Pith. sign in

REVIEW 3 major objections 5 minor 70 references

De-baryonifying halos via optimal transport

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper proposes a field-level de-baryonification method that selects the maximum-likelihood gravity-only halo on a fixed optimal-transport-cost hypersurface and shows it recovers the true convergence power-spectrum suppression in…

desk verdict A sound, clearly written proof-of-concept for optimal-transport de-baryonification, but the headline power-spectrum recovery relies on an oracle transport cost and needs the T-to-proxy gap closed before it is a usable forward model. read the letter →

arxiv 2411.18399 v1 pith:IMQRJIQ5 submitted 2024-11-27 astro-ph.CO

Leander Thiele This is my paper · ORCID
classification astro-ph.CO PACS 98.80.-k98.62.Sb
keywords baryonicfeedbackoptimaltransportweakgravitationallensingde-baryonificationnormalizingflowconvergencepowerspectrumIllustrisTNGfield-levelinference
open problems Dark Matter
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

Baryonic feedback—gas being blown out of halos by supermassive black holes and supernovae—changes the projected matter density in a way that mimics weaker cosmological clustering in weak-lensing surveys. This paper proposes that the right way to remove that effect is optimal transport: instead of fitting nuisance parameters, find the gravity-only mass map that costs the least (in a transport sense) to reach from the observed full-physics map, subject to a fixed total cost. As a proof of concept on IllustrisTNG halos, the author samples gravity-only halos from a normalizing flow trained on dark-matter-only simulations, constrained to lie on the surface of fixed optimal transport cost around each full-physics halo. The maximum-posterior samples of this constrained distribution reproduce the true suppression of the convergence power spectrum; the posterior average does not. If this generalizes to full convergence maps, it would give weak-lensing analyses a field-level way to fold in baryonic feedback without assuming a specific feedback model.

What carries the argument

The central object is the entropy-regularized optimal transport plan $T_{hd}$ between the full-physics projected halo and a candidate gravity-only halo, computed with the Sinkhorn algorithm using the squared Euclidean cost matrix $M_{ab} = \tfrac{1}{2}\|r_a - r_b\|^2$. The likelihood for a candidate is Eq. (5): the learned gravity-only density $p(x_d|M_{\mathrm{vir}})$ times a narrow Gaussian in $\log(|T_{hd}|/T)$ with $\sigma_{\log T} = 0.01\,\mathrm{dex}$ times a power law $|T_{hd}|^{-\alpha}$ with $\alpha = 10$ that counteracts the growing volume of transport plans. A masked autoregressive normalizing flow learns the gravity-only halo distribution from dark-matter-only simulations, pre-trained on a range of simulation boxes and fine-tuned on a run matched to the IllustrisTNG resolution, and Hamiltonian Monte Carlo samples the posterior; the maximum-likelihood sample is the de-baryonified halo.

What would settle it

Run the de-baryonification pipeline with the transport cost replaced by a value predicted from the thermal Sunyaev-Zel'dovich or baryon-fraction correlation plotted in Fig. 1, and check whether the resulting set of halos still recovers the true convergence power-spectrum suppression; if it does not, the method is not usable as a forward model. A second test: repeat the whole procedure on a hydrodynamic simulation with a different feedback implementation—if the squared-Euclidean cost matrix and the empirical cost–feedback correlation fail to reproduce that simulation's suppression, the method does not generalize beyond IllustrisTNG.

Watch

Extended reading notes

Core claim

The central claim is that baryonic feedback can be undone at the field level without a detailed feedback model. For each full-physics halo $x_h$, the author defines the de-baryonified halo as the point of maximum posterior under the learned gravity-only distribution $p(x_d|M_{\mathrm{vir}})$ on the hypersurface where the entropy-regularized optimal transport cost between $x_h$ and $x_d$ equals the true cost $T$ (Eq. 5). Across $3 \times 3926$ halos from IllustrisTNG-300 at $z=0$, the maximum-posterior samples of this constrained distribution reproduce the true one-halo suppression $C_h/C_d - 1$ of the convergence power spectrum, while the posterior average does not. The paper interprets the match as evidence that the fixed-transport-cost slice through the gravity-only posterior is highly informative, and that individual-halo scatter is large because many gravity-only configurations share the same transport cost.

