{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T06:10:23Z","timestamp":1784268623321,"version":"3.55.0"},"reference-count":78,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T00:00:00Z","timestamp":1606435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2020,12,31]]},"abstract":"<jats:p>We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand that is cheap to integrate. We show that a set of neural networks can face that challenge: a normalizing flow that approximates the shape of the integrand and another neural network that infers the solution of the integral equation. We also propose to leverage a neural importance sampler to estimate the difference between the original integrand and the learned control variate. To optimize the resulting parametric estimator, we derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. When applied to light transport simulation, neural control variates are capable of matching the state-of-the-art performance of other unbiased approaches, while providing means to develop more performant, practical solutions. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.<\/jats:p>","DOI":"10.1145\/3414685.3417804","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T21:51:05Z","timestamp":1606513865000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":59,"title":["Neural control variates"],"prefix":"10.1145","volume":"39","author":[{"given":"Thomas","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"NVIDIA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fabrice","family":"Rousselle","sequence":"additional","affiliation":[{"name":"NVIDIA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Keller","sequence":"additional","affiliation":[{"name":"NVIDIA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jan","family":"Nov\u00e1k","sequence":"additional","affiliation":[{"name":"NVIDIA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2020,11,27]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Mart\u00edn Abadi Ashish Agarwal Paul Barham Eugene Brevdo Zhifeng Chen Craig Citro Greg S. Corrado Andy Davis Jeffrey Dean etal 2015. TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. http:\/\/tensorflow.org\/  Mart\u00edn Abadi Ashish Agarwal Paul Barham Eugene Brevdo Zhifeng Chen Craig Citro Greg S. Corrado Andy Davis Jeffrey Dean et al. 2015. TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. http:\/\/tensorflow.org\/"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.83.4682"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-011-0377-0"},{"key":"e_1_2_2_4_1","volume-title":"A custom designed Density Estimation Method for Light Transport. MPI-I-2003-4-004 (April","author":"Bekaert Philippe","year":"2003","unstructured":"Philippe Bekaert , Philipp Slusallek , Ronald Cools , Vlastimil Havran , and Hans-Peter Seidel . 2003. A custom designed Density Estimation Method for Light Transport. MPI-I-2003-4-004 (April 2003 ). Philippe Bekaert, Philipp Slusallek, Ronald Cools, Vlastimil Havran, and Hans-Peter Seidel. 2003. A custom designed Density Estimation Method for Light Transport. MPI-I-2003-4-004 (April 2003)."},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2487228.2487239"},{"key":"e_1_2_2_6_1","unstructured":"Benedikt Bitterli. 2016. Rendering resources. https:\/\/benedikt-bitterli.me\/resources\/.  Benedikt Bitterli. 2016. Rendering resources. https:\/\/benedikt-bitterli.me\/resources\/."},{"key":"e_1_2_2_7_1","volume-title":"Risk Management and Analysis, Volume 1: Measuring and Modelling Financial Risk","author":"Broadie Mark","unstructured":"Mark Broadie and Paul Glasserman . 1998. Risk Management and Analysis, Volume 1: Measuring and Modelling Financial Risk . Wiley , New York , Chapter Simulation for option pricing and risk management, 173--208. Mark Broadie and Paul Glasserman. 