with R200c = 1035.84 kpc/h and M200c = 2.58 × 1014h −1M⊙ with the three different binning methods. The M∗,half and Rhalf values for this halo from the CAESAR catalog are 6.85 × 1011h −1M⊙ and 23.18 kpc/h, respectively, while the half-mass radiu…
Figure 7
Figure 7. Figure 7: Architecture of the ‘single-channel’ CNN used in our study. Our network employs two convolutional pooling layers for feature extraction and two fully connected layers for parameter estimation. However, the scatter of the relative errors for the CNN pre￾dictions is slig…
Figure 8
Figure 8. Figure 8: The t1/2 predictions and their accuracy assessment for all three CNN models. The first panel corresponds to the model that used bin￾ning Methodology 1, the middle panel to binning Methodology 2, and the last panel to binning Methodology 3. The left column of the plot s…
Figure 9
Figure 9. Figure 9: Correlation between the halo mass M200c and t1/2 across different RF and CNN models. The first and second rows show the correlation trends for the six RF models discussed in Section 3, while the third row corresponds to the three CNN models described in Section 4. In e…
Figure 10
Figure 10. Figure 10: Scatter plot depicting the relation between the concentration pa￾rameter cNFW and t1/2 in Gyr for selected sample of halos from The300. The red line depicts the best-fit line obtained by fitting a simple linear relationship between cNFW and t1/2. decreases to 3.5%, ma…
Figure 11
Figure 11. Figure 11: Correlation between the halo concentration parameter cNFW and t1/2 across different RF and CNN models. The first and second rows show the correlation trends for the six RF models discussed in Section 3, while the third row corresponds to the three CNN models described…
Figure 12
Figure 12. Figure 12: The first panel compares the t1/2 predictions with the actual values for the test dataset using a linear model based solely on the mag￾nitude gap M12. The second and third panels show the linear model predictions when additional observable properties from Tables 2 and…

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Reference graph

Works this paper leans on

118 extracted references · 59 canonical work pages

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 ...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

  3. [3]

    M., Barnes , D

    Alonso Asensio , I., Dalla Vecchia , C., Bah \'e , Y. M., Barnes , D. J., & Kay , S. T. 2020, , 494, 1859

    2020

  4. [4]

    & Geetha, M

    Aloysius, N. & Geetha, M. 2017, in 2017 international conference on communication and signal processing (ICCSP), IEEE, 0588--0592

    2017

  5. [5]

    R., Perrott, Y

    Arendt, A. R., Perrott, Y. C., Contreras-Santos, A., et al. 2024, Monthly Notices of the Royal Astronomical Society, 530, 20

    2024

  6. [6]

    J., Kay, S

    Armitage, T. J., Kay, S. T., & Barnes, D. J. 2019, Monthly Notices of the Royal Astronomical Society, 484, 1526

    2019

  7. [7]

    2023, Astronomy & Astrophysics, 674, A179

    Bartalucci, I., Molendi, S., Rasia, E., et al. 2023, Astronomy & Astrophysics, 674, A179

    2023

  8. [8]

    2000, Dr

    Bradski, G. 2000, Dr. Dobb's Journal of Software Tools

    2000

Show all 118 references
  1. [9]

    2001, Machine learning, 45, 5

    Breiman, L. 2001, Machine learning, 45, 5

    2001

  2. [10]

    L., Bah \'e , Y

    Brough, S., Ahad, S. L., Bah \'e , Y. M., et al. 2024, Monthly Notices of the Royal Astronomical Society, 528, 771

    2024

  3. [11]

    S., Kolatt, T

    Bullock, J. S., Kolatt, T. S., Sigad, Y., et al. 2001, Monthly Notices of the Royal Astronomical Society, 321, 559

    2001

  4. [12]

    2015, Monthly Notices of the Royal Astronomical Society, 449, 2353

    Burke, C., Hilton, M., & Collins, C. 2015, Monthly Notices of the Royal Astronomical Society, 449, 2353

    2015

  5. [13]

    2021, Monthly Notices of the Royal Astronomical Society, 503, 6155

    Capalbo, V., De Petris, M., De Luca, F., et al. 2021, Monthly Notices of the Royal Astronomical Society, 503, 6155

    2021

  6. [14]