Load-bearing premise

The whole pipeline succeeds only when the optimal transport cost between a full-physics halo and its gravity-only counterpart is taken from the true simulated gravity-only halo; in a real analysis that cost would have to be predicted from observable feedback proxies, and the paper does not show that prediction works.

Editorial extensions

If this is right

  • If the method holds at full-map level, weak lensing field-level analyses can account for baryonic feedback by conditioning on an optimal transport cost instead of adding nuisance parameters to a baryonification model.
  • The posterior mean is not a valid de-baryonified map; only the maximum-posterior point recovers the power spectrum, so any field-level use of this approach must preserve the MAP solution.
  • Because the transport cost correlates with both thermal Sunyaev-Zel'dovich Y-deviation and baryon fraction, astrophysical feedback measurements could in principle provide the cost estimate needed to run the method on real data without knowing the gravity-only truth.
  • Individual halo de-baryonification is multimodal—there are many plausible gravity-only configurations at one transport cost—so aggregate statistics, not single-halo matching, are the right target for validation.

Reading between the lines

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

  • If the empirical cost–feedback correlation survives across different feedback models, de-baryonification could replace baryonification as the default field-level feedback model, since it starts from maximum ignorance and adds only the transport cost as an external input.
  • The sensitivity of the result to the cost matrix (squared versus square-rooted Euclidean) suggests the method is implicitly choosing a metric; finding a physically motivated metric, perhaps tied to gravitational potential energy, could make the method transferable to other feedback implementations.
  • The normalizing flow's poor out-of-distribution behavior, which the paper observes but says does not affect these results, is likely to matter more when applying the method to full convergence maps where the target lives far from the training distribution; energy-based models or diffusion alternatives may be needed.
  • A fully Bayesian de-baryonification without a fixed $T$ would require computing the volume element of the transport-cost hypersurface; the power-law approximation in Eq. (5) is a placeholder, and deriving that volume term would remove the need for an external feedback proxy.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper proposes a field-level 'de-baryonification' method based on optimal transport: given a projected full-physics halo map, it samples gravity-only maps from a normalizing-flow prior subject to a likelihood that fixes the optimal transport cost between the full-physics and gravity-only maps. The transport cost is argued to correlate with baryonic feedback strength (Fig. 1). The method is applied to individual halos from IllustrisTNG-300, using a normalizing flow pre-trained on several gravity-only simulations and fine-tuned on miniUchuu. Hamiltonian Monte Carlo sampling of the likelihood (Eq. 5) yields posterior samples; the maximum-posterior samples are then used to compute the one-halo convergence power spectrum suppression. The paper reports that these MAP de-baryonified halos reproduce the true suppression Ch/Cd - 1 in Fig. 3, while the posterior average does not. The authors are careful to frame the work as a proof of concept and to list several open issues, including the need to connect transport cost to observable feedback proxies and the cost-matrix dependence.

Significance. If the result holds, it is a novel and interesting proof-of-concept: it demonstrates that a macroscopic, simulation-based prior plus an optimal-transport constraint can recover a nontrivial field-level summary of baryonic feedback, complementing existing baryonification approaches. The design has genuine strengths: the prior is trained on independent gravity-only simulations, so the central demonstration is not circular; the use of HMC with a normalizing-flow likelihood is technically sound; and the paper is admirably honest about its limitations, including the oracle nature of the transport cost and the heuristic likelihood. However, the current evidence for the central claim is conditional on knowing the true optimal transport cost T, and the absence of uncertainty estimates on Fig. 3 leaves the strength of the claim somewhat open. The significance is therefore substantial but presently partial: the method is demonstrated as an oracle-conditioned inversion, not yet as a usable forward model from observable feedback indicators.

