ZeroGrads: Learning Local Surrogates for Non-Differentiable Graphics
Article No.: 49, Pages 1 - 15
Abstract
Gradient-based optimization is now ubiquitous across graphics, but unfortunately can not be applied to problems with undefined or zero gradients. To circumvent this issue, the loss function can be manually replaced by a "surrogate" that has similar minima but is differentiable. Our proposed framework, ZeroGrads, automates this process by learning a neural approximation of the objective function, which in turn can be used to differentiate through arbitrary black-box graphics pipelines. We train the surrogate on an actively smoothed version of the objective and encourage locality, focusing the surrogate's capacity on what matters at the current training episode. The fitting is performed online, alongside the parameter optimization, and self-supervised, without pre-computed data or pre-trained models. As sampling the objective is expensive (it requires a full rendering or simulator run), we devise an efficient sampling scheme that allows for tractable run-times and competitive performance at little overhead. We demonstrate optimizing diverse non-convex, non-differentiable black-box problems in graphics, such as visibility in rendering, discrete parameter spaces in procedural modelling or optimal control in physics-driven animation. In contrast to other derivative-free algorithms, our approach scales well to higher dimensions, which we demonstrate on problems with up to 35k interlinked variables.
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References
[1]
Navid Ansari, Hans-Peter Seidel, Nima Vahidi Ferdowsi, and Vahid Babaei. 2022. Autoinverse: Uncertainty aware inversion of neural networks. Advances in Neural Information Processing Systems 35 (2022), 8675--8686.
[2]
Sai Bangaru, Lifan Wu, Tzu-Mao Li, Jacob Munkberg, Gilbert Bernstein, Jonathan Ragan-Kelley, Fredo Durand, Aaron Lefohn, and Yong He. 2023. SLANG.D: Fast, Modular and Differentiable Shader Programming. ACM Transactions on Graphics (SIGGRAPH Asia) 42, 6 (December 2023), 1--28.
[3]
Sai Praveen Bangaru, Michaël Gharbi, Tzu-Mao Li, Fujun Luan, Kalyan Sunkavalli, Miloš Hašan, Sai Bi, Zexiang Xu, Gilbert Bernstein, and Frédo Durand. 2022. Differentiable Rendering of Neural SDFs through Reparameterization. arXiv preprint arXiv:2206.05344 (2022).
[4]
Sai Praveen Bangaru, Jesse Michel, Kevin Mu, Gilbert Bernstein, Tzu-Mao Li, and Jonathan Ragan-Kelley. 2021. Systematically differentiating parametric discontinuities. ACM Trans. Graph. 40, 4 (2021), 1--18.
[5]
Russell R Barton. 1994. Metamodeling: a state of the art review. In Proceedings of Winter Simulation Conference. IEEE, 237--244.
[6]
Gabriel Belouze. 2022. Optimization without Backpropagation. arXiv preprint arXiv:2209.06302 (2022).
[7]
Quentin Berthet, Mathieu Blondel, Olivier Teboul, Marco Cuturi, Jean-Philippe Vert, and Francis Bach. 2020. Learning with differentiable pertubed optimizers. Advances in neural information processing systems 33 (2020), 9508--9519.
[8]
George EP Box and Norman R Draper. 1987. Empirical model-building and response surfaces. John Wiley & Sons.
[9]
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang. 2018. JAX: composable transformations of Python+NumPy programs. http://github.com/google/jax
[10]
Kartik Chandra. 2021. An Unexpected Challenge in Using Forward-Mode Automatic Differentiation for Low-Memory Deep Learning. Undergrad Theses (2021).
[11]
Kartik Chandra, Tzu-Mao Li, Joshua Tenenbaum, and Jonathan Ragan-Kelley. 2022. Designing Perceptual Puzzles by Differentiating Probabilistic Programs. In Proc. SIGRAPH. Article 21, 9 pages.
[12]
Michael B Chang, Tomer Ullman, Antonio Torralba, and Joshua B Tenenbaum. 2016. A compositional object-based approach to learning physical dynamics. arXiv preprint arXiv:1612.00341 (2016).