    2022, Monthly Notices of the Royal Astronomical Society, 514, 2692

    Chen, X., Zu, Y., Shao, Z., & Shan, H. 2022, Monthly Notices of the Royal Astronomical Society, 514, 2692

    2022

  7. [15]

    J., Li , C., et al

    Chen , Y., Mo , H. J., Li , C., et al. 2020, The Astrophysical Journal, 899, 81

    2020

  8. [16]

    2023, The Astrophysical Journal, 943, 148

    Chun, K., Shin, J., Smith, R., Ko, J., & Yoo, J. 2023, The Astrophysical Journal, 943, 148

    2023

  9. [17]

    2021, Galaxies, 9, 60

    Contini, E. 2021, Galaxies, 9, 60

    2021

  10. [18]

    2022, The Astrophysical Journal, 928, 99

    Contini, E., Chen, H., & Gu, Q. 2022, The Astrophysical Journal, 928, 99

    2022

  11. [19]

    2014, Monthly Notices of the Royal Astronomical Society, 437, 3787

    Contini, E., De Lucia, G., Villalobos, \'A ., & Borgani, S. 2014, Monthly Notices of the Royal Astronomical Society, 437, 3787

    2014

  12. [20]

    Contini, E. & Gu, Q. 2020, The Astrophysical Journal, 901, 128

    2020

  13. [21]

    Contini, E. & Gu, Q. 2021, The Astrophysical Journal, 915, 106

    2021

  14. [22]

    Contini, E., Rhee, J., Han, S., Jeon, S., & Sukyoung, K. Y. 2023, The Astronomical Journal, 167, 7

    2023

  15. [23]

    2024, arXiv preprint arXiv:2401.08283

    Contreras-Santos, A., Knebe, A., Cui, W., et al. 2024, arXiv preprint arXiv:2401.08283

    2024 arXiv

  16. [24]

    2023, Monthly Notices of the Royal Astronomical Society, 522, 1270

    Contreras-Santos, A., Knebe, A., Cui, W., et al. 2023, Monthly Notices of the Royal Astronomical Society, 522, 1270

    2023

  17. [25]

    2022, Monthly Notices of the Royal Astronomical Society, 511, 2897

    Contreras-Santos, A., Knebe, A., Pearce, F., et al. 2022, Monthly Notices of the Royal Astronomical Society, 511, 2897

    2022

  18. [26]

    A., Wyithe, J

    Correa, C. A., Wyithe, J. S. B., Schaye, J., & Duffy, A. R. 2015, Monthly Notices of the Royal Astronomical Society, 450, 1514

    2015

  19. [27]

    J., Gao, L., & White, S

    Croton, D. J., Gao, L., & White, S. D. 2007, Monthly Notices of the Royal Astronomical Society, 374, 1303

    2007

  20. [28]

    2022, Monthly Notices of the Royal Astronomical Society, 514, 977

    Cui, W., Dave, R., Knebe, A., et al. 2022, Monthly Notices of the Royal Astronomical Society, 514, 977

    2022

  21. [29]

    A., Angl \'e s-Alc \'a zar , D., & Yang , X

    Cui , W., Dav \'e , R., Peacock , J. A., Angl \'e s-Alc \'a zar , D., & Yang , X. 2021, Nature Astronomy, 5, 1069

    2021

  22. [30]

    2024, Monthly Notices of the Royal Astronomical Society, 534, 1247

    Cui, W., Jennings, F., Dave, R., Babul, A., & Gozaliasl, G. 2024, Monthly Notices of the Royal Astronomical Society, 534, 1247

    2024

  23. [31]

    2018, Monthly Notices of the Royal Astronomical Society, 480, 2898

    Cui, W., Knebe, A., Yepes, G., et al. 2018, Monthly Notices of the Royal Astronomical Society, 480, 2898

    2018

  24. [32]

    2014, Monthly Notices of the Royal Astronomical Society, 437, 816

    Cui, W., Murante, G., Monaco, P., et al. 2014, Monthly Notices of the Royal Astronomical Society, 437, 816

    2014

  25. [33]

    2016, Monthly Notices of the Royal Astronomical Society, 464, 2502

    Cui, W., Power, C., Borgani, S., et al. 2016, Monthly Notices of the Royal Astronomical Society, 464, 2502

