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arxiv: 2607.01275 · v1 · pith:ZXGOMZECnew · submitted 2026-06-30 · 📊 stat.ML · cs.LG

eXact-Prior Variational Autoencoder (X-VAE): Learning Data-Adaptive Gaussian Mixture Priors for Latent Distributions

Qijun Chen , Shaofan Li This is my paper

Pith reviewed 2026-07-03 21:40 UTC · model grok-4.3

classification 📊 stat.ML cs.LG
keywords variational autoencoderdata-adaptive priorGaussian priorlatent distributionpretrained autoencoderKL divergencesample generation
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The pith

X-VAE replaces the standard normal prior with a Gaussian prior whose mean and variance come from latent codes of a pretrained autoencoder.

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

The paper seeks to fix the common mismatch in variational autoencoders where a fixed standard normal prior does not reflect the actual spread of learned latent codes on complex data. It does so by first training a separate autoencoder, then setting the VAE prior to a Gaussian whose parameters are the empirical mean and standard deviation of that autoencoder's latent representations. The resulting prior is data-adaptive, and the paper derives the matching KL divergence term for optimization. A latent scaling factor is added at generation time to tune sample variance directly. A sympathetic reader would care because this change aims to keep reconstruction quality while producing samples whose statistics better match the training distribution.

Core claim

The central claim is that the empirical mean and standard deviation of latent codes from a separately pretrained autoencoder can be used to parameterize a Gaussian prior for a VAE, that the corresponding KL divergence term can be written in closed form, and that the resulting model produces latent representations that align more closely with the empirical data distribution while preserving reconstruction quality and allowing explicit variance control via a scaling factor.

What carries the argument

The data-adaptive Gaussian prior whose mean and standard deviation are set to the sample statistics of latent codes from a pretrained autoencoder.

If this is right

  • X-VAE produces latent representations whose statistics more closely match the empirical distribution of the training data.
  • Generated samples remain realistic while the latent scaling factor gives direct control over diversity versus fidelity.
  • The method is presented as suitable for engineering design tasks that require both constraint satisfaction and exploration.
  • The KL divergence objective for the new prior is derived without introducing additional fitting artifacts.

Where Pith is reading between the lines

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

  • The two-stage training (AE then VAE) adds a preprocessing step whose cost might be offset if the same AE is reused across multiple VAE runs.
  • Replacing only the first two moments leaves higher-order structure of the latent distribution unmodeled, so the approach may still underperform on data with strong multimodality.
  • The scaling factor at generation time could be made learnable rather than fixed, turning it into an additional degree of freedom during inference.

Load-bearing premise

The empirical mean and standard deviation computed from the latent codes of a separately pretrained autoencoder form a suitable and stable prior for the subsequent VAE training.

What would settle it

Train both a standard VAE and an X-VAE on the same benchmark datasets and check whether the X-VAE version shows lower reconstruction error or visibly better sample fidelity; if it does not, or if the KL term causes training divergence, the central claim fails.

Figures

Figures reproduced from arXiv: 2607.01275 by Qijun Chen, Shaofan Li.