[13]
Swarat Chaudhuri and Armando Solar-Lezama. 2010. Smooth interpretation. ACM Sigplan Notices 45, 6 (2010), 279--291.
[14]
Per Christensen, Julian Fong, Jonathan Shade, Wayne Wooten, Brenden Schubert, Andrew Kensler, Stephen Friedman, Charlie Kilpatrick, Cliff Ramshaw, Marc Bannister, et al. 2018. Renderman: An advanced path-tracing architecture for movie rendering. ACM Trans. Graph. 37, 3 (2018), 1--21.
[15]
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. 2009. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference on computer vision and pattern recognition. Ieee, 248--255.
[16]
Xi Deng, Fujun Luan, Bruce Walter, Kavita Bala, and Steve Marschner. 2022. Reconstructing translucent objects using differentiable rendering. In ACM SIGGRAPH 2022 Conference Proceedings. 1--10.
[17]
John C Duchi, Peter L Bartlett, and Martin J Wainwright. 2012. Randomized smoothing for stochastic optimization. SIAM Journal on Optimization 22, 2 (2012), 674--701.
[18]
Hadi Esmaeilzadeh, Adrian Sampson, Luis Ceze, and Doug Burger. 2012. Neural acceleration for general-purpose approximate programs. In 2012 45th Annual IEEE/ACM International Symposium on Microarchitecture. IEEE, 449--460.
[19]
Michael Fischer, Konstantin Kobs, and Andreas Hotho. 2020. NICER: Aesthetic image enhancement with humans in the loop. arXiv preprint arXiv:2012.01778 (2020).
[20]
Michael Fischer and Tobias Ritschel. 2022a. Metappearance: Meta-Learning for Visual Appearance Reproduction. ACM Trans. Graph. 41, 6 (2022), 1--13.
[21]
Michael Fischer and Tobias Ritschel. 2022b. Plateau-free Differentiable Path Tracing. arXiv preprint arXiv:2211.17263 (2022).
[22]
Alexander IJ Forrester and Andy J Keane. 2009. Recent advances in surrogate-based optimization. Progress in aerospace sciences 45, 1--3 (2009), 50--79.
[23]
Marc-André Gardner, Yannick Hold-Geoffroy, Kalyan Sunkavalli, Christian Gagné, and Jean-François Lalonde. 2019. Deep parametric indoor lighting estimation. In Proc. ICCV. 7175--83.
[24]
Josif Grabocka, Randolf Scholz, and Lars Schmidt-Thieme. 2019. Learning surrogate losses. arXiv preprint arXiv:1905.10108 (2019).
[25]
Radek Grzeszczuk, Demetri Terzopoulos, and Geoffrey Hinton. 1998. Neuroanimator: Fast neural network emulation and control of physics-based models. In Proc. SIGGRAPH. 9--20.
[26]
Paul Guerrero, Miloš Hašan, Kalyan Sunkavalli, Radomír Měch, Tamy Boubekeur, and Niloy J Mitra. 2022. Matformer: A generative model for procedural materials. arXiv preprint arXiv:2207.01044 (2022).
[27]
H-M Gutmann. 2001. A radial basis function method for global optimization. J global optimization 19, 3 (2001), 201--227.
[28]
John K Haas. 2014. A history of the unity game engine. Diss. WORCESTER POLYTECHNIC INSTITUTE 483 (2014), 484.
[29]
Marc Habermann, Lingjie Liu, Weipeng Xu, Michael Zollhoefer, Gerard Pons-Moll, and Christian Theobalt. 2021. Real-time deep dynamic characters. ACM Trans. Graph. 40, 4 (2021), 1--16.
[30]
Nikolaus Hansen. 2016. The CMA evolution strategy: A tutorial. arXiv preprint arXiv:1604.00772 (2016).
[31]
Philipp Holl, Vladlen Koltun, and Nils Thuerey. 2020. Learning to control pdes with differentiable physics. arXiv preprint arXiv:2001.07457 (2020).