    2016

  26. [34]

    2017, Monthly Notices of the Royal Astronomical Society, 464, 2502

    Cui, W., Power, C., Borgani, S., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 2502

    2017

  27. [35]

    B., Rasia , E., et al

    Darragh-Ford , E., Mantz , A. B., Rasia , E., et al. 2023, , 521, 790

    2023

  28. [36]

    2019, Monthly Notices of the Royal Astronomical Society, 486, 2827

    Dav \'e , R., Angl \'e s-Alc \'a zar, D., Narayanan, D., et al. 2019, Monthly Notices of the Royal Astronomical Society, 486, 2827

    2019

  29. [37]

    2022, Nature Astronomy, 6, 1325

    de Andres, D., Cui, W., Ruppin, F., et al. 2022, Nature Astronomy, 6, 1325

    2022

  30. [38]

    2024, Monthly Notices of the Royal Astronomical Society, 528, 1517

    de Andres, D., Cui, W., Yepes, G., et al. 2024, Monthly Notices of the Royal Astronomical Society, 528, 1517

    2024

  31. [39]

    2023, Monthly Notices of the Royal Astronomical Society, 518, 111

    de Andres, D., Yepes, G., Sembolini, F., et al. 2023, Monthly Notices of the Royal Astronomical Society, 518, 111

    2023

  32. [40]

    2021, Monthly Notices of the Royal Astronomical Society, 504, 5383

    De Luca, F., De Petris, M., Yepes, G., et al. 2021, Monthly Notices of the Royal Astronomical Society, 504, 5383

    2021

  33. [41]

    2018, Physics reports, 733, 1

    Desjacques, V., Jeong, D., & Schmidt, F. 2018, Physics reports, 733, 1

    2018

  34. [42]

    2023, Monthly Notices of the Royal Astronomical Society, 520, 4000

    Ferragamo, A., de Andres, D., Sbriglio, A., et al. 2023, Monthly Notices of the Royal Astronomical Society, 520, 4000

    2023

  35. [43]

    Gao, L., Springel, V., & White, S. D. 2005, Monthly Notices of the Royal Astronomical Society: Letters, 363, L66

    2005

  36. [44]

    2023, Monthly Notices of the Royal Astronomical Society, 518, 4238

    Gianfagna, G., Rasia, E., Cui, W., et al. 2023, Monthly Notices of the Royal Astronomical Society, 518, 4238

    2023

  37. [45]

    B., Miller, C., Zhang, Y., et al

    Golden-Marx, J. B., Miller, C., Zhang, Y., et al. 2022, The Astrophysical Journal, 928, 28

    2022

  38. [46]

    Golden-Marx, J. B. & Miller, C. J. 2018, The Astrophysical Journal, 860, 2

    2018

  39. [47]

    Golden-Marx, J. B. & Miller, C. J. 2019, The Astrophysical Journal, 878, 14

    2019

  40. [48]

    B., Zhang, Y., Ogando, R., et al

    Golden-Marx, J. B., Zhang, Y., Ogando, R., et al. 2024, arXiv preprint arXiv:2409.02184

    2024 arXiv

  41. [49]

    H., Zabludoff, A

    Gonzalez, A. H., Zabludoff, A. I., & Zaritsky, D. 2005, The Astrophysical Journal, 618, 195

    2005

  42. [50]

    E., Pearce, F

    Haggar, R., Gray, M. E., Pearce, F. R., et al. 2020, Monthly Notices of the Royal Astronomical Society, 492, 6074

    2020

  43. [51]

    2010, The Astrophysical Journal, 717, 420

    Jee, M. 2010, The Astrophysical Journal, 717, 420

    2010

  44. [52]

    & Dupke, R

    Jim \'e nez-Teja, Y. & Dupke, R. 2016, The Astrophysical Journal, 820, 49

    2016

  45. [53]

    2018, , 857, 79

    Jim \'e nez-Teja , Y., Dupke , R., Ben \' tez , N., et al. 2018, , 857, 79

    2018

  46. [54]

    2018, The Astrophysical Journal, 857, 79

    Jim \'e nez-Teja, Y., Dupke, R., Ben \' tez, N., et al. 2018, The Astrophysical Journal, 857, 79