1998. Risk Management and Analysis, Volume 1: Measuring and Modelling Financial Risk. Wiley, New York, Chapter Simulation for option pricing and risk management, 173--208."},{"key":"e_1_2_2_8_1","volume-title":"Neural Ordinary Differential Equations. arXiv:1806.07366 (June","author":"Chen Tian Qi","year":"2018","unstructured":"Tian Qi Chen , Yulia Rubanova , Jesse Bettencourt , and David Duvenaud . 2018. Neural Ordinary Differential Equations. arXiv:1806.07366 (June 2018 ). Tian Qi Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud. 2018. Neural Ordinary Differential Equations. arXiv:1806.07366 (June 2018)."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01250.x"},{"key":"e_1_2_2_10_1","volume-title":"Learning Light Transport the Reinforced Way","author":"Dahm Ken","unstructured":"Ken Dahm and Alexander Keller . 2018. Learning Light Transport the Reinforced Way . In Monte Carlo and Quasi-Monte Carlo Methods, Art B. Owen and Peter W. Glynn (Eds.). Springer International Publishing , 181--195. Ken Dahm and Alexander Keller. 2018. Learning Light Transport the Reinforced Way. In Monte Carlo and Quasi-Monte Carlo Methods, Art B. Owen and Peter W. Glynn (Eds.). Springer International Publishing, 181--195."},{"key":"e_1_2_2_11_1","volume-title":"NICE: Non-linear Independent Components Estimation. arXiv:1410.8516 (Oct.","author":"Dinh Laurent","year":"2014","unstructured":"Laurent Dinh , David Krueger , and Yoshua Bengio . 2014 . NICE: Non-linear Independent Components Estimation. arXiv:1410.8516 (Oct. 2014). Laurent Dinh, David Krueger, and Yoshua Bengio. 2014. NICE: Non-linear Independent Components Estimation. arXiv:1410.8516 (Oct. 2014)."},{"key":"e_1_2_2_12_1","volume-title":"Density Estimation using Real NVP. arXiv:1605.08803 (March","author":"Dinh Laurent","year":"2016","unstructured":"Laurent Dinh , Jascha Sohl-Dickstein , and Samy Bengio . 2016. Density Estimation using Real NVP. arXiv:1605.08803 (March 2016 ). Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. 2016. Density Estimation using Real NVP. arXiv:1605.08803 (March 2016)."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2006.00954.x"},{"key":"e_1_2_2_14_1","first-page":"6","article-title":"Integral formulations of volumetric transmittance","volume":"38","author":"Georgiev Iliyan","year":"2019","unstructured":"Iliyan Georgiev , Zackary Misso , Toshiya Hachisuka , Derek Nowrouzezahrai , Jaroslav K\u0159iv\u00e1nek , and Wojciech Jarosz . 2019 . Integral formulations of volumetric transmittance . ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 38 , 6 (Nov. 2019). https:\/\/doi.org\/10\/dffn Iliyan Georgiev, Zackary Misso, Toshiya Hachisuka, Derek Nowrouzezahrai, Jaroslav K\u0159iv\u00e1nek, and Wojciech Jarosz. 2019. Integral formulations of volumetric transmittance. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 38, 6 (Nov. 2019). https:\/\/doi.org\/10\/dffn","journal-title":"ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)"},{"key":"e_1_2_2_15_1","volume-title":"MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning. 881--889","author":"Germain Mathieu","year":"2015","unstructured":"Mathieu Germain , Karol Gregor , Iain Murray , and Hugo Larochelle . 2015 . MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning. 881--889 . Mathieu Germain, Karol Gregor, Iain Murray, and Hugo Larochelle. 2015. MADE: Masked Autoencoder for Distribution Estimation. In International Conference on Machine Learning. 881--889."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74496-2_20"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-41095-6_4"},{"key":"e_1_2_2_18_1","volume-title":"Proc. 13th International Conference on Artificial Intelligence and Statistics (May 13--15)","author":"Glorot Xavier","year":"2010","unstructured":"Xavier Glorot and Yoshua Bengio . 