Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

Arkaprabha Ganguli; Emil Constantinescu; Julie Bessac; Nesar Ramachandra

REVIEW 5 major objections 6 minor 59 references

Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets

T0 review · 5 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read Aux-VAE aligns each known generative factor with a dedicated latent dimension while residual latents absorb unknown factors and preserve reconstruction.

desk verdict A plausible semi-supervised disentanglement method for scientific images, but the paper currently overclaims because the regularizer as written and the LDS evaluation targets may both be about encoder means, not the sampled latent space. read the letter →

arxiv 2507.00298 v1 pith:VRGW3OE6 submitted 2025-06-30 stat.ML cs.LG

Arkaprabha Ganguli , Nesar Ramachandra , Julie Bessac , Emil Constantinescu This is my paper · ORCID

classification stat.MLcs.LG MSC 68T0762H20

keywords disentangledrepresentationlearningvariationalautoencoderauxiliaryvariablesposteriorregularizationgenerativefactorsLinearDisentanglementScorescientificimagedatasetsgalaxysimulations

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

The paper introduces Aux-VAE, a modification of the variational autoencoder that uses observed auxiliary variables to separate known generative factors from everything else. It claims that by conditioning the latent prior on these auxiliary variables and adding two correlation-based regularizers, each known factor aligns with its own dedicated latent dimension while residual latent dimensions absorb unknown factors and keep reconstruction quality high. The authors report Linear Disentanglement Scores up to 0.94 on simulated galaxy images, well above the 0.73 of the closest competing method, with reconstruction matching a plain VAE. A reader should care because scientific datasets often come with partial side information about the physical parameters that generated the data, and this method promises to use that information to make learned representations interpretable without sacrificing generative accuracy.

What carries the argument

The central object is the conditional Gaussian prior of Eq. (3), which places the auxiliary values $u_j$ on the first $d$ latent coordinates with small variance $1/n$ and a standard normal prior on the remaining coordinates. Working from it, the paper derives inter-independence ($u\perp z_{\mathrm{recon}}$), intra-independence ($u_j\perp z_{\mathrm{aux},j'}$ for $j\neq j'$), and explicitness ($\mathbb{E}[z_{\mathrm{aux},j}|u]=u_j$) as properties of the ideal posterior. Because the KL divergence to the expected variational posterior is intractable, the method replaces it with regularizers that measure, through polynomial powers of the variables, correlations between $u$ and the encoder mean $\mu_\phi$; these become the $R^K_0$ and $R^K_1$ terms in the loss. The Linear Disentanglement Score then evaluates the result by comparing the strongest absolute correlation between each $u_j$ and a latent dimension against the sum over all latent dimensions.

What would settle it

Recompute the reported LDS and latent-traversal results using sampled latent values $z\sim q_\phi(z|x)$ instead of the encoder means $\mu_\phi(x)$; if the sampled-latent LDS falls substantially below the mean-based LDS on the galaxy dataset, the claim that the regularized objective disentangles the generative distribution rather than only its conditional means is false.

Watch

Extended reading notes

Core claim

The paper's core claim is that a VAE whose prior is set to $p(z|u)=\mathcal{N}((u_1,\ldots,u_d,0,\ldots,0),\operatorname{diag}(n^{-1} I_d, I_{d_Z-d}))$, with the latent vector partitioned into $z_{\mathrm{aux}}$ and $z_{\mathrm{recon}}$, and whose loss adds polynomial-correlation regularizers between the auxiliary variables and the encoder means, produces a latent space in which each known generative factor $u_j$ is captured almost exclusively by one latent dimension $z_{\mathrm{aux},j}$. The residual dimensions are intentionally left entangled so they can collectively represent unknown factors, and the method is scored with a new bounded metric, the Linear Disentanglement Score, that measures how sharply each generative factor correlates with a single latent dimension. On simulated galaxy images the method achieves LDS scores of 0.88, 0.94, and 0.81 in three settings, versus 0.65, 0.73, and 0.59 for IDVAE, while SSIM reconstruction remains comparable to the baseline VAE.

Load-bearing premise

The load-bearing assumption is that regularizing correlations with the encoder's mean values is enough to disentangle the actual latent samples; if the encoder's per-input variability is large, the sampled latent distribution can stay entangled even when the means align.

Editorial extensions

If this is right

On galaxy simulations, supplying all or most known physical parameters as auxiliary variables lets each parameter be controlled by turning a single latent dimension, enabling interpretable generative manipulation.
When important factors are missing from the auxiliary set, the residual latent dimensions automatically take over their representation, keeping reconstruction accuracy high.
The LDS metric provides a cheap way to score disentanglement from a single trained model, bounded between $1/d_Z$ and 1, without retraining supervised regressors.
Adversarial robustness experiments reported in the supplement indicate that Aux-VAE's disentangled representations degrade less under FGSM perturbation than entangled VAE representations.