    2018

  47. [55]

    C., Brough, S., Dolag, K., et al

    Kimmig, L. C., Brough, S., Dolag, K., et al. 2025, arXiv preprint arXiv:2503.20857

    2025 arXiv

  48. [56]

    Kingma, D. P. & Ba, J. 2014, arXiv preprint arXiv:1412.6980

    2014 arXiv

  49. [57]

    2016, Monthly Notices of the Royal Astronomical Society, 457, 4340

    Klypin, A., Yepes, G., Gottl \"o ber, S., Prada, F., & Hess, S. 2016, Monthly Notices of the Royal Astronomical Society, 457, 4340

    2016

  50. [58]

    Knollmann, S. R. & Knebe, A. 2009, The Astrophysical Journal Supplement Series, 182, 608

    2009

  51. [59]

    2018, Astronomy Letters, 44, 8

    Kravtsov, A., Vikhlinin, A., & Meshcheryakov, A. 2018, Astronomy Letters, 44, 8

    2018

  52. [60]

    & Bernstein, R

    Krick, J. & Bernstein, R. 2007, The Astronomical Journal, 134, 466

    2007

  53. [61]

    2015, nature, 521, 436

    LeCun, Y., Bengio, Y., & Hinton, G. 2015, nature, 521, 436

    2015

  54. [62]

    1998, Proceedings of the IEEE, 86, 2278

    LeCun, Y., Bottou, L., Bengio, Y., & Haffner, P. 1998, Proceedings of the IEEE, 86, 2278

    1998

  55. [63]

    2008, Monthly Notices of the Royal Astronomical Society, 389, 1419

    Li, Y., Mo, H., & Gao, L. 2008, Monthly Notices of the Royal Astronomical Society, 389, 1419

    2008

  56. [64]

    2016, Monthly Notices of the Royal Astronomical Society, 455, 499

    Lim, S., Mo, H., Wang, H., & Yang, X. 2016, Monthly Notices of the Royal Astronomical Society, 455, 499

    2016

  57. [65]

    2016, The Astrophysical Journal, 819, 119

    Lin, Y.-T., Mandelbaum, R., Huang, Y.-H., et al. 2016, The Astrophysical Journal, 819, 119

    2016

  58. [66]

    C., Wilkins, S

    Lovell, C. C., Wilkins, S. M., Thomas, P. A., et al. 2022, Monthly Notices of the Royal Astronomical Society, 509, 5046

    2022

  59. [67]

    2023, Monthly Notices of the Royal Astronomical Society, 524, 1746

    Lucie-Smith, L., Barreira, A., & Schmidt, F. 2023, Monthly Notices of the Royal Astronomical Society, 524, 1746

    2023

  60. [68]

    D., Navarro, J

    Ludlow, A. D., Navarro, J. F., Li, M., et al. 2012, Monthly Notices of the Royal Astronomical Society, 427, 1322

    2012

  61. [69]

    Mann, A. W. & Ebeling, H. 2012, Monthly Notices of the Royal Astronomical Society, 420, 2120

    2012

  62. [70]

    A., et al

    Matthee, J., Schaye, J., Crain, R. A., et al. 2016, Monthly Notices of the Royal Astronomical Society, stw2884

    2016

  63. [71]

    G., Schaye, J., Ponman, T

    McCarthy, I. G., Schaye, J., Ponman, T. J., et al. 2010, Monthly Notices of the Royal Astronomical Society, 406, 822

    2010

  64. [72]

    C., Harding, P., Feldmeier, J., & Morrison, H

    Mihos, J. C., Harding, P., Feldmeier, J., & Morrison, H. 2005, The Astrophysical Journal, 631, L41

    2005

  65. [73]

    2016, Physical Review Letters, 116, 041301

    Miyatake, H., More, S., Takada, M., et al. 2016, Physical Review Letters, 116, 041301

    2016

  66. [74]

    2010, Galaxy formation and evolution (Cambridge University Press)

    Mo, H., Van den Bosch, F., & White, S. 2010, Galaxy formation and evolution (Cambridge University Press)

    2010

  67. [75]

    2020, Interpretable machine learning (Lulu

    Molnar, C. 2020, Interpretable machine learning (Lulu. com)