2010 . Understanding the Difficulty of Training Deep Feedforward Neural Networks . In Proc. 13th International Conference on Artificial Intelligence and Statistics (May 13--15) . JMLR.org, 249--256. Xavier Glorot and Yoshua Bengio. 2010. Understanding the Difficulty of Training Deep Feedforward Neural Networks. In Proc. 13th International Conference on Artificial Intelligence and Statistics (May 13--15). JMLR.org, 249--256."},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-56046-0_3"},{"key":"e_1_2_2_20_1","volume-title":"International Conference on Learning Representations.","author":"Grathwohl Will","year":"2018","unstructured":"Will Grathwohl , Dami Choi , Yuhuai Wu , Geoff Roeder , and David Duvenaud . 2018 . Back-propagation through the Void: Optimizing control variates for black-box gradient estimation . International Conference on Learning Representations. Will Grathwohl, Dami Choi, Yuhuai Wu, Geoff Roeder, and David Duvenaud. 2018. Back-propagation through the Void: Optimizing control variates for black-box gradient estimation. International Conference on Learning Representations."},{"key":"e_1_2_2_21_1","volume-title":"Deep Residual Learning for Image Recognition. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR).","author":"He Kaiming","year":"2016","unstructured":"Kaiming He , Xiangyu Zhang , Shaoqing Ren , and Jian Sun . 2016 . Deep Residual Learning for Image Recognition. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. 2016. Deep Residual Learning for Image Recognition. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR)."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1998.0471"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1318-5_4"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/3230635"},{"key":"e_1_2_2_25_1","volume-title":"Deep-learning the Latent Space of Light Transport. Computer Graphics Forum 38, 4","author":"Hermosilla Pedro","year":"2019","unstructured":"Pedro Hermosilla , Sebastian Maisch , Tobias Ritschel , and Timo Ropinski . 2019. Deep-learning the Latent Space of Light Transport. Computer Graphics Forum 38, 4 ( 2019 ). Pedro Hermosilla, Sebastian Maisch, Tobias Ritschel, and Timo Ropinski. 2019. Deep-learning the Latent Space of Light Transport. Computer Graphics Forum 38, 4 (2019)."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.44.9.1295"},{"key":"e_1_2_2_27_1","volume-title":"Courville","author":"Huang Chin-Wei","year":"2018","unstructured":"Chin-Wei Huang , David Krueger , Alexandre Lacoste , and Aaron C . Courville . 2018 . Neural Autoregressive Flows . arXiv:1804.00779 (April 2018). Chin-Wei Huang, David Krueger, Alexandre Lacoste, and Aaron C. Courville. 2018. Neural Autoregressive Flows. arXiv:1804.00779 (April 2018)."},{"key":"e_1_2_2_28_1","volume-title":"Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. arXiv:1502.03167","author":"Ioffe Sergey","year":"2015","unstructured":"Sergey Ioffe and Christian Szegedy . 2015 . Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. arXiv:1502.03167 (2015). Sergey Ioffe and Christian Szegedy. 2015. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. arXiv:1502.03167 (2015)."},{"key":"e_1_2_2_29_1","unstructured":"Wenzel Jakob. 2010. Mitsuba Renderer. http:\/\/www.mitsuba-renderer.org.  Wenzel Jakob. 2010. Mitsuba Renderer. http:\/\/www.mitsuba-renderer.org."},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/3130800.3130880"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(00)00248-2"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4266(90)90039-5"},{"key":"e_1_2_2_33_1","volume-title":"Kingma and Jimmy Ba","author":"Diederik","year":"2014","unstructured":"Diederik P. Kingma and Jimmy Ba . 2014 . Adam : A Method for Stochastic Optimization . arXiv:1412.6980 (June 2014). Diederik P. Kingma and Jimmy Ba. 2014. Adam: A Method for Stochastic Optimization. arXiv:1412.6980 (June 2014)."},{"key":"e_1_2_2_34_1","volume-title":"Kingma and Prafulla Dhariwal","author":"Diederik","year":"2018","unstructured":"Diederik P. Kingma and Prafulla Dhariwal . 