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Optimizing Information-theoretical Generalization Bounds via Anisotropic Noise in SGLD [article]

Bohan Wang, Huishuai Zhang, Jieyu Zhang, Qi Meng, Wei Chen, Tie-Yan Liu
<span title="2021-11-03">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we optimize the information-theoretical generalization bound by manipulating the noise structure in SGLD.  ...  Recently, the information-theoretical framework has been proven to be able to obtain non-vacuous generalization bounds for large models trained by Stochastic Gradient Langevin Dynamics (SGLD) with isotropic  ...  Ziming Liu for helpful theoretical discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.13750v2">arXiv:2110.13750v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r7dfq5uisrbghkqmlvu2y7jtva">fatcat:r7dfq5uisrbghkqmlvu2y7jtva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211108063209/https://arxiv.org/pdf/2110.13750v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/27/0b/270bbab271658cb221943c36a0e7be1fe7a488fe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.13750v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Stability Based Generalization Bounds for Exponential Family Langevin Dynamics [article]

Arindam Banerjee, Tiancong Chen, Xinyan Li, Yingxue Zhou
<span title="2022-01-09">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Generalization bounds for noisy sign-SGD are implied by that of EFLD and we also establish optimization guarantees for the algorithm.  ...  Second, we introduce Exponential Family Langevin Dynamics(EFLD) which is a substantial generalization of SGLD and which allows exponential family noise to be used with stochastic gradient descent (SGD)  ...  Besides the works mentioned above, other theories of deriving generalization bounds for noisy iterative algorithms have been proposed via information-theoretic approaches (Russo and Zou, 2016; Xu and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.03064v1">arXiv:2201.03064v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z7a7b4rg7rav7kmzdzwdntlski">fatcat:z7a7b4rg7rav7kmzdzwdntlski</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220112005803/https://arxiv.org/pdf/2201.03064v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/c7/7cc71e9d2642e18f17f6ec3d03ac0efbac2d9922.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.03064v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

An Empirical Study of Large-Batch Stochastic Gradient Descent with Structured Covariance Noise [article]

Yeming Wen, Kevin Luk, Maxime Gazeau, Guodong Zhang, Harris Chan, Jimmy Ba
<span title="2020-02-28">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
To address the problem of improving generalization while maintaining optimal convergence in large-batch training, we propose to add covariance noise to the gradients.  ...  The choice of batch-size in a stochastic optimization algorithm plays a substantial role for both optimization and generalization.  ...  Generalization bounds of sgld for non-convex learn- ing: Two theoretical viewpoints. arXiv preprint arXiv:1707.05947, 2017. Eric Moulines and Francis R Bach.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.08234v4">arXiv:1902.08234v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/656pntkmmnhcldlmtgzxktoniy">fatcat:656pntkmmnhcldlmtgzxktoniy</a> </span>
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Artificial Neural Variability for Deep Learning: On Overfitting, Noise Memorization, and Catastrophic Forgetting

Zeke Xie, Fengxiang He, Shaopeng Fu, Issei Sato, Dacheng Tao, Masashi Sugiyama
<span title="2021-05-26">2021</span> <i title="MIT Press - Journals"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rckx6fqoszfvva5c53bqivu5am" style="color: black;">Neural Computation</a> </i> &nbsp;
We rigorously prove that ANV plays as an implicit regularizer of the mutual information between the training data and the learned model.  ...  This result theoretically guarantees ANV a strictly improved generalizability, robustness to label noise, and robustness to catastrophic forgetting.  ...  (A.5) Appendix B: The Mutual-Information Generalization Bound We formulate a mutual information theoretical foundation of (b, δ)-neural variability, which is more related to the neuroscience mechanism  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/neco_a_01403">doi:10.1162/neco_a_01403</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/34310675">pmid:34310675</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u5tzeigrzrhsxjgozxrpbjgszm">fatcat:u5tzeigrzrhsxjgozxrpbjgszm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210617083305/https://watermark.silverchair.com/neco_a_01403.pdf?token=AQECAHi208BE49Ooan9kkhW_Ercy7Dm3ZL_9Cf3qfKAc485ysgAAAqowggKmBgkqhkiG9w0BBwagggKXMIICkwIBADCCAowGCSqGSIb3DQEHATAeBglghkgBZQMEAS4wEQQMquEBR3Yu5noeXC6DAgEQgIICXVmxtJHxk_tw25RlfaU5xhMBEjtqgjOPgr34n8Bi_D3F23Kn-nPfgAmgA-EiNpED8tmw6yF_Gb66Bd69DO2kVigzsOX3xwGlOTZUOVy15Kp-ZNMqsGDzy4tPV18o1g0wQNqXPtK7srAVRqg0xJtJ0DTsbXXz_huJl4LlgBZibaeXHm_vHKLhLKHIoK_SXcUAvqdAO3OwjXcRUYhaydBEwkvFLXMX3wyc22ikm21I_0H6Y29fSvWz1UERIE46SUTLKrW2xbvNFuk_Ff-k12p7zkPs2ydJ0yLrSwZr5GxGU1QANujUAB740xwduqBmZ-dXN2rtYb27j6lqCz5zUrFXxO96SCnSm8WnE9XzyLNNbYycYoFZqx060REktrAWY7X12kjjN44cI4UO7BA42rWHMMy-OguwXy620R9trHmJNSJKcoMnuT3lwIwwtYRmCoymPhYXrsGXnmMcRuauFApeblACae0iZyzf5x607sqwfyx87muuClfld5EMQ3-NGG-Q6EkmOlteWXo-76seMl89HPLbgruqFBeWeVSY2poLH0rbFibRMLrbaDN3m1sFX6R1eIOP1jeErtmEFyDat5U-Qm7vamTpZLhiQC7WPfohYGBa87MJ9QEf2RkqdSAFWmUH9pohdKZB7dh0GFs1lXarrwTN2rvAzPNuKilumWq83ihkhj3jX-U1_nPGWemi6MsmA7957-FBnYwnEQboIcTrzMw1XJkIO3vdvkTycS7nz2f9dauRZfSqzGPhdlvzVNiswUjQn1DUPeKW9Tb164SHkRsDuq3ndaZJdc07JvAj" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/af/59/af5970be518282b7bda3671ecbe2efb18baf1d0b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1162/neco_a_01403"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> mitpressjournals.org </button> </a>