    2020

  68. [76]

    S., & Santucci, G

    Montes, M., Brough, S., Owers, M. S., & Santucci, G. 2021, The Astrophysical Journal, 910, 45

    2021

  69. [77]

    2016, The Astrophysical Journal, 825, 39

    More, S., Miyatake, H., Takada, M., et al. 2016, The Astrophysical Journal, 825, 39

    2016

  70. [78]

    2019, Monthly Notices of the Royal Astronomical Society, 483, 3390

    Mostoghiu, R., Knebe, A., Cui, W., et al. 2019, Monthly Notices of the Royal Astronomical Society, 483, 3390

    2019

  71. [79]

    & Hinton, G

    Nair, V. & Hinton, G. E. 2010, in Proceedings of the 27th international conference on machine learning (ICML-10), 807--814

    2010

  72. [80]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. 1997, The Astrophysical Journal, 490, 493

    1997

  73. [81]

    2011, the Journal of machine Learning research, 12, 2825

    Pedregosa, F., Varoquaux, G., Gramfort, A., et al. 2011, the Journal of machine Learning research, 12, 2825

    2011

  74. [82]

    2018, Monthly Notices of the Royal Astronomical Society, 475, 648

    Pillepich, A., Nelson, D., Hernquist, L., et al. 2018, Monthly Notices of the Royal Astronomical Society, 475, 648

    2018

  75. [83]

    Planck Collaboration , e. a. 2016, Astronomy &amp; Astrophysics, 594, A13

    2016

  76. [84]

    Power, C., Knebe, A., & Knollmann, S. R. 2012, Monthly Notices of the Royal Astronomical Society, 419, 1576

    2012

  77. [85]

    A., Cuesta, A

    Prada, F., Klypin, A. A., Cuesta, A. J., Betancort-Rijo, J. E., & Primack, J. 2012, Monthly Notices of the Royal Astronomical Society, 423, 3018

    2012

  78. [86]

    2014, Astronomy and Astrophysics, 565, A126

    Presotto , V., Girardi , M., Nonino , M., et al. 2014, Astronomy and Astrophysics, 565, A126

    2014

  79. [87]

    2022, Astronomy & Astrophysics, 666, A22

    Ragagnin, A., Andreon, S., & Puddu, E. 2022, Astronomy & Astrophysics, 666, A22

    2022

  80. [88]

    2013, The Astronomical Review, 8, 40

    Rasia , E., Meneghetti , M., & Ettori , S. 2013, The Astronomical Review, 8, 40

    2013

  81. [89]

    2017, Monthly Notices of the Royal Astronomical Society, 464, 3742

    Remus, R.-S., Dolag, K., Naab, T., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 3742

    2017

  82. [90]

    S., Mihos, J

    Rudick, C. S., Mihos, J. C., Harding, P., et al. 2010, The Astrophysical Journal, 720, 569

    2010

  83. [91]

    2024, arXiv preprint arXiv:2405.17239

    Santoni, S., De Petris, M., Yepes, G., et al. 2024, arXiv preprint arXiv:2405.17239

    2024 arXiv

  84. [92]

    D., Weller, J., Ostriker, J

    Shaw, L. D., Weller, J., Ostriker, J. P., & Bode, P. 2006, The Astrophysical Journal, 646, 815

    2006

  85. [93]

    2013, arXiv preprint arXiv:1312.6034

    Simonyan, K., Vedaldi, A., & Zisserman, A. 2013, arXiv preprint arXiv:1312.6034

    2013 arXiv

  86. [94]

    R., et al

    Srisawat, C., Knebe, A., Pearce, F. R., et al. 2013, Monthly Notices of the Royal Astronomical Society, 436, 150

    2013

  87. [95]

    2024, Monthly Notices of the Royal Astronomical Society, 528, 4451

    Srivastava, A., Cui, W., Meneghetti, M., et al. 2024, Monthly Notices of the Royal Astronomical Society, 528, 4451

    2024

  88. [96]

    2010, The Astrophysical Journal, 718, 23

    Stott, J., Collins, C., Sahl \'e n, M., et al. 2010, The Astrophysical Journal, 718, 23

    2010

  89. [97]