Reading between the lines

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

Beyond the paper, a cheap strengthening for high-complexity data would regularize correlations with actual sampled latents rather than encoder means; the paper itself notes this alternative for finer-grained relationships.
Beyond the paper, because the method only needs paired observations $(x,u)$, it should transfer to non-image scientific measurements such as spectra or sensor time series with the same loss and latent partition.
Beyond the paper, recording both mean-based and sample-based LDS on every dataset would give a free check of whether the reported disentanglement holds at the level of the generative distribution or only its conditional averages.

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.

Desk Editor's Note

read the letter

Colleague, quick take on arXiv:2507.00298: the central idea is worth taking seriously, but the evidence as presented is weaker than it looks. The paper proposes Aux-VAE, where the prior for an auxiliary block z_aux is centered on observed factors u with variance 1/n, residual latents z_recon carry the rest, and polynomial-correlation regularizers push the encoder means to align with u. That is a sensible, cheap way to get interpretable latent dimensions on scientific datasets where some ground-truth factors are known. The LDS metric is a useful bounded correlation-based alternative to SAP, and the galaxy simulation experiments nicely show that z_recon compensates when auxiliary factors are missing, with reconstruction SSIM roughly intact.

The soft spots are real but fixable. The R0/R1 definitions in Eqs (7)-(8) exclude k=k' pairs, so the "explicitness" regularizer R1(u_j, mu_aux,j) does not directly penalize low linear correlation between u_j and mu_j; it only uses cross-degree polynomials. Either the equation is a typo or the regularizer is not doing what the text says, and the polynomial degree K is never reported. More importantly, the text never states whether the LDS scores in Table 1 are computed on sampled latents z or on encoder means mu. The metric definition says z, but the regularizers and the SM's covariance identity work with mu, and the authors themselves note in the SM that direct regularization of Corr(u_j, z_aux,j) may be needed for complex data. If the reported 0.94 is on mu, it largely re-states the alignment the prior and regularizer enforce on means, and says little about the stochastic latents the decoder actually sees. That needs to be clarified.

Also, no error bars or repeated-seed runs anywhere in Table 1, and hyperparameters are selected using the same LDS metric used for evaluation. Minor, but it matters for a method paper. None of this sinks the core idea; it just means the current version overclaims empirical support. A careful revision should fix the regularizer definitions, report K, give seeded error bars, and state plainly whether LDS is mean-based or sample-based.

Verdict: send it to peer review, but expect major revisions. It's a useful contribution for the scientific-ML crowd.

Referee Report

5 major / 6 minor

Summary. The paper introduces Aux-VAE, a variational autoencoder variant that partitions the latent space into auxiliary-informed factors (z_aux) and residual factors (z_recon). It uses a conditional prior p(z|u) = N((u_1,...,u_d,0,...), diag(1/n I_d, I_{dZ-d})) and augments the ELBO with polynomial-correlation regularizers (Eqs. 7-9) that encourage each auxiliary variable u_j to align with a distinct z_aux dimension while leaving z_recon free to encode unknown factors. The authors propose a new Linear Disentanglement Score (LDS, Eq. 10) and report experiments on a GalSim galaxy image dataset and on Cars3D and DSprites, comparing against beta-VAE and IDVAE. The main claims are that Aux-VAE achieves high LDS scores (up to 0.94 in galaxy Case 2) while preserving reconstruction quality on par with a standard VAE.

Significance. If the reported results hold, Aux-VAE is a practical and minimally invasive semi-supervised disentanglement method for scientific datasets with partial auxiliary information; the code is publicly available and the construction is simple to implement on top of a standard VAE. The paper also proposes the LDS metric, which is intuitively appealing though its definition requires correction. The principal technical risk is that the regularizer operates on encoder means rather than on sampled latent variables, and the manuscript does not clarify which quantity the reported LDS scores are computed on. This ambiguity affects the central claim that the stochastic latent space itself is disentangled.

major comments (5)