Figure 1
Figure 1. Figure 1: Architecture of the proposed X-VAE. A pretrained autoencoder learns latent [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Routed-transport sampling (one latent coordinate). The encoder produces per [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Architecture of the proposed X-VAE. Top: a deterministic autoencoder is trained first, and a K-component diagonal Gaussian mixture is fit once on its latent codes to give the fixed prior {π p k , µ p k , σ p k } K k=1 (9), which is frozen during VAE training. Bottom: the VAE encoder emits a per-coordinate Gaussian posterior and routing weights (π q k , µ q k , σ q k ); each latent coordinate is then formed… view at source ↗
Figure 4
Figure 4. Figure 4: Left: MNIST reconstructions, Right: Celeba reconstructions [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: MNIST training curves (total / reconstruction / KL vs. epoch) for our method [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: CelebA training curves (total / reconstruction / KL vs. epoch). [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Clustered data: original two-dimensional data, reconstructions by our method, [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Clustered-data training curves (total / reconstruction / KL vs. epoch). [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Generated samples for CelebA 14 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Generated samples for MNIST The clustered data exposes the routing-and-split mechanism most directly ( [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Generated Sample for three clusterings No single routing or split is best everywhere, which is itself informative. On CelebA the K−1 + 1 routing with the prior-source coupling (π q , N p ) and a two-thirds transport split are strongest, whereas on MNIST a smaller transport fraction ( 1 3K) wins. The spread across our configurations is nonetheless small on each dataset, so the benefit comes from anchoring … view at source ↗
Figure 12
Figure 12. Figure 12: MNIST reconstructions 32 [PITH_FULL_IMAGE:figures/full_fig_p032_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: CelebA reconstructions 33 [PITH_FULL_IMAGE:figures/full_fig_p033_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Clustering reconstructions 34 [PITH_FULL_IMAGE:figures/full_fig_p034_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: MNIST generations 35 [PITH_FULL_IMAGE:figures/full_fig_p035_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: CelebA generations 36 [PITH_FULL_IMAGE:figures/full_fig_p036_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Clustered data: samples generated by our method (preserving the three modes) [PITH_FULL_IMAGE:figures/full_fig_p037_17.png] view at source ↗
read the original abstract

Variational Autoencoders (VAEs) commonly assume a standard isotropic Gaussian prior over the latent space, an assumption that often fails to capture the true distribution of latent representations for complex datasets. This mismatch can limit reconstruction accuracy, reduce sample quality, and constrain the expressive power of the learned latent space. We propose the eXact-Prior Variational Autoencoder (X-VAE), a framework that replaces the conventional standard normal prior with a Gaussian prior derived from the latent representations of a pretrained autoencoder (AE). Specifically, the empirical mean and standard deviation of the AE latent codes are used to parameterize a data-adaptive prior that more closely reflects the underlying structure of the training data. During generation, X-VAE introduces a latent scaling factor that enables explicit control over the variance of the sampled latent vectors, providing a simple mechanism for balancing sample diversity and fidelity. This flexibility makes the proposed approach particularly well suited for applications such as industrial and engineering design, where generated solutions must satisfy strict structural or functional constraints while still permitting meaningful design exploration. We present the mathematical formulation of well-suited X-VAE, derive the corresponding KL divergence objective for the proposed prior, and evaluate the method on standard benchmark datasets. Experimental results demonstrate that X-VAE preserves reconstruction quality while producing latent representations that better align with the empirical data distribution, leading to improved controllability and more realistic generated samples.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes the eXact-Prior Variational Autoencoder (X-VAE), which replaces the standard normal prior in VAEs with a data-adaptive Gaussian prior whose mean and standard deviation are computed from the latent codes of a separately pretrained deterministic autoencoder. The abstract states that the corresponding KL divergence is derived, a latent scaling factor is added for controllable generation, and experiments on benchmark datasets show preserved reconstruction quality with better alignment to the empirical latent distribution.

Significance. If the claimed KL derivation is correct and the prior alignment holds without introducing fitting artifacts, the approach offers a lightweight way to adapt the prior to data structure, which could benefit applications requiring constrained yet explorable generation such as engineering design. However, the absence of any equations, quantitative results, or ablation studies in the provided abstract limits assessment of whether the central claim is supported.

major comments (3)
  1. [Title and Abstract] Title vs. Abstract: The title claims 'Gaussian Mixture Priors' but the method description uses a single Gaussian N(μ_AE, σ_AE) parameterized by empirical statistics from the AE; this mismatch is load-bearing for the stated contribution and must be corrected.
  2. [Abstract] Abstract: The central claim requires a derivation of the KL term for the data-adaptive prior, yet no equations are shown; without the explicit form it is impossible to verify whether the closed-form KL between the variational posterior and N(μ_AE, σ_AE) is correctly obtained or whether the AE-derived statistics introduce misalignment with the VAE marginal.
  3. [Abstract] Abstract (method description): The prior parameters are extracted from a separately pretrained deterministic AE on the same data; the manuscript must demonstrate (via analysis or experiment) that this fixed target aligns with the distribution induced by the VAE encoder, as the skeptic concern about under-regularization or artifacts is not addressed.
minor comments (1)
  1. [Abstract] Abstract contains the awkward phrase 'mathematical formulation of well-suited X-VAE'; rephrase for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and detailed comments on our submission. We address each major comment below and indicate the planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [Title and Abstract] Title vs. Abstract: The title claims 'Gaussian Mixture Priors' but the method description uses a single Gaussian N(μ_AE, σ_AE) parameterized by empirical statistics from the AE; this mismatch is load-bearing for the stated contribution and must be corrected.