    M., Prijon, T., & Seljak, U

    Sullivan, J. M., Prijon, T., & Seljak, U. 2023, Journal of Cosmology and Astroparticle Physics, 2023, 004

    2023

  90. [98]

    & More, S

    Sunayama, T. & More, S. 2019, Monthly Notices of the Royal Astronomical Society, 490, 4945

    2019

  91. [99]

    A., et al

    Tojeiro , R., Eardley , E., Peacock , J. A., et al. 2017, , 470, 3720

    2017

  92. [100]

    2016, , 821, 116

    Umetsu , K., Zitrin , A., Gruen , D., et al. 2016, , 821, 116

    2016

  93. [101]

    2021, The Astrophysical Journal, 915, 71

    Villaescusa-Navarro, F., Angl \'e s-Alc \'a zar, D., Genel, S., et al. 2021, The Astrophysical Journal, 915, 71

    2021

  94. [102]

    Z., Cypriano, E

    Vitorelli, A. Z., Cypriano, E. S., Makler, M., et al. 2018, Monthly Notices of the Royal Astronomical Society, 474, 866

    2018

  95. [103]

    2020, arXiv preprint arXiv:2012.00111

    Wadekar, D., Villaescusa-Navarro, F., Ho, S., & Perreault-Levasseur, L. 2020, arXiv preprint arXiv:2012.00111

    2020 arXiv

  96. [104]

    J., Chen , Y., et al

    Wang , K., Mo , H. J., Chen , Y., et al. 2024, Monthly Notices of the Royal Astronomical Society, 528, 2046

    2024

  97. [105]

    M., De Lucia, G., & Yang, X

    Wang, L., Weinmann, S. M., De Lucia, G., & Yang, X. 2013, Monthly Notices of the Royal Astronomical Society, 433, 515

    2013

  98. [106]

    F., Hearin, A

    Watson, D. F., Hearin, A. P., Berlind, A. A., et al. 2015, Monthly Notices of the Royal Astronomical Society, 446, 651

    2015

  99. [107]

    H., Bullock , J

    Wechsler , R. H., Bullock , J. S., Primack , J. R., Kravtsov , A. V., & Dekel , A. 2002, , 568, 52

    2002

  100. [108]

    Wechsler, R. H. & Tinker, J. L. 2018, Annual Review of Astronomy and Astrophysics, 56, 435

    2018

  101. [109]

    H., Zentner , A

    Wechsler , R. H., Zentner , A. R., Bullock , J. S., Kravtsov , A. V., & Allgood , B. 2006, , 652, 71

    2006

  102. [110]

    White, S. D. M. & Rees, M. J. 1978, Monthly Notices of the Royal Astronomical Society, 183, 341

    1978

  103. [111]

    Wong, A. W. & Taylor, J. E. 2012, The Astrophysical Journal, 757, 102

    2012

  104. [112]

    Yang, X., Mo, H., & van den Bosch, F. C. 2006, The Astrophysical Journal, 638, L55

    2006

  105. [113]

    2018, The Astrophysical Journal, 853, 84

    Zehavi, I., Contreras, S., Padilla, N., et al. 2018, The Astrophysical Journal, 853, 84

    2018

  106. [114]

    2022, Monthly Notices of the Royal Astronomical Society, 516, 26

    Zhang, B., Cui, W., Wang, Y., Dave, R., & De Petris, M. 2022, Monthly Notices of the Royal Astronomical Society, 516, 26

    2022

  107. [115]

    2019, The astrophysical journal, 874, 165

    Zhang, Y., Yanny, B., Palmese, A., et al. 2019, The astrophysical journal, 874, 165

    2019

  108. [116]

    D., Schneider, D

    Zibetti, S., White, S. D., Schneider, D. P., & Brinkmann, J. 2005, Monthly Notices of the Royal Astronomical Society, 358, 949

    2005

  109. [117]

    Zu, Y., Mandelbaum, R., Simet, M., Rozo, E., & Rykoff, E. S. 2017, Monthly Notices of the Royal Astronomical Society, 470, 551

    2017

  110. [118]

    2021, Monthly Notices of the Royal Astronomical Society, 505, 5117

    Zu, Y., Shan, H., Zhang, J., et al. 2021, Monthly Notices of the Royal Astronomical Society, 505, 5117

    2021

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