[32]
John H Holland. 1973. Genetic algorithms and the optimal allocation of trials. SIAM journal on computing 2, 2 (1973), 88--105.
[33]
Yuanming Hu, Luke Anderson, Tzu-Mao Li, Qi Sun, Nathan Carr, Jonathan Ragan-Kelley, and Frédo Durand. 2019. Difftaichi: Differentiable programming for physical simulation. arXiv preprint arXiv:1910.00935 (2019).
[34]
Yiwei Hu, Paul Guerrero, Milos Hasan, Holly Rushmeier, and Valentin Deschaintre. 2022a. Node Graph Optimization Using Differentiable Proxies. In Proc. SIGGRAPH. 1--9.
[35]
Yiwei Hu, Chengan He, Valentin Deschaintre, Julie Dorsey, and Holly Rushmeier. 2022b. An inverse procedural modeling pipeline for svbrdf maps. ACM Trans. Graph. 41, 2 (2022), 1--17.
[36]
Wenzel Jakob, Sébastien Speierer, Nicolas Roussel, Merlin Nimier-David, Delio Vicini, Tizian Zeltner, Baptiste Nicolet, Miguel Crespo, Vincent Leroy, and Ziyi Zhang. 2022b. Mitsuba 3 Renderer, 2022.
[37]
Wenzel Jakob, Sébastien Speierer, Nicolas Roussel, and Delio Vicini. 2022a. Dr. jit: A just-in-time compiler for differentiable rendering. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1--19.
[38]
Kevin G Jamieson, Robert Nowak, and Ben Recht. 2012. Query complexity of derivative-free optimization. Advances in Neural Information Processing Systems 25 (2012).
[39]
Donald R Jones, Matthias Schonlau, and William J Welch. 1998. Efficient global optimization of expensive black-box functions. J Global optimization 13, 4 (1998), 455--92.
[40]
Herman Kahn. 1950. Random sampling (Monte Carlo) techniques in neutron attenuation problems. I. Nucleonics (US) Ceased publication 6, See also NSA 3--990 (1950).
[41]
James T Kajiya. 1986. The rendering equation. In Proceedings of the 13th annual conference on Computer graphics and interactive techniques. 143--150.
[42]
Hiroharu Kato, Yoshitaka Ushiku, and Tatsuya Harada. 2018. Neural 3D mesh renderer. In Proc. CVPR. 3907--16.
[43]
Diederik P Kingma and Max Welling. 2013. Auto-encoding variational bayes. arXiv preprint arXiv:1312.6114 (2013).
[44]
Scott Kirkpatrick, C Daniel Gelatt Jr, and Mario P Vecchi. 1983. Optimization by simulated annealing. science 220, 4598 (1983), 671--680.
[45]
Thomas Kiser, Michael Eigensatz, Minh Man Nguyen, Philippe Bompas, and Mark Pauly. 2013. Architectural caustics---controlling light with geometry. In Advances in architectural geometry 2012. Springer, 91--106.
[46]
Averill M Law, W David Kelton, and W David Kelton. 2007. Simulation modeling and analysis. Vol. 3. Mcgraw-hill New York.
[47]
Quentin Le Lidec, Ivan Laptev, Cordelia Schmid, and Justin Carpentier. 2021. Differentiable rendering with perturbed optimizers. Advances in Neural Information Processing Systems 34 (2021), 20398--20409.
[48]
Yann LeCun. 1998. The MNIST database of handwritten digits. http://yann.lecun.com/exdb/mnist/ (1998).
[49]
Wonyeol Lee, Hangyeol Yu, and Hongseok Yang. 2018. Reparameterization gradient for non-differentiable models. Proc. NeurIPS 31 (2018).
[50]
Beichen Li, Liang Shi, and Wojciech Matusik. 2023. End-to-End Procedural Material Capture with Proxy-Free Mixed-Integer Optimization. ACM Transactions on Graphics (TOG) 42, 4 (2023), 1--15.