    Authors: We agree with this observation. The title incorrectly refers to Gaussian Mixture Priors, whereas the method implements a single Gaussian prior using empirical mean and standard deviation from the pretrained AE. This is an oversight in the title. We will revise the title to remove 'Mixture' and accurately describe the single Gaussian prior. revision: yes

  2. Referee: [Abstract] Abstract: The central claim requires a derivation of the KL term for the data-adaptive prior, yet no equations are shown; without the explicit form it is impossible to verify whether the closed-form KL between the variational posterior and N(μ_AE, σ_AE) is correctly obtained or whether the AE-derived statistics introduce misalignment with the VAE marginal.

    Authors: The manuscript derives the KL divergence in the main text using the standard closed-form expression for the KL between two univariate Gaussians (extended to multivariate diagonal case). The abstract is a high-level summary and conventionally omits equations. We will ensure the derivation is clearly presented and will consider adding a short statement in the abstract if space permits. The AE statistics are computed on the same dataset, and the VAE is trained to match this prior, minimizing the risk of misalignment. revision: partial

  3. Referee: [Abstract] Abstract (method description): The prior parameters are extracted from a separately pretrained deterministic AE on the same data; the manuscript must demonstrate (via analysis or experiment) that this fixed target aligns with the distribution induced by the VAE encoder, as the skeptic concern about under-regularization or artifacts is not addressed.

    Authors: This is a valid concern. While the experiments show preserved reconstruction quality and better alignment to the empirical latent distribution, we do not provide a direct quantitative comparison between the AE latent distribution and the VAE encoder outputs post-training. We will add an ablation study or analysis in the revised manuscript to address potential under-regularization or artifacts. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained modeling choice

full rationale

The paper defines a data-adaptive Gaussian prior by computing empirical mean and std from latent codes of a separately pretrained AE on the same data, then uses the standard closed-form KL between two Gaussians in the VAE objective. This is an explicit modeling decision, not a derivation that reduces to its inputs by construction. No equations equate a 'prediction' to a fitted parameter, no self-citation chains support load-bearing claims, and no uniqueness theorems or ansatzes are smuggled in. The approach is evaluated on external benchmarks and remains independent of the target result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that AE-derived empirical statistics form a valid prior and that the corresponding KL term can be written in closed form; no free parameters beyond the user-chosen scaling factor are declared.

free parameters (1)
  • latent scaling factor
    User-tunable multiplier applied to sampled latent vectors to control variance; its value is chosen at generation time rather than learned.
axioms (1)
  • domain assumption Empirical mean and standard deviation of latent codes from a pretrained autoencoder provide a suitable Gaussian prior for VAE training
    This replaces the standard isotropic normal and is invoked to justify the data-adaptive prior.

pith-pipeline@v0.9.1-grok · 5787 in / 1281 out tokens · 32013 ms · 2026-07-03T21:40:28.923509+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

45 extracted references · 29 canonical work pages · 20 internal anchors

  1. [1]

    Fixing a Broken ELBO

    Alexander A Alemi et al. “Fixing a broken ELBO”. In:International Conference on Machine Learning(2018).url:https://arxiv.org/abs/1711.00464

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  2. [2]