2018 . Glow : Generative Flow with Invertible 1x1 Convolutions . arXiv:1807.03039 (July 2018). Diederik P. Kingma and Prafulla Dhariwal. 2018. Glow: Generative Flow with Invertible 1x1 Convolutions. arXiv:1807.03039 (July 2018)."},{"key":"e_1_2_2_35_1","unstructured":"Diederik P. Kingma Tim Salimans Rafal Jozefowicz Xi Chen Ilya Sutskever and Max Welling. 2016. Improved Variational Inference with inverse Autoregressive Flow. In Advances in Neural Information Processing Systems. 4743--4751.  Diederik P. Kingma Tim Salimans Rafal Jozefowicz Xi Chen Ilya Sutskever and Max Welling. 2016. Improved Variational Inference with inverse Autoregressive Flow. In Advances in Neural Information Processing Systems. 4743--4751."},{"key":"e_1_2_2_36_1","volume-title":"Brubaker","author":"Kobyzev Ivan","year":"2019","unstructured":"Ivan Kobyzev , Simon Prince , and Marcus A . Brubaker . 2019 . Normalizing Flows : An Introduction and Review of Current Methods . arXiv:stat.ML\/1908.09257 Ivan Kobyzev, Simon Prince, and Marcus A. Brubaker. 2019. Normalizing Flows: An Introduction and Review of Current Methods. arXiv:stat.ML\/1908.09257"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323009"},{"key":"e_1_2_2_38_1","volume-title":"Willems","author":"Lafortune Eric P.","year":"1994","unstructured":"Eric P. Lafortune and Yves D . Willems . 1994 . The Ambient Term as a Variance Reducing Technique for Monte Carlo Ray Tracing. In Proc. EGWR. 163--171. Eric P. Lafortune and Yves D. Willems. 1994. The Ambient Term as a Variance Reducing Technique for Monte Carlo Ray Tracing. In Proc. EGWR. 163--171."},{"key":"e_1_2_2_39_1","volume-title":"Willems","author":"Lafortune Eric P.","year":"1995","unstructured":"Eric P. Lafortune and Yves D . Willems . 1995 . A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing. In Proc. EGWR. 11--20. Eric P. Lafortune and Yves D. Willems. 1995. A 5D Tree to Reduce the Variance of Monte Carlo Ray Tracing. In Proc. EGWR. 11--20."},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.30.1.182"},{"key":"e_1_2_2_41_1","unstructured":"Jaakko Lehtinen Jacob Munkberg Jon Hasselgren Samuli Laine Tero Karras Miika Aittala and Timo Aila. 2018. Noise2Noise: Learning Image Restoration without Clean Data. arXiv:cs.CV\/1803.04189  Jaakko Lehtinen Jacob Munkberg Jon Hasselgren Samuli Laine Tero Karras Miika Aittala and Timo Aila. 2018. Noise2Noise: Learning Image Restoration without Clean Data. arXiv:cs.CV\/1803.04189"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323020"},{"key":"e_1_2_2_43_1","volume-title":"Deep Appearance Maps. In The IEEE International Conference on Computer Vision (ICCV).","author":"Maximov Maxim","year":"2019","unstructured":"Maxim Maximov , Laura Leal-Taixe , Mario Fritz , and Tobias Ritschel . 2019 . Deep Appearance Maps. In The IEEE International Conference on Computer Vision (ICCV). Maxim Maximov, Laura Leal-Taixe, Mario Fritz, and Tobias Ritschel. 2019. Deep Appearance Maps. In The IEEE International Conference on Computer Vision (ICCV)."},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323027"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-012-9344-6"},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/3305366.3328091"},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13227"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1145\/3341156"},{"key":"e_1_2_2_49_1","volume-title":"Deep Shading: Convolutional Neural Networks for Screen-Space Shading. 36, 4","author":"Nalbach Oliver","year":"2017","unstructured":"Oliver Nalbach , Elena Arabadzhiyska , Dushyant Mehta , Hans-Peter Seidel , and Tobias Ritschel . 2017 . Deep Shading: Convolutional Neural Networks for Screen-Space Shading. 36, 4 (2017). Oliver Nalbach, Elena Arabadzhiyska, Dushyant Mehta, Hans-Peter Seidel, and Tobias Ritschel. 