[Section 3, Eq. (9); Section 4.2.2; SM Section A, Eqs. (17)-(20)] The objective in Eq. (9) regularizes polynomial correlations between u and the encoder means mu_phi, not between u and sampled latent variables z. The covariance identity in SM Eq. (17) is valid for Cov(u, mu_phi) only when the within-encoder covariance term vanishes, and SM Eq. (20) explicitly gives Corr(u_j, z_aux,j) < Corr(u_j, mu_phi,j) unless E[var(z_j|x)] is negligible. The manuscript never states whether the LDS scores in Table 1 and Figure 3 are computed on z or on mu; Figure 3 displays both. If LDS is computed on mu, the reported scores largely restate the alignment directly enforced by the KL term and the regularizer, and do not establish that the stochastic latent variables used by the decoder are disentangled. The authors' own caveat at the end of SM Section A, that higher-complexity datasets may require directly regularizing Corr(u_j, z_aux,j), is load-bearing here; please report LDS on sampled z and, if necessary, regularize the sample-level correlation or provide evidence that the conditional variance E[var(z_j|x)] is negligible.
[Eqs. (7)-(9) and Section 4.1] The polynomial degree K in Eqs. (7)-(8) is never specified in the experimental settings (Section 4.1). Because both sums run over k,k'=1..K with k≠k', for K=1 the regularizers R0 and R1 vanish identically, reducing the Aux-VAE loss in Eq. (9) to the plain VAE objective. The paper must report the value of K used for each dataset and justify the exclusion of same-degree (including linear-linear) correlation terms, which otherwise makes the 'explicitness' regularizer not directly target the stated alignment Corr(u_j, z_aux,j).
[Table 1] Table 1 reports single point estimates for LDS and SAP with no error bars, no repeated-seed runs, and no significance tests. Given the well-documented variance of disentanglement metrics across training runs (Locatello et al., 2019), the claimed margins (e.g., 0.94 vs 0.73 for galaxy Case 2) are not statistically grounded. Please report mean and standard deviation over at least five seeds, and use paired evaluations where possible.
[Eq. (10)] The LDS metric in Eq. (10) uses max_l Corr(u_j, z_l) in the numerator without an absolute value, while the denominator sums |Corr(u_j, z_l)|. As written, a factor that is perfectly anti-correlated with a latent dimension yields a negative contribution, contradicting the claimed range LDS ∈ [1/dZ, 1] and the interpretation that scores near 1 indicate optimal separation. The numerator should be max_l |Corr(u_j, z_l)|, or the metric should be redefined accordingly. This correction is essential because LDS is used both for hyperparameter selection (SM Section C.1) and for all reported comparisons.
[SM Section C.1] The hyperparameter selection described in SM Section C.1 uses the product MSE(1 - LDS) on the validation split, where LDS is the same metric reported in Table 1. This makes the reported scores a selected maximum rather than an independent evaluation; the manuscript should acknowledge this and, ideally, evaluate a final model chosen without LDS on a held-out set.

minor comments (6)

[SM Section A] In the Explicitness proof, the limit of the correlation expression is written as '→ ∞' as n → ∞; the correct limit is '→ 1'.
[Table 1 caption] The caption contains 'Card3D'; this should be 'Cars3D'.
[After Eq. (8)] The text says the metrics aggregate 'all possible polynomial combinations up to degree K', but the sums exclude k=k' terms; please rephrase to describe the actual definition.
[Figure 3 caption] The caption does not specify whether the LDS values are computed from the grey dots (Z) or the maroon dots (µ); please clarify.
[SM Section C.1] The text refers to 'test MSE and test LDS' while describing a search on the validation split; make the terminology consistent.
[Eq. (3)] The prior variance 1/n is presented without motivation; since n is the sample size, the prior becomes degenerate as n grows, so the authors should explain the rationale and the sensitivity to this choice.

Circularity Check

1 steps flagged · score 3.0 of 10

Reported LDS partly re-states the training objective; latent-sample disentanglement is not independently established.

fitted input called prediction [Section 3, Eq. (9) and Eq. (10); Appendix C.1; SM Eq. (20)]
"LAux−V AE= LV AE+ λ1 Σ_{j=1}^d ( R^K_1 (u_j, µ_φ,aux,j) + R^K_0 (u_j, µ_φ,aux,−j) ) + λ2 R^K_0 (u, µ_φ,rec) (9) ... LDS = 1/d Σ_{j=1}^d max_l Corr (u_j, z_l) / Σ_{l=1}^{dZ} |Corr (u_j, z_l)| (10)"

The loss in Eq. (9) directly penalizes 1−|Corr(u_j, μ_φ,aux,j)| for K=1 and drives the cross-correlations in R^K_0 toward zero, i.e., it optimizes the same u-versus-latent correlation structure that the proposed LDS metric in Eq. (10) scores. Appendix C.1 then selects hyperparameters using validation LDS, and Table 1 reports test LDS as the headline evidence of disentanglement. The reported scores therefore substantially re-state the training objective rather than independently confirming a naturally discovered factor structure; for the encoder means μ_φ the alignment is enforced by construction. SM Eq.

full rationale

No significant self-citation chain or imported uniqueness theorem is used; the method is evaluated against external datasets (Cars3D, DSprites) and against β-VAE and IDVAE, and it reports independent reconstruction and latent-traversal evidence. The circularity concern is limited to the evaluation metric: LDS is proposed in the paper, used as the model-selection criterion, and reported as the main quantitative confirmation, while the loss function explicitly maximizes the same correlation family (on encoder means). This makes the high LDS partially a reflection of the objective rather than an independent discovery. The paper never specifies whether Table 1 LDS is computed on sampled z or on μ_φ, and SM Eq. (20) acknowledges that regularizing μ_φ correlations is not the same as regularizing z correlations. This does not void the reconstruction or traversal results, so the circularity is partial rather than total.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central result rests on the auxiliary variables being faithful proxies for distinct ground-truth factors, on conditional independence x independent of u given z, and on the heuristic that polynomial correlations of encoder means are sufficient to enforce disentanglement of sampled latents. No new physical entities are introduced. The regularization weights, prior variance scale, polynomial degree, and total latent dimension are free choices that affect the outcome.