    Latent Space Oddity: on the Curvature of Deep Generative Models

    Georgios Arvanitidis, Lars Kai Hansen, and Soren Hauberg. “Latent Space Oddity: on the Curvature of Deep Generative Models”. In:International Conference on Learning Representations (ICLR). 2018.url:https://arxiv.org/abs/1710.11379

    work page arXiv 2018

  3. [3]

    dpVAEs: Fixing Sample Generation for Regularized VAEs

    Riddhish Bhalodia and Ahmed Elgammal. “dpVAEs: Fixing Sample Generation for Regularized VAEs”. In:Proceedings of the Asian Conference on Computer Vision (ACCV). Nov. 2020.url:https://arxiv.org/abs/1911.10506

    work page arXiv 2020

  4. [4]

    Diagnosing and Enhancing VAE Models

    Bin Dai and David Wipf. “Diagnosing and Enhancing VAE Models”. In:International Conference on Learning Representations. 2019.url:https://arxiv.org/abs/1903. 05789

    2019

  5. [5]

    Nat Dilokthanakul et al.Deep Unsupervised Clustering with Gaussian Mixture Varia- tional Autoencoders. 2017. arXiv:1611.02648 [cs.LG].url:https://arxiv.org/ abs/1611.02648

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    Emilien Dupont.Learning Disentangled Joint Continuous and Discrete Representa- tions. 2018. arXiv:1804.00104 [stat.ML].url:https://arxiv.org/abs/1804. 00104

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  7. [7]

    From Variational to Deterministic Autoencoders

    Partha Ghosh et al. “From Variational to Deterministic Autoencoders”. In:Interna- tional Conference on Learning Representations (ICLR). 2020

    2020

  8. [8]

    MIT Press, 2016

    Ian Goodfellow, Yoshua Bengio, and Aaron Courville.Deep Learning. MIT Press, 2016

    2016

  9. [9]

    Junxian He et al.Lagging Inference Networks and Posterior Collapse in Variational Autoencoders. 2019. arXiv:1901.05534 [cs.LG].url:https://arxiv.org/abs/ 1901.05534

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  10. [10]

    Approximating the Kullback Leibler divergence be- tween Gaussian mixture models

    John Hershey and Peder Olsen. “Approximating the Kullback Leibler divergence be- tween Gaussian mixture models”. In:2007 IEEE International Conference on Acous- tics, Speech and Signal Processing (ICASSP). Vol. 4. IEEE. 2007, pp. IV–905

    2007

  11. [11]

    Martin Heusel et al.GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium. 2018. arXiv:1706.08500 [cs.LG].url:https://arxiv. org/abs/1706.08500

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  12. [12]

    beta-VAE: Learning basic visual concepts with a constrained variational framework

    Irina Higgins et al. “beta-VAE: Learning basic visual concepts with a constrained variational framework”. In: (2017)

    2017

  13. [13]

    Reducing the Dimensionality of Data with Neural Networks

    Geoffrey E. Hinton and Ruslan R. Salakhutdinov. “Reducing the Dimensionality of Data with Neural Networks”. In:Science313.5786 (2006), pp. 504–507

    2006

  14. [14]

    ELBO Surgery: Yet Another Way to Carve Up the Variational Evidence Lower Bound

    Matthew D. Hoffman and Matthew J. Johnson. “ELBO Surgery: Yet Another Way to Carve Up the Variational Evidence Lower Bound”. In:Advances in Neural Informa- tion Processing Systems Workshops. NeurIPS Workshop on Advances in Approximate Bayesian Inference. 2016. 20

    2016

  15. [15]

    Springer Texts in Statistics

    Gareth James et al.An Introduction to Statistical Learning: with Applications in R. Springer Texts in Statistics. Springer, 2013.isbn: 978-1-4614-7137-0.url:https : //www.statlearning.com/

    2013

  16. [16]

    Eric Jang, Shixiang Gu, and Ben Poole.Categorical Reparameterization with Gumbel- Softmax. 2017. arXiv:1611.01144 [stat.ML].url:https://arxiv.org/abs/1611. 01144

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  17. [17]