[51]
Tzu-Mao Li, Miika Aittala, Frédo Durand, and Jaakko Lehtinen. 2018. Differentiable Monte Carlo ray tracing through edge sampling. ACM Trans. Graph. 37, 6 (2018), 1--11.
[52]
Tzu-Mao Li, Michal Lukáč, Michaël Gharbi, and Jonathan Ragan-Kelley. 2020. Differentiable vector graphics rasterization for editing and learning. ACM Trans. Graph. 39, 6 (2020), 1--15.
[53]
Shichen Liu, Tianye Li, Weikai Chen, and Hao Li. 2019. Soft rasterizer: A differentiable renderer for image-based 3D reasoning. In Proc. ICCV. 7708--17.
[54]
Matthew M Loper and Michael J Black. 2014. OpenDR: An approximate differentiable renderer. In Proc. ECCV. Springer, 154--169.
[55]
Guillaume Loubet, Nicolas Holzschuch, and Wenzel Jakob. 2019. Reparameterizing discontinuous integrands for differentiable rendering. ACM Trans. Graph. 38, 6 (2019), 1--14.
[56]
Joe Marks, Brad Andalman, Paul A Beardsley, William Freeman, Sarah Gibson, Jessica Hodgins, Thomas Kang, Brian Mirtich, Hanspeter Pfister, Wheeler Ruml, et al. 1997. Design galleries: A general approach to setting parameters for computer graphics and animation. In Proc. SIGGRAPH. 389--400.
[57]
Luke Metz, C Daniel Freeman, Samuel S Schoenholz, and Tal Kachman. 2021. Gradients are not all you need. arXiv preprint arXiv:2111.05803 (2021).
[58]
Shakir Mohamed, Mihaela Rosca, Michael Figurnov, and Andriy Mnih. 2020. Monte Carlo Gradient Estimation in Machine Learning. J. Mach. Learn. Res. 21 (2020).
[59]
Louis Montaut, Quentin Le Lidec, Antoine Bambade, Vladimir Petrik, Josef Sivic, and Justin Carpentier. 2023. Differentiable collision detection: a randomized smoothing approach. In 2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 3240--3246.
[60]
Damian Mrowca, Chengxu Zhuang, Elias Wang, Nick Haber, Li F Fei-Fei, Josh Tenenbaum, and Daniel L Yamins. 2018. Flexible neural representation for physics prediction. Proc. NeurIPS 31 (2018).
[61]
Andreas Munk, Adam Ścibior, Atılım Güneş Baydin, Andrew Stewart, Goran Fernlund, Anoush Poursartip, and Frank Wood. 2019. Deep probabilistic surrogate networks for universal simulator approximation. arXiv preprint arXiv:1910.11950 (2019).
[62]
Oliver Nalbach, Elena Arabadzhiyska, Dushyant Mehta, H-P Seidel, and Tobias Ritschel. 2017. Deep shading: convolutional neural networks for screen space shading. In Comp. Graph. Forum, Vol. 36. 65--78.
[63]
Jiří Navrátil, Alan King, Jesus Rios, Georgios Kollias, Ruben Torrado, and Andrés Codas. 2019. Accelerating physics-based simulations using end-to-end neural network proxies: An application in oil reservoir modeling. Frontiers in big Data 2 (2019), 33.
[64]
Yurii Nesterov and Vladimir Spokoiny. 2017. Random gradient-free minimization of convex functions. Foundations of Computational Mathematics 17 (2017), 527--566.
[65]
Chuong H Nguyen, Tobias Ritschel, Karol Myszkowski, Elmar Eisemann, and HansPeter Seidel. 2012. 3D material style transfer. In Computer Graphics Forum, Vol. 31. Wiley Online Library, 431--438.
[66]
Baptiste Nicolet, Alec Jacobson, and Wenzel Jakob. 2021. Large Steps in Inverse Rendering of Geometry. ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia) 40, 6 (Dec. 2021).