free parameters (4)

Regularization weights beta, lambda1, lambda2 = beta=5, lambda1=1, lambda2=0.1 (galaxy); beta=5, lambda1=2, lambda2=1 (Cars3D); beta=10, lambda1=2, lambda2=2 (DSprites)
Selected by grid search on validation MSE and LDS in Section C.1; the choices affect the balance between reconstruction quality and disentanglement.
Prior variance scale for auxiliary dimensions (1/n) = 1/n with n the dataset size, e.g., 1/16384 for the galaxy images
Eq (3) sets Sigma_0 = diag(1/n I_d, I); the scale is chosen by hand and controls how strongly z_aux is pulled toward the auxiliary values u, but no sensitivity analysis is reported.
Polynomial degree K in R0 and R1 = not reported in the paper
Eqs (7)-(9) depend on K through sums over polynomial degrees, but the value used in experiments is never stated.
Latent dimension dZ = 10 for the galaxy data, with 5, 3, or 2 auxiliary-supervised dimensions depending on the case
The total latent dimensionality is fixed by the architecture in Table 3 and determines how much residual capacity z_recon has for unknown factors.

assumptions (4)

domain assumption The observed auxiliary variables u are faithful one-to-one encodings of distinct ground-truth generative factors
Section 4.1.1 assigns u to physical parameters such as flux, radius, g1, g2, and psf, and assumes each corresponds to a single factor; if factors are correlated or u is noisy, intra-independence may be impossible.
domain assumption Conditional independence x is independent of u given z
The supplementary material Eq (12) assumes p_theta(x|z,u)=p_theta(x|z); if important generative information is only in u and not captured by z, reconstruction can degrade.
ad hoc to paper Correlations between u and encoder means mu_phi suffice to enforce disentanglement of the full latent distribution
The objective Eq (9) and the derivations in Eqs (17)-(19) regularize Corr(x,u)(u,mu_phi) rather than Corr(u,z); the paper acknowledges this is an approximation in supplementary Eq (20).
domain assumption Polynomial Pearson correlations up to degree K capture the nonlinear dependencies relevant for disentanglement
R0 and R1 in Eqs (7)-(8) aggregate correlations of polynomial powers, which is a heuristic measure of nonlinear dependence; K is unspecified in the paper.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets." pith.science (2026). https://pith.science/paper/VRGW3OE6

@misc{pith2026250700298,
  author       = {Pith},
  title        = {Pith review of: Enhancing Interpretability in Generative Modeling: Statistically Disentangled Latent Spaces Guided by Generative Factors in Scientific Datasets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRGW3OE6}},
  note         = {Machine review of arXiv:2507.00298}
}

read the original abstract

This study addresses the challenge of statistically extracting generative factors from complex, high-dimensional datasets in unsupervised or semi-supervised settings. We investigate encoder-decoder-based generative models for nonlinear dimensionality reduction, focusing on disentangling low-dimensional latent variables corresponding to independent physical factors. Introducing Aux-VAE, a novel architecture within the classical Variational Autoencoder framework, we achieve disentanglement with minimal modifications to the standard VAE loss function by leveraging prior statistical knowledge through auxiliary variables. These variables guide the shaping of the latent space by aligning latent factors with learned auxiliary variables. We validate the efficacy of Aux-VAE through comparative assessments on multiple datasets, including astronomical simulations.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 44 canonical work pages

[1]

, Durrer , R

barticle Bonvin , C. , Durrer , R. : What galaxy surveys really measure . Physical Review D 84 ( 6 ), 063505 ( 2011 ) barticle

work page 2011
[2]

DeepHyper: A Python Package for Scalable Neural Architecture and Hyperparameter Search

botherref Balaprakash , P. , Egele , R. , Salim , M. , Maulik , R. , Vishwanath , V. , Wild , S. , et al.: "DeepHyper: A Python Package for Scalable Neural Architecture and Hyperparameter Search" (2018). https://github.com/deephyper/deephyper botherref

work page 2018
[3]

, Freeman , K.C

bchapter Block , D.L. , Freeman , K.C. : A Walk with Dr Allan Sandage Changing the History of Galaxy Morphology, Forever: A Conference in honour of David Block and Bruce Elmegreen . In: Lessons from the Local Group: A Conference in Honor of David Block and Bruce Elmegreen , pp. 1 -- 20 ( 2015 ). 10.1007/978-3-319-10614-4_1 bchapter

work page doi:10.1007/978-3-319-10614-4_1 2015
[4]