major comments (3)
  1. [Sec. II D and Sec. III (Eq. 5, Fig. 3)] The central result is obtained by conditioning on the true optimal transport cost T, evaluated on the matched gravity-only halo from the simulation. In a real weak-lensing application T is not observed; as the paper itself states in Sec. IV, the relation between optimal transport cost and observable feedback strength (e.g., tSZ Y or baryon fraction) is only an empirical correlation with visible scatter and no calibration. Thus, the claim that 'the set of de-baryonified halos reproduces the correct convergence power spectrum suppression' is currently demonstrated only for an oracle input. To make the forward-model claim load-bearing, the paper should either demonstrate end-to-end de-baryonification with T estimated from the proxies of Fig. 1 (including a scatter model), or explicitly re-frame the result as a conditional proof of concept with a quantitative sensitivity analysis to errors in T.
  2. [Sec. III (Fig. 3)] Fig. 3 shows the MAP suppression recovering the ground truth, but no error bars or uncertainty bands are provided. Given that the posterior average fails, it is important to establish that the MAP result is not an artifact of HMC noise, chain non-convergence, or the particular set of 3926 halos. At minimum, the authors should report uncertainties from multiple chains, bootstrap resampling of halos, or the posterior spread of the suppression; without this, the reader cannot judge whether the agreement is statistically significant or fortuitous.
  3. [Sec. II C and II D (Eq. 4, Eq. 5)] The likelihood is a heuristic construction: a log-normal term in |T_hd| with sigma_logT = 0.01 dex, plus an ad hoc power-law volume correction with alpha = 10. The paper states that the results are not very sensitive to alpha, but no evidence is shown for this claim. In addition, the cost matrix choice (squared Euclidean versus square-rooted) changes the prediction qualitatively, and the paper notes it is unclear whether the chosen cost matrix generalizes to other feedback implementations. Since these choices are made after seeing the IllustrisTNG test set, the key result lacks a validation on an independent hydrodynamical simulation or a systematic sensitivity analysis. This is not a fatal flaw for a proof of concept, but it needs to be addressed or explicitly scoped to make the central claim robust.
minor comments (5)
  1. [Sec. II B] The word 'dimesional' should be 'dimensional' in the discussion of the tSNE visualizations.
  2. [Sec. IV] There are several typos: 'oberved' should be 'observed', and 'astrohpysical' should be 'astrophysical'.
  3. [Introduction] The sentence 'This partial degeneracy may be responsible for the apparent mismatch in measurements of the clustering amplitude S8 between the cosmicmicrowavebackgroundandweakgravitational lensing' has missing spaces and should be reworded.
  4. [Fig. 3] The horizontal axis is labeled 'angular wavenumber', but the text refers to the convergence power spectrum; please clarify whether the axis is multipole ell or wavenumber k, and consistently use the corresponding notation.
  5. [Sec. II C] The sentence 'Thus, the presented methodology does indeed perform something non-trivial' would be clearer as 'Thus, the presented methodology does indeed perform something non-trivial, in that the result depends on the cost metric.'

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the de-baryonification result is conditional on an oracle transport cost, but the target power-spectrum suppression is not defined by that cost and the derivation uses an independently trained gravity-only prior.

full rationale

The load-bearing steps are: (1) training the normalizing flow prior p(xd|Mvir) on gravity-only simulations (miniUchuu, Quijote, MDPL2/SMDPL, Uchuu), which are independent of the IllustrisTNG test set; (2) defining the optimal transport cost |Thd| via Eqs. (3)-(4); (3) the likelihood Eq. (5), which conditions on a fixed cost T evaluated on the true gravity-only halo; and (4) taking the maximum-posterior sample from HMC. The reported success is that these MAP halos reproduce the convergence power-spectrum suppression Ch/Cd - 1. This suppression is not an input anywhere: T is a scalar summary of the true map, not the suppression itself, and many maps with the same T exist (Fig. 4 shows large per-halo scatter). The paper's own controls demonstrate non-triviality: the posterior average, which also lies on the same fixed-cost slice, fails to reproduce the suppression, and the square-rooted cost matrix gives an incorrect prediction, so the MAP result is not forced by the conditioning alone. The use of the true T is an explicit proof-of-concept choice; Section IV states that relating T to observable feedback proxies requires future work. That is a missing demonstration of a full forward model, not a circular derivation. The only self-citation ([5], Grandon et al.) is contextual in the introduction and not load-bearing.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

No new physical entities are introduced. The method has three hand-chosen parameters or choices (alpha, sigma_log_T, cost metric), plus the empirical correlation between OT cost and feedback as a central assumption.