[67]
Baptiste Nicolet, Fabrice Rousselle, Jan Novak, Alexander Keller, Wenzel Jakob, and Thomas Müller. 2023. Recursive Control Variates for Inverse Rendering. ACM Transactions on Graphics (TOG) 42, 4 (2023), 1--13.
[68]
Marios Papas, Wojciech Jarosz, Wenzel Jakob, Szymon Rusinkiewicz, Wojciech Matusik, and Tim Weyrich. 2011. Goal-based caustics. In Computer Graphics Forum, Vol. 30. Wiley Online Library, 503--511.
[69]
Konstantinos E Parsopoulos and Michael N. Vrahatis. 2002. Recent approaches to global optimization problems through particle swarm optimization. Natural computing 1, 2 (2002), 235--306.
[70]
Adam Paszke, Sam Gross, Soumith Chintala, Gregory Chanan, Edward Yang, Zachary DeVito, Zeming Lin, Alban Desmaison, Luca Antiga, and Adam Lerer. 2017. Automatic differentiation in pytorch. (2017).
[71]
Yash Patel, Tomáš Hodaň, and Jiří Matas. 2020. Learning surrogates via deep embedding. In Proc. ECCV. Springer, 205--221.
[72]
Felix Petersen, Bastian Goldluecke, Christian Borgelt, and Oliver Deussen. 2022. GenDR: A Generalized Differentiable Renderer. In Proc. CVPR. 4002--4011.
[73]
Michael JD Powell. 1994. A direct search optimization method that models the objective and constraint functions by linear interpolation. In Advances in optimization and numerical analysis. Springer, 51--67.
[74]
Nestor V Queipo, Raphael T Haftka, Wei Shyy, Tushar Goel, Rajkumar Vaidyanathan, and P Kevin Tucker. 2005. Surrogate-based analysis and optimization. Progress in aerospace sciences 41, 1 (2005), 1--28.
[75]
Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred Hamprecht, Yoshua Bengio, and Aaron Courville. 2019. On the spectral bias of neural networks. In International Conference on Machine Learning. PMLR, 5301--5310.
[76]
Gilles Rainer, Wenzel Jakob, Abhijeet Ghosh, and Tim Weyrich. 2019. Neural BTF compression and interpolation. In Comp. Graph. Forum, Vol. 38. 235--44.
[77]
Tom Rainforth, Rob Cornish, Hongseok Yang, Andrew Warrington, and Frank Wood. 2018. On nesting Monte Carlo estimators. In Proc. ICML. PMLR, 4267--4276.
[78]
Alex Renda, Yishen Chen, Charith Mendis, and Michael Carbin. 2020. Difftune: Optimizing cpu simulator parameters with learned differentiable surrogates. In 2020 53rd Annual IEEE/ACM International Symposium on Microarchitecture (MICRO). IEEE.
[79]
Helge Rhodin, Nadia Robertini, Christian Richardt, Hans-Peter Seidel, and Christian Theobalt. 2015. A versatile scene model with differentiable visibility applied to generative pose estimation. In Proceedings of the IEEE International Conference on Computer Vision. 765--773.
[80]
Luis Miguel Rios and Nikolaos V Sahinidis. 2013. Derivative-free optimization: a review of algorithms and comparison of software implementations. J Global Optimization 56, 3 (2013), 1247--1293.
[81]
Connor Schenck and Dieter Fox. 2018. Spnets: Differentiable fluid dynamics for deep neural networks. In Conference on Robot Learning. PMLR, 317--335.
[82]
Yuliy Schwartzburg, Romain Testuz, Andrea Tagliasacchi, and Mark Pauly. 2014. High-contrast computational caustic design. ACM Transactions on Graphics (TOG) (2014).
[83]
Liang Shi, Beichen Li, Miloš Hašan, Kalyan Sunkavalli, Tamy Boubekeur, Radomir Mech, and Wojciech Matusik. 2020. Match: differentiable material graphs for procedural material capture. ACM Trans. Graph. 39, 6 (2020), 1--15.