Shape Matters: Understanding the Implicit Bias of the Noise Covariance [article]

Jeff Z. HaoChen, Colin Wei, Jason D. Lee, Tengyu Ma
<span title="2020-06-18">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Prior theoretical work largely focuses on spherical Gaussian noise, whereas empirical studies demonstrate the phenomenon that parameter-dependent noise -- induced by mini-batches or label perturbation  ...  This paper theoretically characterizes this phenomenon on a quadratically-parameterized model introduced by Vaskevicius et el. and Woodworth et el.  ...  JDL acknowledges support of the ARO under MURI Award W911NF-11-1-0303, the Sloan Research Fellowship, and NSF CCF 2002272. TM acknowledges support of Google Faculty Award.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.08680v2">arXiv:2006.08680v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g2jg27ryybbpzi2kxh5p7cy3ny">fatcat:g2jg27ryybbpzi2kxh5p7cy3ny</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200624065938/https://arxiv.org/pdf/2006.08680v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.08680v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Geometry-informed irreversible perturbations for accelerated convergence of Langevin dynamics [article]

Benjamin J. Zhang, Youssef M. Marzouk, Konstantinos Spiliopoulos
<span title="2021-08-18">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm.  ...  We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation.  ...  The lower bound is then the optimal spectral gap.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.08247v1">arXiv:2108.08247v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cxvbbrjf4bhbbm5qesxzjqu3c4">fatcat:cxvbbrjf4bhbbm5qesxzjqu3c4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210831061723/https://arxiv.org/pdf/2108.08247v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/17/d3/17d3d8c0eedea001cbb0e951bab0d7647cfa4f35.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2108.08247v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Solving Inverse Problems with Hybrid Deep Image Priors: the challenge of preventing overfitting [article]

Zhaodong Sun
<span title="2021-02-21">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
However, due to the large number of parameters of the neural network and noisy data, DIP overfits to the noise in the image as the number of iterations grows.  ...  When the noise level is small, it does not considerably reduce the overfitting problem.  ...  We can still use the prior information from denoising algorithms via the proximal operator.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.01748v2">arXiv:2011.01748v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o23wwxmed5genl5gdkpd6k5qaa">fatcat:o23wwxmed5genl5gdkpd6k5qaa</a> </span>
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Benefit of deep learning with non-convex noisy gradient descent: Provable excess risk bound and superiority to kernel methods [article]

Taiji Suzuki, Shunta Akiyama
<span title="2020-12-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Establishing a theoretical analysis that explains why deep learning can outperform shallow learning such as kernel methods is one of the biggest issues in the deep learning literature.  ...  We consider a teacher-student regression model, and eventually show that any linear estimator can be outperformed by deep learning in a sense of the minimax optimal rate especially for a high dimension  ...  Generalization bound of globally optimal non-convex neural network training: Trans- portation map estimation by infinite dimensional langevin dynamics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.03224v1">arXiv:2012.03224v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xawtcfmgvnfanavinz72j2cqg4">fatcat:xawtcfmgvnfanavinz72j2cqg4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201209060648/https://arxiv.org/pdf/2012.03224v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/c5/77c530612412c36c3d2b1ee0a1cea6b37a7f518f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.03224v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges [article]