free parameters (3)
  • Volume-correction power-law index alpha = 10
    Introduced in Eq. (5) to counteract the volume effect of transport plans; the paper states results are insensitive to this choice without showing sensitivity.
  • Transport-cost spread sigma_log_T = 0.01 dex
    Width of the log-normal likelihood in Eq. (5); chosen small to approximate a hard slice at fixed OT cost.
  • Transport cost metric choice = squared Euclidean (1/2 ||r_a - r_b||^2)
    A modeling choice: the square-rooted metric leads to an incorrect power spectrum suppression (Section II C), so the metric is selected after seeing test results.
assumptions (3)
  • domain assumption Optimal transport cost correlates with baryonic feedback strength (Fig. 1)
    The entire method is motivated by this empirical correlation; it is not derived and is known to be noisy.
  • ad hoc to paper The likelihood Eq. (5) adequately approximates the conditional distribution at fixed OT cost
    The slice of p(xd|Mvir) at fixed |Thd| is modeled as a log-normal plus power-law volume correction; no exact construction is provided.
  • domain assumption Gravity-only simulations (miniUchuu etc.) are an adequate prior for TNG gravity-only halos
    The normalizing flow is trained on external gravity-only simulations and used as p(xd|Mvir) for TNG halos; resolution and cosmology are matched approximately.

how reviews work

0 comments
Cite this review

Pith. "Pith review of De-baryonifying halos via optimal transport." pith.science (2026). https://pith.science/paper/IMQRJIQ5

@misc{pith2026241118399,
  author       = {Pith},
  title        = {Pith review of: De-baryonifying halos via optimal transport},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMQRJIQ5}},
  note         = {Machine review of arXiv:2411.18399}
}
read the original abstract

Baryonic feedback uncertainty is a limiting systematic for next-generation weak gravitational lensing analyses. At the same time, high-resolution weak lensing maps are best analyzed at the field-level. Thus, robustly accounting for the baryonic effects in the projected matter density field is required. Ideally, constraints on feedback strength from astrophysical probes should be folded into the weak lensing field-level likelihood. We propose a macroscopic method based on an empirical correlation between feedback strength and an optimal transport cost. Since feedback is local re-distribution of matter, optimal transport is a promising concept. In this proof-of-concept, we de-baryonify projected mass around individual halos in the IllustrisTNG simulation. We choose the de-baryonified solution as the point of maximum likelihood on the hypersurface defined by fixed optimal transport cost around the observed full-physics halos. The likelihood is approximated through a normalizing flow trained on multiple gravity-only simulations. We find that the set of de-baryonified halos reproduces the correct convergence power spectrum suppression. There is considerable scatter when considering individual halos. We outline how the optimal transport de-baryonification concept can be generalized to full convergence maps.

Figures

Figures reproduced from arXiv: 2411.18399 by the authors.

Figure 1
Figure 1. Illustration of the relationship between optimal [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Visualizations of latent space in our generative [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The power spectrum suppression computed as de [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Illustration of the structure of probability space. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 4
Figure 4. Figure 4: Some randomly chosen example halos. Left column [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

70 extracted references · 18 canonical work pages

  1. [1]

    Since all elements of xd are physically expected to be non-zero positive,xd takes values on the standard simplex.2 It is beneficial to map the 256 dimensional simplex to R255

    Data transformation Due to the normalization to unit mass, the data di- mensionality is 16 × 16 − 1 = 255 . Since all elements of xd are physically expected to be non-zero positive,xd takes values on the standard simplex.2 It is beneficial to map the 256 dimensional simplex to R255. We perform this mapping using the isometric log-ratio (ILR) trans- form [...

    work page

  2. [2]

    We will use the Illustris TNG-300 simulation [45–50] as a test set

    Training data Constructingthetrainingsetisslightlynon-trivial. We will use the Illustris TNG-300 simulation [45–50] as a test set. Therefore, ideally we need to match both resolution and cosmological parameters in our training set. Among the publically available gravity-only simulations, we find miniUchuu [51–55] to be the ideal choice as its cosmol- ogy ...

    work page

  3. [3]

    overlap bias

    Inspecting the trained model Sampling from the trained normalizing flow yields the correct mean and covariance matrix. 3 For the MAF, we use the implementation inzuko. Figure 2. Visualizations of latent space in our generative model for gravity-only halos. The compression from 256 to 2 dimensions is performed using tSNE. From left to right, we progress th...

    work page

  4. [4]