, Higgins , I

botherref Burgess , C.P. , Higgins , I. , Pal , A. , Matthey , L. , Watters , N. , Desjardins , G. , Lerchner , A. : Understanding disentangling in beta-vae. arXiv preprint arXiv:1804.03599 (2018) botherref

arXiv 2018
[5]

, Kucukelbir , A

barticle Blei , D.M. , Kucukelbir , A. , McAuliffe , J.D. : Variational inference: A review for statisticians . Journal of the American statistical Association 112 ( 518 ), 859 -- 877 ( 2017 ) barticle

work page 2017
[6]

, Thorpe , A

barticle Bauer , P. , Thorpe , A. , Brunet , G. : The quiet revolution of numerical weather prediction . Nature 525 ( 7567 ), 47 -- 55 ( 2015 ) barticle

work page 2015
[7]

, Tomioka , R

bchapter Bouchacourt , D. , Tomioka , R. , Nowozin , S. : Multi-level variational autoencoder: Learning disentangled representations from grouped observations . In: Proceedings of the AAAI Conference on Artificial Intelligence , vol. 32 ( 2018 ) bchapter

work page 2018
[8]

, : The lsst desc dc2 simulated sky survey

barticle Collaboration , L.D.E.S. , : The lsst desc dc2 simulated sky survey . Astrophysical Journal, Supplement Series 253 ( 1 ), 34 ( 2021 ) barticle

work page 2021

Show all 59 references

[9]

, Batmanghelich , K

barticle Chen , J. , Batmanghelich , K. : Weakly supervised disentanglement by pairwise similarities . Proceedings of the AAAI Conference on Artificial Intelligence 34 ( 04 ), 3495 -- 3502 ( 2020 ) 10.1609/aaai.v34i04.5754 barticle

2020 doi
[10]

, Livezey , J.A

botherref Cheung , B. , Livezey , J.A. , Bansal , A.K. , Olshausen , B.A. : Discovering hidden factors of variation in deep networks. arXiv preprint arXiv:1412.6583 (2014) botherref

2014 arXiv
[11]

, Li , X

bchapter Chen , R.T.Q. , Li , X. , Grosse , R. , Duvenaud , D. : Isolating sources of disentanglement in variational autoencoders . In: Advances in Neural Information Processing Systems ( 2018 ) bchapter

2018
[12]

, Phillips , A.S

barticle Deser , C. , Phillips , A.S. , Alexander , M.A. , Smoliak , B.V. : Projecting north american climate over the next 50 years: Uncertainty due to internal variability . Journal of Climate 27 ( 6 ), 2271 -- 2296 ( 2014 ) barticle

2014
[13]

, Hastie , T

botherref Efron , B. , Hastie , T. , Johnstone , I. , Tibshirani , R. : Least angle regression (2004) botherref

2004
[14]

, Yanny , B

barticle Everett , S. , Yanny , B. , Kuropatkin , N. , Huff , E. , Zhang , Y. , Myles , J. , Masegian , A. , Elvin-Poole , J. , Allam , S. , Bernstein , G. , : Dark energy survey year 3 results: measuring the survey transfer function with balrog . The Astrophysical Journal Sup...

2022
[15]

, Ramachandra , N

botherref Ganguli , A. , Ramachandra , N. , Bessac , J. , Constantinescu , E. : Aux-VAE: Variational AutoEncoder with Auxiliary Variables for Disentangled Representations. GitHub (2024). https://github.com/ArkaStatistics/Aux-VAE botherref

2024
[16]

, Shlens , J

botherref Goodfellow , I.J. , Shlens , J. , Szegedy , C. : Explaining and harnessing adversarial examples. arXiv preprint arXiv:1412.6572 (2014) botherref

2014 arXiv
[17]

: Quantification of Unknown Unknowns in Astronomy and Physics

botherref Hatfield , P. : Quantification of Unknown Unknowns in Astronomy and Physics . arXiv e-prints, 2207--13993 (2022) 10.48550/arXiv.2207.13993 https://arxiv.org/abs/2207.13993 arXiv:2207.13993 [astro-ph.IM] botherref

2022 doi arXiv
[18]

, Matthey , L

bchapter Higgins , I. , Matthey , L. , Pal , A. , Burgess , C. , Glorot , X. , Botvinick , M. , Mohamed , S. , Lerchner , A. : beta- VAE : Learning basic visual concepts with a constrained variational framework . In: International Conference on Learning Representations ( 2017 ...

2017
[19]

: Group-based learning of disentangled representations with generalizability for novel contents

botherref Hosoya , H. : Group-based learning of disentangled representations with generalizability for novel contents. arXiv preprint arXiv:1809.02383 (2018) botherref

2018 arXiv
[20]

, Hearin , A

barticle Korytov , D. , Hearin , A. , Kovacs , E. , Larsen , P. , Rangel , E. , Hollowed , J. , Benson , A.J. , Heitmann , K. , Mao , Y.-Y. , Bahmanyar , A. , : Cosmodc2: A synthetic sky catalog for dark energy science with lsst . The Astrophysical Journal Supplement Series 24...