    Diederik P Kingma and Max Welling.Auto-Encoding Variational Bayes. 2022. arXiv: 1312.6114 [stat.ML].url:https://arxiv.org/abs/1312.6114

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  18. [18]

    Kingma and Jimmy Ba.Adam: A Method for Stochastic Optimization

    Diederik P. Kingma and Jimmy Ba.Adam: A Method for Stochastic Optimization

  19. [19]

    arXiv:1412.6980 [cs.LG].url:https://arxiv.org/abs/1412.6980

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    Improving Variational Inference with Inverse Autoregressive Flow

    Diederik P. Kingma et al.Improving Variational Inference with Inverse Autoregressive Flow. 2017. arXiv:1606.04934 [cs.LG].url:https://arxiv.org/abs/1606.04934

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

    AutoVAE: Mismatched Variational Autoencoder with Irregular Posterior-Prior Pairing

    Toshiaki Koike-Akino and Ye Wang. “AutoVAE: Mismatched Variational Autoencoder with Irregular Posterior-Prior Pairing”. In:2022 IEEE International Symposium on Information Theory (ISIT). IEEE. 2022, pp. 1885–1890.doi:10.1109/ISIT50566. 2022.9834769

    work page doi:10.1109/isit50566 2022

  22. [22]

    Autoencoding beyond pixels using a learned similarity metric

    Anders Boesen Lindbo Larsen et al. “Autoencoding beyond pixels using a learned similarity metric”. In:International conference on machine learning. PMLR. 2016, pp. 1558–1566.url:https://arxiv.org/abs/1512.09300

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  23. [23]

    Backpropagation Applied to Handwritten Zip Code Recognition

    Y. LeCun et al. “Backpropagation Applied to Handwritten Zip Code Recognition”. In: Neural Computation1.4 (1989), pp. 541–551.doi:10.1162/neco.1989.1.4.541

    work page doi:10.1162/neco.1989.1.4.541 1989

  24. [24]

    Machine learning in aerody- namic shape optimization

    Jichao Li, Xiaosong Du, and Joaquim R.R.A. Martins. “Machine learning in aerody- namic shape optimization”. In:Progress in Aerospace Sciences134 (2022), p. 100849. issn: 0376-0421.doi:https://doi.org/10.1016/j.paerosci.2022.100849.url: https://www.sciencedirect.com/science/article/pii/S0376042122000410

    work page doi:10.1016/j.paerosci.2022.100849.url: 2022

  25. [25]

    Shuyu Lin et al.Balancing Reconstruction Quality and Regularisation in ELBO for VAEs. 2019. arXiv:1909 . 03765 [cs.LG].url:https : / / arxiv . org / abs / 1909 . 03765

    2019

  26. [26]

    Deep Learning Face Attributes in the Wild

    Ziwei Liu et al. “Deep Learning Face Attributes in the Wild”. In:Proceedings of the IEEE International Conference on Computer Vision (ICCV). 2015, pp. 3730–3738. url:https://arxiv.org/abs/1411.7766

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  27. [27]

    Understanding posterior collapse in generative latent variable models

    James Lucas et al. “Understanding posterior collapse in generative latent variable models”. In:Workshop on Deep Generative Models at ICLR(2019)

    2019

  28. [28]

    Alireza Makhzani et al.Adversarial Autoencoders. 2016. arXiv:1511.05644 [cs.LG]. url:https://arxiv.org/abs/1511.05644

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  29. [29]

    Sampling via Measure Transport: An Introduction

    Youssef Marzouk et al. “Sampling via Measure Transport: An Introduction”. In:Hand- book of Uncertainty Quantification. Springer International Publishing, 2016, pp. 1– 41.isbn: 9783319112596.doi:10 . 1007 / 978 - 3 - 319 - 11259 - 6 _ 23 - 1.url:http : //dx.doi.org/10.1007/978-3-319-11259-6_23-1. 21

    work page doi:10.1007/978-3-319-11259-6_23-1 2016

  30. [30]