[84]
Sergey Shirobokov, Vladislav Belavin, Michael Kagan, Andrei Ustyuzhanin, and Atilim Gunes Baydin. 2020. Black-box optimization with local generative surrogates. Proc. NeurIPS 33 (2020), 14650--14662.
[85]
Ping Tat Sin, Hiu Fung Ng, and Hong Va Leong. 2021. Neural Proxy: Empowering Neural Volume Rendering for Animation. In Proc. Pacific Graphics. 1--6.
[86]
James C Spall. 1992. Multivariate stochastic approximation using a simultaneous perturbation gradient approximation. IEEE Trans Automatic Control (1992).
[87]
Joe Staines and David Barber. 2013. Optimization by Variational Bounding. In ESANN.
[88]
Hyung Ju Suh, Max Simchowitz, Kaiqing Zhang, and Russ Tedrake. 2022b. Do differentiable simulators give better policy gradients?. In International Conference on Machine Learning. PMLR, 20668--20696.
[89]
Hyung Ju Terry Suh, Tao Pang, and Russ Tedrake. 2022a. Bundled gradients through contact via randomized smoothing. IEEE Robotics and Automation Letters 7, 2 (2022), 4000--4007.
[90]
Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. 2020. Fourier features let networks learn high frequency functions in low dimensional domains. Advances in Neural Information Processing Systems 33 (2020), 7537--7547.
[91]
Ethan Tseng, Felix Yu, Yuting Yang, Fahim Mannan, Karl ST Arnaud, Derek Nowrouzezahrai, Jean-François Lalonde, and Felix Heide. 2019. Hyperparameter optimization in black-box image processing using differentiable proxies. ACM Trans. Graph. 38, 4 (2019), 27--1.
[92]
Ethan Tseng, Yuxuan Zhang, Lars Jebe, Xuaner Zhang, Zhihao Xia, Yifei Fan, Felix Heide, and Jiawen Chen. 2022. Neural Photo-Finishing. ACM Trans. Graph. 41, 6 (2022), 1--15.
[93]
Eric Veach. 1998. Robust Monte Carlo methods for light transport simulation. Stanford University.
[94]
Delio Vicini, Sébastien Speierer, and Wenzel Jakob. 2022. Differentiable signed distance function rendering. ACM Transactions on Graphics (TOG) 41, 4 (2022), 1--18.
[95]
Xiaotao Wan, Joseph F Pekny, and Gintaras V Reklaitis. 2005. Simulation-based optimization with surrogate models---application to supply chain management. Computers & chemical engineering 29, 6 (2005), 1317--1328.
[96]
Ronald J Williams. 1992. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine learning 8 (1992), 229--256.
[97]
Chris Wyman and Scott Davis. 2006. Interactive image-space techniques for approximating caustics. In 2006 Symposium on Interactive 3D Graphics and Games.
[98]
Jiankai Xing, Fujun Luan, Ling-Qi Yan, Xuejun Hu, Houde Qian, and Kun Xu. 2022. Differentiable Rendering using RGBXY Derivatives and Optimal Transport. ACM Transactions on Graphics (TOG) 41, 6 (2022), 1--13.
[99]
Kai Yan, Fujun Luan, Miloš Hašan, Thibault Groueix, Valentin Deschaintre, and Shuang Zhao. 2023. Psdr-room: Single photo to scene using differentiable rendering. In SIGGRAPH Asia 2023 Conference Papers. 1--11.
[100]
Jiaxin Zhang, Hoang Tran, Dan Lu, and Guannan Zhang. 2020. A scalable evolution strategy with directional Gaussian smoothing for blackbox optimization. arXiv preprint (2020).
[101]
Dongzhan Zhou, Xinchi Zhou, Wenwei Zhang, Chen Change Loy, Shuai Yi, Xuesen Zhang, and Wanli Ouyang. 2020. Econas: Finding proxies for economical neural architecture search. In Proceedings of the IEEE/CVF Conference on computer vision and pattern recognition. 11396--11404.
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Published: 19 July 2024
Published in TOG Volume 43, Issue 4
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