    Amon and G

    A. Amon and G. Efstathiou, Mon. Not. Roy. Astron. Soc. 516, 5355 (2022), arXiv:2206.11794 [astro-ph.CO]

    arXiv 2022

  5. [5]

    Hadzhiyskaet al., arXiv e-prints , arXiv:2407.07152 (2024), arXiv:2407.07152 [astro-ph.CO]

    B. Hadzhiyskaet al., arXiv e-prints , arXiv:2407.07152 (2024), arXiv:2407.07152 [astro-ph.CO]

    arXiv 2024

  6. [6]

    Elbers et al., arXiv e-prints , arXiv:2403.12967 (2024), arXiv:2403.12967 [astro-ph.CO]

    W. Elbers et al., arXiv e-prints , arXiv:2403.12967 (2024), arXiv:2403.12967 [astro-ph.CO]

    arXiv 2024

  7. [7]

    Bigwood et al., arXiv e-prints , arXiv:2404.06098 (2024), arXiv:2404.06098 [astro-ph.CO]

    L. Bigwood et al., arXiv e-prints , arXiv:2404.06098 (2024), arXiv:2404.06098 [astro-ph.CO]

    arXiv 2024

  8. [8]

    Grandón, G

    D. Grandón, G. A. Marques, L. Thiele, S. Cheng, M. Shi- rasaki, and J. Liu, arXiv e-prints , arXiv:2403.03807 (2024), arXiv:2403.03807 [astro-ph.CO]

    arXiv 2024

Show all 70 references
  1. [9]

    Terasawa et al., arXiv e-prints , arXiv:2403.20323 (2024), arXiv:2403.20323 [astro-ph.CO]

    R. Terasawa et al., arXiv e-prints , arXiv:2403.20323 (2024), arXiv:2403.20323 [astro-ph.CO]

    2024 arXiv

  2. [10]

    Salcido and I

    J. Salcido and I. G. McCarthy, arXiv e-prints , arXiv:2409.05716 (2024), arXiv:2409.05716 [astro- ph.CO]

    2024 arXiv

  3. [11]

    M.Fong, M.Choi, V.Catlett, B.Lee, A.Peel, R.Bowyer, L. J. King, and I. G. McCarthy, Mon. Not. Roy. Astron. Soc. 488, 3340 (2019), arXiv:1907.03161 [astro-ph.CO]

    2019 arXiv

  4. [12]

    Liu and M

    J. Liu and M. S. Madhavacheril, Phys. Rev. D99, 083508 (2019), arXiv:1809.10747 [astro-ph.CO]

    2019 arXiv

  5. [13]

    Ferlitoet al., Mon

    F. Ferlitoet al., Mon. Not. Roy. Astron. Soc.524, 5591 (2023), arXiv:2304.12338 [astro-ph.CO]

    2023 arXiv

  6. [14]

    Asgariet al., Astron

    M. Asgariet al., Astron. Astrophys.645, A104 (2021), arXiv:2007.15633 [astro-ph.CO]

    2021 arXiv

  7. [15]

    Amon et al., Phys

    A. Amon et al., Phys. Rev. D 105, 023514 (2022), arXiv:2105.13543 [astro-ph.CO]

    2022

  8. [16]

    Dalal et al., Phys

    R. Dalal et al., Phys. Rev. D 108, 123519 (2023), arXiv:2304.00701 [astro-ph.CO]

    2023 arXiv

  9. [17]

    Li et al

    X. Li et al. , Phys. Rev. D 108, 123518 (2023), arXiv:2304.00702 [astro-ph.CO]

    2023 arXiv

  10. [18]

    A. J. Mead, J. A. Peacock, C. Heymans, S. Joudaki, and A. F. Heavens, Mon. Not. Roy. Astron. Soc.454, 1958 (2015), arXiv:1505.07833 [astro-ph.CO]

    2015 arXiv

  11. [19]

    A. J. Mead, C. Heymans, L. Lombriser, J. A. Peacock, O. I. Steele, and H. A. Winther, Mon. Not. Roy. Astron. Soc. 459, 1468 (2016), arXiv:1602.02154 [astro-ph.CO]

    2016 arXiv

  12. [20]

    Huang, T

    H.-J. Huang, T. Eifler, R. Mandelbaum, and S. Do- delson, Mon. Not. Roy. Astron. Soc.488, 1652 (2019), arXiv:1809.01146 [astro-ph.CO]