Moloud Abdar, Farhad Pourpanah, Sadiq Hussain, Dana Rezazadegan, Li Liu, Mohammad Ghavamzadeh, Paul Fieguth, Xiaochun Cao, Abbas Khosravi, U Rajendra Acharya, Vladimir Makarenkov, Saeid Nahavandi
<span title="2021-01-06">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes.  ...  Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods.  ...  [520] introduced a novel theoretical perspective of data noising in RNN language models.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.06225v4">arXiv:2011.06225v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wwnl7duqwbcqbavat225jkns5u">fatcat:wwnl7duqwbcqbavat225jkns5u</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210113234503/https://arxiv.org/pdf/2011.06225v4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f1/4f/f14fc9e399d44463a17cc47a9b339b58f6ef7502.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.06225v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Efficient MCMC Sampling with Dimension-Free Convergence Rate using ADMM-type Splitting [article]

Maxime Vono and Daniel Paulin and Arnaud Doucet
<span title="2021-12-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we propose a detailed theoretical study of one of these algorithms known as the split Gibbs sampler.  ...  We focus here on a recent alternative class of MCMC schemes exploiting a splitting strategy akin to the one used by the celebrated alternating direction of multipliers (ADMM) optimization algorithm.  ...  We thank Solomon Jacobs and Andreas Eberle for pointing out an error in the proof of Proposition 6 in a previous version of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1905.11937v6">arXiv:1905.11937v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cji5txyqebfxlfi7uw6ny4kcsu">fatcat:cji5txyqebfxlfi7uw6ny4kcsu</a> </span>
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Noise and Fluctuation of Finite Learning Rate Stochastic Gradient Descent [article]

Kangqiao Liu, Liu Ziyin, Masahito Ueda
<span title="2021-06-11">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Examples of applications of the proposed theory considered in this work include the approximation error of variants of SGD, the effect of minibatch noise, the optimal Bayesian inference, the escape rate  ...  The main contributions of this work are to derive the stationary distribution for discrete-time SGD in a quadratic loss function with and without momentum; in particular, one implication of our result  ...  JP15H05855) from the Japan Society for the Promotion of Science.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.03636v4">arXiv:2012.03636v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qdfckohjlzh6tks3e2ry3ajrje">fatcat:qdfckohjlzh6tks3e2ry3ajrje</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210615105319/https://arxiv.org/pdf/2012.03636v4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/30/0b/300b0335abcca6748555e98dfd744b9d39bbbf51.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2012.03636v4" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Well-calibrated predictive uncertainty in medical imaging with Bayesian Deep Learning [article]

Max-Heinrich Viktor Laves, University, My
<span title="2021-12-20">2021</span>
We propose BatchPL, a sample acquisition scheme that selects highly informative samples for pseudo-labeling in self- and unsupervised learning scenarios.  ...  Due to increasing availability and the reduction of costs, the number of medical imaging examinations is continuously growing, resulting in a huge amount of data that has to be assessed by medical experts  ...  Figure 4.3: Peak signal-to-noise ratio between denoised image x and ground truth x vs. number of optimizer iterations. DIP and SGLD(+NLL) quickly overfit the noisy image.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15488/11588">doi:10.15488/11588</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hkyyhvzumrecxeuar2m6mjyosi">fatcat:hkyyhvzumrecxeuar2m6mjyosi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211225052436/https://www.repo.uni-hannover.de/bitstream/handle/123456789/11679/Laves_Max-Heinrich_Viktor_2021.pdf;jsessionid=8F251A743E655B4FCBC28BE105026F94?sequence=3" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/80/d9/80d9463965ae01c630c75adf420fff51330422b3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15488/11588"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

CHARMM: The biomolecular simulation program

B. R. Brooks, C. L. Brooks, A. D. Mackerell, L. Nilsson, R. J. Petrella, B. Roux, Y. Won, G. Archontis, C. Bartels, S. Boresch, A. Caflisch, L. Caves (+23 others)
<span title="2009-07-30">2009</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/72zcmi3smndcrdvxgve7ny6ytq" style="color: black;">Journal of Computational Chemistry</a> </i> &nbsp;
This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article  ...  For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization,  ...  Diagram depicting the general scheme of the information flow in a CHARMM project.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200321122444/http://www.mmtsb.org/workshops/mmtsb-ctbp_workshop_2009/ReadingMaterials/09_JCC_30_1545.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/cb/e1cb312fac9fc9b47b551c8c646684140536f27d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jcc.21287"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2810661" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Reservoir modeling and inversion using generative adversarial network priors

Lukas J. Mosser, Olivier Dubrule, Martin Blunt
<span title="2020-06-24">2020</span>
Generative Adversarial Networks (GANs) are deep generative models that learn a representation of the probability distribution implicitly defined by a set of training images using two competing neural networks  ...  Recently, deep generative modeling has enabled multi-modal probability distributions of large three-dimensional natural images to be represented.  ...  Instead, we optimize a lower bound on the model evidence (Evidence Lower BOund -ELBO) which can be shown to be equivalent to minimizing the KL-divergence.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200702183754/https://spiral.imperial.ac.uk:8443/bitstream/10044/1/80165/1/Mosser-L-2019-PhD-Thesis.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/57/e9/57e9a5c7b756577215c3906ab12813b7f4709614.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.25560/80165"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>