2017. Deep Shading: Convolutional Neural Networks for Screen-Space Shading. 36, 4 (2017)."},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.38.6.974"},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/2661229.2661292"},{"key":"e_1_2_2_52_1","doi-asserted-by":"publisher","DOI":"10.1111\/rssb.12185"},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2000.10473909"},{"key":"e_1_2_2_54_1","unstructured":"George Papamakarios Iain Murray and Theo Pavlakou. 2017. Masked Autoregressive Flow for Density Estimation. In Advances in Neural Information Processing Systems. 2338--2347.  George Papamakarios Iain Murray and Theo Pavlakou. 2017. Masked Autoregressive Flow for Density Estimation. In Advances in Neural Information Processing Systems. 2338--2347."},{"key":"e_1_2_2_55_1","volume-title":"Shakir Mohamed, and Balaji Lakshminarayanan.","author":"Papamakarios George","year":"2019","unstructured":"George Papamakarios , Eric Nalisnick , Danilo Jimenez Rezende , Shakir Mohamed, and Balaji Lakshminarayanan. 2019 . Normalizing Flows for Probabilistic Modeling and Inference . arXiv:stat.ML\/1912.02762 George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, and Balaji Lakshminarayanan. 2019. Normalizing Flows for Probabilistic Modeling and Inference. arXiv:stat.ML\/1912.02762"},{"key":"e_1_2_2_56_1","volume-title":"Proceedings of the 3rd IEEE Symposium on Interactive Ray Tracing. 107--114","author":"Pegoraro Vincent","unstructured":"Vincent Pegoraro , Carson Brownlee , Peter S. Shirley , and Steven G. Parker . 2008a. Towards Interactive Global Illumination Effects via Sequential Monte Carlo Adaptation . In Proceedings of the 3rd IEEE Symposium on Interactive Ray Tracing. 107--114 . Vincent Pegoraro, Carson Brownlee, Peter S. Shirley, and Steven G. Parker. 2008a. Towards Interactive Global Illumination Effects via Sequential Monte Carlo Adaptation. In Proceedings of the 3rd IEEE Symposium on Interactive Ray Tracing. 107--114."},{"key":"e_1_2_2_57_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01247.x"},{"key":"e_1_2_2_58_1","volume-title":"Physically Based Rendering - From Theory to Implementation. Morgan Kaufmann","author":"Pharr Matt","unstructured":"Matt Pharr , Wenzel Jacob , and Greg Humphreys . 2016. Physically Based Rendering - From Theory to Implementation. Morgan Kaufmann , Third Edition. Matt Pharr, Wenzel Jacob, and Greg Humphreys. 2016. Physically Based Rendering - From Theory to Implementation. Morgan Kaufmann, Third Edition."},{"key":"e_1_2_2_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2462009"},{"key":"e_1_2_2_60_1","volume-title":"Variational Inference with Normalizing Flows. In International Conference on Machine Learning. 1530--1538","author":"Rezende Danilo","year":"2015","unstructured":"Danilo Rezende and Shakir Mohamed . 2015 . Variational Inference with Normalizing Flows. In International Conference on Machine Learning. 1530--1538 . Danilo Rezende and Shakir Mohamed. 2015. Variational Inference with Normalizing Flows. In International Conference on Machine Learning. 1530--1538."},{"key":"e_1_2_2_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982443"},{"key":"e_1_2_2_62_1","doi-asserted-by":"publisher","DOI":"10.1145\/2070781.2024193"},{"key":"e_1_2_2_63_1","doi-asserted-by":"crossref","unstructured":"Vincent Sitzmann Justus Thies Felix Heide Matthias Nie\u00dfner Gordon Wetzstein and Michael Zollh\u00f6fer. 2018. DeepVoxels: Learning Persistent 3D Feature Embeddings. In CVPR.  Vincent Sitzmann Justus Thies Felix Heide Matthias Nie\u00dfner Gordon Wetzstein and Michael Zollh\u00f6fer. 2018. DeepVoxels: Learning Persistent 3D Feature Embeddings. In CVPR.","DOI":"10.1109\/CVPR.2019.00254"},{"key":"e_1_2_2_64_1","volume-title":"Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability","volume":"602","author":"Stein Charles","year":"1972","unstructured":"Charles Stein . 