    2019 arXiv

  13. [21]

    A. J. Mead, S. Brieden, T. Tröster, and C. Hey- mans, Mon. Not. Roy. Astron. Soc. 502, 1401 (2021), arXiv:2009.01858 [astro-ph.CO]

    2021 arXiv

  14. [22]

    Huang et al., Mon

    H.-J. Huang et al., Mon. Not. Roy. Astron. Soc. 502, 6010 (2021), arXiv:2007.15026 [astro-ph.CO]

    2021 arXiv

  15. [23]

    M. P. van Daalen, I. G. McCarthy, and J. Schaye, Mon. Not. Roy. Astron. Soc. 491, 2424 (2020), arXiv:1906.00968 [astro-ph.CO]

    2020 arXiv

  16. [24]

    M. L. van Loon and M. P. van Daalen, Mon. Not. Roy. Astron. Soc.528, 4623 (2024), arXiv:2309.06479 [astro- ph.CO]

    2024 arXiv

  17. [25]

    Porqueres, A

    N. Porqueres, A. Heavens, D. Mortlock, G. Lavaux, and T. L. Makinen, arXiv e-prints , arXiv:2304.04785 (2023), arXiv:2304.04785 [astro-ph.CO]

    2023 arXiv

  18. [26]

    Dai and U

    B. Dai and U. Seljak, Proceedings of the National Academy of Science121, e2309624121 (2024)

    2024

  19. [27]

    Schneider and R

    A. Schneider and R. Teyssier, J. Cosmol. Astropart. Phys.2015, 049 (2015), arXiv:1510.06034 [astro-ph.CO]

    2015 arXiv

  20. [28]

    Schneider, N

    A. Schneider, N. Stoira, A. Refregier, A. J. Weiss, M. Kn- abenhans, J. Stadel, and R. Teyssier, J. Cosmol. As- tropart.Phys. 2020,019(2020),arXiv:1910.11357[astro- ph.CO]

    2020 arXiv

  21. [29]

    Aricò, R

    G. Aricò, R. E. Angulo, C. Hernández-Monteagudo, S. Contreras, M. Zennaro, M. Pellejero-Ibañez, and Y. Rosas-Guevara, Mon. Not. Roy. Astron. Soc. 495, 4800 (2020), arXiv:1911.08471 [astro-ph.CO]. 9

    2020 arXiv

  22. [30]

    Aricò and R

    G. Aricò and R. E. Angulo, arXiv e-prints , arXiv:2406.01672 (2024), arXiv:2406.01672 [astro- ph.CO]

    2024 arXiv

  23. [31]

    Anbajagane, S

    D. Anbajagane, S. Pandey, and C. Chang, arXiv e-prints , arXiv:2409.03822 (2024), arXiv:2409.03822 [astro-ph.CO]

    2024 arXiv

  24. [32]

    Aricò, R

    G. Aricò, R. E. Angulo, C. Hernández-Monteagudo, S. Contreras, and M. Zennaro, Mon. Not. Roy. Astron. Soc. 503, 3596 (2021), arXiv:2009.14225 [astro-ph.CO]

    2021 arXiv

  25. [33]

    M. E. Lee, T. Lu, Z. Haiman, J. Liu, and K. Osato, Mon. Not.Roy.Astron.Soc. 519,573(2023),arXiv:2201.08320 [astro-ph.CO]

    2023 arXiv

  26. [34]

    B. Dai, Y. Feng, and U. Seljak, J. Cosmol. Astropart. Phys.2018, 009 (2018), arXiv:1804.00671 [astro-ph.CO]

    2018 arXiv

  27. [35]

    Sharma, B

    D. Sharma, B. Dai, F. Villaescusa-Navarro, and U. Seljak, arXiv e-prints , arXiv:2401.15891 (2024), arXiv:2401.15891 [astro-ph.CO]

    2024 arXiv

  28. [36]

    Laureijs, J

    R. Laureijs, J. Amiaux, S. Arduini, J. L. Auguères, J. Brinchmann, R. Cole, et al. , arXiv e-prints , arXiv:1110.3193 (2011), arXiv:1110.3193 [astro-ph.CO]

    2011 arXiv

  29. [37]