2019
[21]

, Kingma , D

bchapter Khemakhem , I. , Kingma , D. , Monti , R. , Hyvarinen , A. : Variational autoencoders and nonlinear ica: A unifying framework . In: International Conference on Artificial Intelligence and Statistics , pp. 2207 -- 2217 ( 2020 ). PMLR bchapter

2020
[22]

, Lange , C

barticle Kaltenborn , J. , Lange , C. , Ramesh , V. , Brouillard , P. , Gurwicz , Y. , Nagda , C. , Runge , J. , Nowack , P. , Rolnick , D. : Climateset: A large-scale climate model dataset for machine learning . Advances in Neural Information Processing Systems 36 , 21757 -- ...

2023
[23]

, Liu , Y

bchapter Kim , Y.-g. , Liu , Y. , Wei , X.-X. : Covariate-informed representation learning to prevent posterior collapse of ivae . In: International Conference on Artificial Intelligence and Statistics , pp. 2641 -- 2660 ( 2023 ). PMLR bchapter

2023
[24]

, Mnih , A

bchapter Kim , H. , Mnih , A. : Disentangling by factorising . In: Dy , J. , Krause , A. (eds.) Proceedings of the 35th International Conference on Machine Learning . Proceedings of Machine Learning Research , vol. 80 , pp. 2649 -- 2658 . PMLR , ??? ( 2018 ). https://proceedin...

2018
[25]

, Mohamed , S

botherref Kingma , D.P. , Mohamed , S. , Jimenez Rezende , D. , Welling , M. : Semi-supervised learning with deep generative models. Advances in neural information processing systems 27 (2014) botherref

2014
[26]

, Poole , B

bchapter Kumar , A. , Poole , B. : On implicit regularization in - VAE s . In: International Conference on Machine Learning , pp. 5480 -- 5490 ( 2020 ). PMLR bchapter

2020
[27]

, Sattigeri , P

bchapter Kumar , A. , Sattigeri , P. , Balakrishnan , A. : Variational inference of disentangled latent concepts from unlabeled observations . In: 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Tra...

2018
[28]

, Welling , M

barticle Kingma , D.P. , Welling , M. : An introduction to variational autoencoders . Foundations and Trends® in Machine Learning 12 ( 4 ), 307 -- 392 ( 2019 ) 10.1561/2200000056 barticle

2019 doi
[29]

, Welling , M

botherref Kingma , D.P. , Welling , M. : Auto-Encoding Variational Bayes (2022) botherref

2022
[30]

, Abbati , G

botherref Locatello , F. , Abbati , G. , Rainforth , T. , Bauer , S. , Sch \"o lkopf , B. , Bachem , O. : On the fairness of disentangled representations. Advances in neural information processing systems 32 (2019) botherref

2019
[31]

, Bauer , S

bchapter Locatello , F. , Bauer , S. , Lucic , M. , Raetsch , G. , Gelly , S. , Sch \"o lkopf , B. , Bachem , O. : Challenging common assumptions in the unsupervised learning of disentangled representations . In: International Conference on Machine Learning , pp. 4114 -- 4124 ...

2019
[32]

, Gunn , J.E

barticle Lackner , C.N. , Gunn , J.E. : Astrophysically motivated bulge–disc decompositions of Sloan Digital Sky Survey galaxies . Monthly Notices of the Royal Astronomical Society 421 ( 3 ), 2277 -- 2302 ( 2012 ) 10.1111/j.1365-2966.2012.20450.x https://arxiv.org/abs/https://...

2012
[33]

a tsch , G. , Sch \

bchapter Locatello , F. , Poole , B. , R \"a tsch , G. , Sch \"o lkopf , B. , Bachem , O. , Tschannen , M. : Weakly-supervised disentanglement without compromises . In: International Conference on Machine Learning , pp. 6348 -- 6359 ( 2020 ). PMLR bchapter

2020
[34]

, Ullman , T.D

barticle Lake , B.M. , Ullman , T.D. , Tenenbaum , J.B. , Gershman , S.J. : Building machines that learn and think like people . Behavioral and brain sciences 40 , 253 ( 2017 ) barticle

2017
[35]

, Castellano , M

barticle Merlin , E. , Castellano , M. , Bretonni \`e re , H. , Kuchner , U. , Tuccillo , D. , Buitrago , F. , Peterson , J. , Conselice , C. , Caro , F. , Dimauro , P. , : Euclid preparation-xxv. the euclid morphology challenge: Towards model-fitting photometry for billions o...

2023
[36]

, Ekhtiari , N

barticle M\"uller , M.U. , Ekhtiari , N. , Almeida , R.M. , Rieke , C. : Super-resolution of multispectral satellite images using convolutional neural networks . ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences V-1-2020 , 33 -- 40 ( 2020 ) 10...