1972 . A bound for the error in the normal approximation to the distribution of a sum of dependent random variables . In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability , Volume 2: Probability Theory. University of California Press, Berkeley, Calif., 583-- 602 . https:\/\/projecteuclid.org\/euclid.bsmsp\/1200514239 Charles Stein. 1972. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Probability Theory. University of California Press, Berkeley, Calif., 583--602. https:\/\/projecteuclid.org\/euclid.bsmsp\/1200514239"},{"key":"e_1_2_2_65_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2004.00790.x"},{"key":"e_1_2_2_66_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01831.x"},{"key":"e_1_2_2_67_1","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.21423"},{"key":"e_1_2_2_68_1","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2010.v8.n1.a11"},{"key":"e_1_2_2_69_1","doi-asserted-by":"crossref","unstructured":"Ayush Tewari Ohad Fried Justus Thies Vincent Sitzmann Stephen Lombardi Kalyan Sunkavalli Ricardo Martin-Brualla Tomas Simon Jason Saragih Matthias Nie\u00dfner Rohit Pandey Sean Fanello Gordon Wetzstein Jun-Yan Zhu Christian Theobalt Maneesh Agrawala Eli Shechtman Dan B Goldman and Michael Zollh\u00f6fer. 2020. State of the Art on Neural Rendering. arXiv:cs.CV\/2004.03805  Ayush Tewari Ohad Fried Justus Thies Vincent Sitzmann Stephen Lombardi Kalyan Sunkavalli Ricardo Martin-Brualla Tomas Simon Jason Saragih Matthias Nie\u00dfner Rohit Pandey Sean Fanello Gordon Wetzstein Jun-Yan Zhu Christian Theobalt Maneesh Agrawala Eli Shechtman Dan B Goldman and Michael Zollh\u00f6fer. 2020. State of the Art on Neural Rendering. arXiv:cs.CV\/2004.03805","DOI":"10.1111\/cgf.14022"},{"key":"e_1_2_2_70_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323035"},{"key":"e_1_2_2_72_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218498"},{"key":"e_1_2_2_73_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322974"},{"key":"e_1_2_2_74_1","volume-title":"Unbiased deep solvers for parametric PDEs. arXiv:1810.05094 (Oct","author":"Vidales Marc Sabate","year":"2018","unstructured":"Marc Sabate Vidales , David Siska , and Lukasz Szpruch . 2018. Unbiased deep solvers for parametric PDEs. arXiv:1810.05094 (Oct . 2018 ). Marc Sabate Vidales, David Siska, and Lukasz Szpruch. 2018. Unbiased deep solvers for parametric PDEs. arXiv:1810.05094 (Oct. 2018)."},{"key":"e_1_2_2_75_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601203"},{"key":"e_1_2_2_76_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925912"},{"key":"e_1_2_2_77_1","volume-title":"Neural Control Variates for Variance Reduction. arXiv:1806.00159 (Oct","author":"Wan Ruosi","year":"2019","unstructured":"Ruosi Wan , Mingjun Zhong , Haoyi Xiong , and Zhanxing Zhu . 2019. Neural Control Variates for Variance Reduction. arXiv:1806.00159 (Oct . 2019 ). Ruosi Wan, Mingjun Zhong, Haoyi Xiong, and Zhanxing Zhu. 2019. Neural Control Variates for Variance Reduction. arXiv:1806.00159 (Oct. 2019)."},{"key":"e_1_2_2_78_1","doi-asserted-by":"publisher","DOI":"10.2312\/pg.20181271"},{"key":"e_1_2_2_79_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13628"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3414685.3417804","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3414685.3417804","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T22:03:14Z","timestamp":1750197794000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3414685.3417804"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,27]]},"references-count":78,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,12,31]]}},"alternative-id":["10.1145\/3414685.3417804"],"URL":"https:\/\/doi.org\/10.1145\/3414685.3417804","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,27]]},"assertion":[{"value":"2020-11-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}