    Takada, R

    M. Takada, R. S. Ellis, M. Chiba, J. E. Greene, H. Ai- hara, et al., Publ. Astron. Soc. Jpn. 66, R1 (2014), arXiv:1206.0737 [astro-ph.CO]

    2014 arXiv

  30. [38]

    Spergel, N

    D. Spergel, N. Gehrels, C. Baltay, D. Bennett, J. Breck- inridge, et al., arXiv e-prints , arXiv:1503.03757 (2015), arXiv:1503.03757 [astro-ph.IM]

    2015 arXiv

  31. [39]

    Ivezić, S

    Ž. Ivezić, S. M. Kahn, J. A. Tyson, B. Abel, E. Acosta, et al., Astrophys. J. 873, 111 (2019), arXiv:0805.2366 [astro-ph]

    2019 arXiv

  32. [40]

    Nikakhtar, R

    F. Nikakhtar, R. K. Sheth, B. Lévy, and R. Mohayaee, Phys. Rev. Lett.129, 251101 (2022), arXiv:2203.01868 [astro-ph.CO]

    2022 arXiv

  33. [41]

    Nikakhtar, N

    F. Nikakhtar, N. Padmanabhan, B. Lévy, R. K. Sheth, and R. Mohayaee, Phys. Rev. D 108, 083534 (2023), arXiv:2307.03671 [astro-ph.CO]

    2023 arXiv

  34. [42]

    Nikakhtar, R

    F. Nikakhtar, R. K. Sheth, N. Padmanabhan, B. Lévy, and R. Mohayaee, Phys. Rev. D 109, 123512 (2024), arXiv:2403.11951 [astro-ph.CO]

    2024 arXiv

  35. [43]

    Wadekaret al., Mon

    D. Wadekaret al., Mon. Not. Roy. Astron. Soc.522, 2628 (2023), arXiv:2209.02075 [astro-ph.CO]

    2023 arXiv

  36. [44]

    Pandeyet al., Mon

    S. Pandeyet al., Mon. Not. Roy. Astron. Soc.525, 1779 (2023), arXiv:2301.02186 [astro-ph.CO]

    2023 arXiv

  37. [45]

    Martin-Alvarez, V

    S. Martin-Alvarez, V. Iršič, S. Koudmani, M. Bourne, L. Bigwood, and D. Sijacki, arXiv e-prints (2024), arXiv:2407.18349 [astro-ph.CO]

    2024 arXiv

  38. [46]

    P.S.Behroozi, R.H.Wechsler,andH.-Y.Wu,Astrophys. J. 762, 109 (2013), arXiv:1110.4372 [astro-ph.CO]

    2013 arXiv

  39. [47]

    Aitchison, Journal of the Royal Statisti- cal Society: Series B (Methodological) 44, 139 (1982), https://academic.oup.com/jrsssb/article- pdf/44/2/139/49097906/jrsssb_44_2_139.pdf

    J. Aitchison, Journal of the Royal Statisti- cal Society: Series B (Methodological) 44, 139 (1982), https://academic.oup.com/jrsssb/article- pdf/44/2/139/49097906/jrsssb_44_2_139.pdf

    1982

  40. [48]

    Nelsonet al., Mon

    D. Nelsonet al., Mon. Not. Roy. Astron. Soc.475, 624 (2018), arXiv:1707.03395 [astro-ph.GA]

    2018 arXiv

  41. [49]

    Marinacci et al., Mon

    F. Marinacci et al., Mon. Not. Roy. Astron. Soc.480, 5113 (2018), arXiv:1707.03396 [astro-ph.CO]

    2018 arXiv

  42. [50]

    J. P. Naimanet al., Mon. Not. Roy. Astron. Soc.477, 1206 (2018), arXiv:1707.03401 [astro-ph.GA]

    2018 arXiv

  43. [51]

    Pillepichet al., Mon

    A. Pillepichet al., Mon. Not. Roy. Astron. Soc.475, 648 (2018), arXiv:1707.03406 [astro-ph.GA]

    2018 arXiv

  44. [52]

    Springelet al., Mon

    V. Springelet al., Mon. Not. Roy. Astron. Soc.475, 676 (2018), arXiv:1707.03397 [astro-ph.GA]

    2018 arXiv

  45. [53]