2020 doi
[37]

, Filippone , M

bchapter Mita , G. , Filippone , M. , Michiardi , P. : An identifiable double vae for disentangled representations . In: International Conference on Machine Learning , pp. 7769 -- 7779 ( 2021 ). PMLR bchapter

2021
[38]

, Fukami , K

barticle Maulik , R. , Fukami , K. , Ramachandra , N. , Fukagata , K. , Taira , K. : Probabilistic neural networks for fluid flow surrogate modeling and data recovery . Physical Review Fluids 5 ( 10 ), 104401 ( 2020 ) 10.1103/PhysRevFluids.5.104401 https://arxiv.org/abs/2005.0...

2020 arXiv
[39]

, Rainforth , T

bchapter Mathieu , E. , Rainforth , T. , Siddharth , N. , Teh , Y.W. : Disentangling disentanglement in variational autoencoders . In: International Conference on Machine Learning , pp. 4402 -- 4412 ( 2019 ). PMLR bchapter

2019
[40]

, Zhao , J.J

bchapter Mathieu , M.F. , Zhao , J.J. , Zhao , J. , Ramesh , A. , Sprechmann , P. , LeCun , Y. : Disentangling factors of variation in deep representation using adversarial training . In: Lee , D. , Sugiyama , M. , Luxburg , U. , Guyon , I. , Garnett , R. (eds.) Advances in Ne...

2016
[41]

, Gruen , D

barticle Newman , J.A. , Gruen , D. : Photometric redshifts for next-generation surveys . Annual Review of Astronomy and Astrophysics 60 , 363 -- 414 ( 2022 ) barticle

2022
[42]

, Gross , S

botherref Paszke , A. , Gross , S. , Massa , F. , Lerer , A. , Bradbury , J. , Chanan , G. , Killeen , T. , Lin , Z. , Gimelshein , N. , Antiga , L. , et al.: Pytorch: An imperative style, high-performance deep learning library. Advances in neural information processing system...

2019
[43]

, Van De Meent , J.-W

botherref Paige , B. , Van De Meent , J.-W. , Desmaison , A. , Goodman , N. , Kohli , P. , Wood , F. , Torr , P. , et al.: Learning disentangled representations with semi-supervised deep generative models. Advances in neural information processing systems 30 (2017) botherref

2017
[44]

, Gupta , H.V

barticle Razavi , S. , Gupta , H.V. : A new framework for comprehensive, robust, and efficient global sensitivity analysis: 1. theory . Water Resources Research 52 ( 1 ), 423 -- 439 ( 2016 ) barticle

2016
[45]

, Jarvis , M

barticle Rowe , B.T.P. , Jarvis , M. , Mandelbaum , R. , Bernstein , G.M. , Bosch , J. , Simet , M. , Meyers , J.E. , Kacprzak , T. , Nakajima , R. , Zuntz , J. , Miyatake , H. , Dietrich , J.P. , Armstrong , R. , Melchior , P. , Gill , M.S.S. : GALSIM: The modular galaxy imag...

2015 arXiv
[46]

, Pantula , S.G

bbook Rawlings , J.O. , Pantula , S.G. , Dickey , D.A. (eds.): Polynomial Regression , pp. 235 -- 268 . Springer , New York, NY ( 1998 ). 10.1007/0-387-22753-9_8 . https://doi.org/10.1007/0-387-22753-9_8 bbook

1998 doi
[47]

, Funk , C

barticle Raghavan Sathyan , A. , Funk , C. , Aenis , T. , Winker , P. , Breuer , L. : Sensitivity analysis of a climate vulnerability index-a case study from indian watershed development programmes . Climate Change Responses 5 , 1 -- 14 ( 2018 ) barticle

2018
[48]

, Zhang , Y

bchapter Reed , S.E. , Zhang , Y. , Zhang , Y. , Lee , H. : Deep visual analogy-making . In: Cortes , C. , Lawrence , N. , Lee , D. , Sugiyama , M. , Garnett , R. (eds.) Advances in Neural Information Processing Systems , vol. 28 . Curran Associates, Inc. , ??? ( 2015 ). https...

2015
[49]

, Aussel , H

barticle Scoville , N. , Aussel , H. , Brusa , M. , Capak , P. , Carollo , C.M. , Elvis , M. , Giavalisco , M. , Guzzo , L. , Hasinger , G. , Impey , C. , : The cosmic evolution survey (cosmos): overview . The Astrophysical Journal Supplement Series 172 ( 1 ), 1 ( 2007 ) barticle

2007
[50]

, Chen , Y

botherref Shu , R. , Chen , Y. , Kumar , A. , Ermon , S. , Poole , B. : Weakly supervised disentanglement with guarantees. arXiv preprint arXiv:1910.09772 (2019) botherref

2019 arXiv
[51]