    Generating Diverse High-Fidelity Images with VQ-VAE-2

    Ali Razavi, Aaron Van den Oord, and Oriol Vinyals. “Generating diverse high-fidelity images with vq-vae-2”. In:Advances in neural information processing systems. 2019, pp. 14866–14876.url:https://arxiv.org/abs/1906.00446

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  31. [31]

    Danilo Jimenez Rezende and Shakir Mohamed.Variational Inference with Normalizing Flows. 2016. arXiv:1505.05770 [stat.ML].url:https://arxiv.org/abs/1505. 05770

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  32. [32]

    Danilo Jimenez Rezende, Shakir Mohamed, and Daan Wierstra.Stochastic Backpropa- gation and Approximate Inference in Deep Generative Models. 2014. arXiv:1401.4082 [stat.ML].url:https://arxiv.org/abs/1401.4082

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  33. [33]

    Mihaela Ro¸ sca, Balaji Lakshminarayanan, and Shakir Mohamed.Distribution Match- ing in Variational Inference. 2019. arXiv:1802 . 06847 [stat.ML].url:https : / / arxiv.org/abs/1802.06847

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  34. [34]

    Learning represen- tations by back-propagating errors

    David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. “Learning represen- tations by back-propagating errors”. In:Nature323.6088 (1986), pp. 533–536

    1986

  35. [35]

    Tim Salimans et al.Improved Techniques for Training GANs. 2016. arXiv:1606.03498 [cs.LG].url:https://arxiv.org/abs/1606.03498

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  36. [36]

    Casper Kaae Sønderby et al.Ladder Variational Autoencoders. 2016. arXiv:1602 . 02282 [stat.ML].url:https://arxiv.org/abs/1602.02282

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [37]

    Christian Szegedy et al.Rethinking the Inception Architecture for Computer Vision

  38. [38]

    arXiv:1512.00567 [cs.CV].url:https://arxiv.org/abs/1512.00567

    work page internal anchor Pith review Pith/arXiv arXiv

  39. [39]

    VAE with a VampPrior

    Jakub M. Tomczak and Max Welling.VAE with a VampPrior. 2018. arXiv:1705.07120 [cs.LG].url:https://arxiv.org/abs/1705.07120

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  40. [40]

    Aerodynamics-guided machine learning for design optimization of electric vehicles

    Jonathan Tran et al. “Aerodynamics-guided machine learning for design optimization of electric vehicles”. In:Communications Engineering3 (Nov. 2024).doi:10.1038/ s44172-024-00322-0

    2024

  41. [41]

    Arash Vahdat and Jan Kautz.NVAE: A Deep Hierarchical Variational Autoencoder

  42. [42]

    arXiv:2007.03898 [stat.ML].url:https://arxiv.org/abs/2007.03898

    work page arXiv 2007

  43. [43]

    Stacked Denoising Autoencoders: Learning Useful Representa- tions in a Deep Network with a Local Denoising Criterion

    Pascal Vincent et al. “Stacked Denoising Autoencoders: Learning Useful Representa- tions in a Deep Network with a Local Denoising Criterion”. In:Journal of Machine Learning Research11.11 (2010), pp. 3371–3408.url:http://jmlr.org

    2010

  44. [44]

    Yaniv Yacoby, Weiwei Pan, and Finale Doshi-Velez.Failure Modes of Variational Au- toencoders and Their Effects on Downstream Tasks. 2022. arXiv:2007.07124 [stat.ML]. url:https://arxiv.org/abs/2007.07124

    work page arXiv 2022

  45. [45]

    − 1 2 dX j=1 (zj −µ j)2 σ2 j # .(36) Hence: q(z) = 1 (2π)d/2Qd j=1 σq,j exp

    Bin Yu and Karl Kumbier.Veridical Data Science: The Practice of Responsible Data Analysis and Decision Making. Cambridge, MA: MIT Press, 2020. 22 A Derivation of the Gaussian Mixture-KL Objective We prove the sampled upper bound Equation (18). We first establish the general mixture bound and then specialize to the dimension-wise Gaussian case. Lemma 1(Mix...

    work page arXiv 2020