    Nelsonet al., Computational Astrophysics and Cos- mology 6, 2 (2019), arXiv:1812.05609 [astro-ph.GA]

    D. Nelsonet al., Computational Astrophysics and Cos- mology 6, 2 (2019), arXiv:1812.05609 [astro-ph.GA]

    2019 arXiv

  46. [54]

    Prada, P

    F. Prada, P. Behroozi, T. Ishiyama, A. Klypin, and E. Pérez, arXiv e-prints , arXiv:2304.11911 (2023), arXiv:2304.11911 [astro-ph.GA]

    2023 arXiv

  47. [55]

    Aunget al., Mon

    H. Aunget al., Mon. Not. Roy. Astron. Soc.519, 1648 (2023), arXiv:2209.12918 [astro-ph.GA]

    2023 arXiv

  48. [56]

    C. A. Dong-Páezet al., Mon. Not. Roy. Astron. Soc.528, 7236 (2024), arXiv:2208.00540 [astro-ph.CO]

    2024 arXiv

  49. [57]

    Oogi et al., Mon

    T. Oogi et al., Mon. Not. Roy. Astron. Soc.525, 3879 (2023), arXiv:2207.14689 [astro-ph.GA]

    2023 arXiv

  50. [58]

    506,4210 (2021), arXiv:2007.14720 [astro-ph.CO]

    T.Ishiyama et al.,Mon.Not.Roy.Astron.Soc. 506,4210 (2021), arXiv:2007.14720 [astro-ph.CO]

    2021 arXiv

  51. [59]

    Villaescusa-Navarroet al., Astrophys

    F. Villaescusa-Navarroet al., Astrophys. J. Suppl.250, 2 (2020), arXiv:1909.05273 [astro-ph.CO]

    2020 arXiv

  52. [60]

    Prada, A

    F. Prada, A. A. Klypin, A. J. Cuesta, J. E. Betancort- Rijo, and J. Primack, Mon. Not. Roy. Astron. Soc.423, 3018 (2012), arXiv:1104.5130 [astro-ph.CO]

    2012 arXiv

  53. [61]

    Papamakarios, T

    G. Papamakarios, T. Pavlakou, and I. Murray, in Advances in Neural Information Processing Systems , Vol. 30, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., 2017)

    2017

  54. [62]

    Huang, D

    C.-W. Huang, D. Krueger, A. Lacoste, and A. Courville, in Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Re- search, Vol. 80, edited by J. Dy and A. Krause (PMLR,

  55. [63]

    Van der Maaten and G

    L. Van der Maaten and G. Hinton, Journal of machine learning research9 (2008)

    2008

  56. [64]

    Nalisnick, A

    E. Nalisnick, A. Matsukawa, Y. Teh, D. Gorur, and B. Lakshminarayanan, in International Conference on Learning Representations(2019)

    2019

  57. [65]

    Du and I

    Y. Du and I. Mordatch, inAdvances in Neural Informa- tion Processing Systems, Vol. 32, edited by H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett (Curran Associates, Inc., 2019)

    2019

  58. [66]

    Knopp and R

    P. Knopp and R. Sinkhorn, Pacific Journal of Mathemat- ics 21, 343 (1967)

    1967

  59. [67]

    Feydy, T

    J. Feydy, T. Séjourné, F.-X. Vialard, S.-i. Amari, A. Trouve, and G. Peyré, inProceedings of the Twenty- Second International Conference on Artificial Intelli- gence and Statistics , Proceedings of Machine Learn- ing Research, Vol. 89, edited by K. Chaudhuri and M. Sugiyama (P...

    2019

  60. [68]

    Cooray, W

    A. Cooray, W. Hu, and J. Miralda-Escudé, Astrophys. J. Lett. 535, L9 (2000), arXiv:astro-ph/0003205 [astro-ph]

    2000 arXiv

  61. [69]

    A. Y. Tong, G. Huguet, A. Natik, K. MacDonald, M. Kuchroo, R. Coifman, G. Wolf, and S. Krish- naswamy,in International Conference on Machine Learn- ing (PMLR, 2021) pp. 10336–10346

    2021

  62. [70]

    M.S.Albergo, N.M.Boffi,andE.Vanden-Eijnden,arXiv preprint arXiv:2303.08797 (2023)

    2023 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.