, Dav \'e , R

barticle Somerville , R.S. , Dav \'e , R. : Physical models of galaxy formation in a cosmological framework . Annual Review of Astronomy and Astrophysics 53 , 51 -- 113 ( 2015 ) barticle

2015
[52]

, Hinton , G

barticle Maaten , L. , Hinton , G. : Visualizing data using t-sne . Journal of Machine Learning Research 9 ( 86 ), 2579 -- 2605 ( 2008 ) barticle

2008
[53]

, Schönberger , J.L

barticle Walt , S. , Schönberger , J.L. , Núñez-Iglesias , J. , Boulogne , F. , Warner , J.D. , Yager , N. , Gouillart , E. , Yu , T. , contributors : scikit-image: Image processing in python . PeerJ 2 , 453 ( 2014 ) 10.7717/peerj.453 barticle

2014 doi
[54]

, Balaprakash , P

barticle Wu , X. , Balaprakash , P. , Kruse , M. , Koo , J. , Videau , B. , Hovland , P. , Taylor , V. , Geltz , B. , Jana , S. , Hall , M. : ytopt: Autotuning scientific applications for energy efficiency at large scales . Concurrency and Computation: Practice and Experience ...

2025 doi
[55]

, Bovik , A.C

barticle Wang , Z. , Bovik , A.C. , Sheikh , H.R. , Simoncelli , E.P. : Image quality assessment: from error visibility to structural similarity . IEEE Transactions on Image Processing 13 ( 4 ), 600 -- 612 ( 2004 ) 10.1109/TIP.2003.819861 barticle

2004
[56]

, Chen , H

botherref Wang , X. , Chen , H. , Tang , S. , Wu , Z. , Zhu , W. : Disentangled Representation Learning (2023) botherref

2023
[57]

, Guo , T

barticle Yang , S. , Guo , T. , Wang , Y. , Xu , C. : Adversarial robustness through disentangled representations . Proceedings of the AAAI Conference on Artificial Intelligence 35 ( 4 ), 3145 -- 3153 ( 2021 ) 10.1609/aaai.v35i4.16424 barticle

2021 doi
[58]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...
[59]

write newline

" write newline "" before.all 'output.state := FUNCTION string.to.integer 't := t text.length 'k := #1 'char.num := t char.num #1 substring 's := s is.num s "." = or char.num k = not and char.num #1 + 'char.num := while char.num #1 - 'char.num := t #1 char.num substring FUNCTI...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

, Durrer , R

barticle Bonvin , C. , Durrer , R. : What galaxy surveys really measure . Physical Review D 84 ( 6 ), 063505 ( 2011 ) barticle

work page 2011

[2] [2]

DeepHyper: A Python Package for Scalable Neural Architecture and Hyperparameter Search

botherref Balaprakash , P. , Egele , R. , Salim , M. , Maulik , R. , Vishwanath , V. , Wild , S. , et al.: "DeepHyper: A Python Package for Scalable Neural Architecture and Hyperparameter Search" (2018). https://github.com/deephyper/deephyper botherref

work page 2018

[3] [3]

, Freeman , K.C

bchapter Block , D.L. , Freeman , K.C. : A Walk with Dr Allan Sandage Changing the History of Galaxy Morphology, Forever: A Conference in honour of David Block and Bruce Elmegreen . In: Lessons from the Local Group: A Conference in Honor of David Block and Bruce Elmegreen , pp. 1 -- 20 ( 2015 ). 10.1007/978-3-319-10614-4_1 bchapter

work page doi:10.1007/978-3-319-10614-4_1 2015

[4] [4]

, Higgins , I

botherref Burgess , C.P. , Higgins , I. , Pal , A. , Matthey , L. , Watters , N. , Desjardins , G. , Lerchner , A. : Understanding disentangling in beta-vae. arXiv preprint arXiv:1804.03599 (2018) botherref

arXiv 2018

[5] [5]

, Kucukelbir , A

barticle Blei , D.M. , Kucukelbir , A. , McAuliffe , J.D. : Variational inference: A review for statisticians . Journal of the American statistical Association 112 ( 518 ), 859 -- 877 ( 2017 ) barticle

work page 2017

[6] [6]

, Thorpe , A

barticle Bauer , P. , Thorpe , A. , Brunet , G. : The quiet revolution of numerical weather prediction . Nature 525 ( 7567 ), 47 -- 55 ( 2015 ) barticle

work page 2015

[7] [7]

, Tomioka , R

bchapter Bouchacourt , D. , Tomioka , R. , Nowozin , S. : Multi-level variational autoencoder: Learning disentangled representations from grouped observations . In: Proceedings of the AAAI Conference on Artificial Intelligence , vol. 32 ( 2018 ) bchapter

work page 2018

[8] [8]

, : The lsst desc dc2 simulated sky survey

barticle Collaboration , L.D.E.S. , : The lsst desc dc2 simulated sky survey . Astrophysical Journal, Supplement Series 253 ( 1 ), 34 ( 2021 ) barticle

work page 2021