{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T08:17:40Z","timestamp":1783066660379,"version":"3.54.6"},"reference-count":113,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"NSF grants","award":["2341952"],"award-info":[{"award-number":["2341952"]}]},{"name":"NSF grants","award":["2212085"],"award-info":[{"award-number":["2212085"]}]},{"name":"ONR grant","award":["N00014-23-1-2526"],"award-info":[{"award-number":["N00014-23-1-2526"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>Monte Carlo integration is widely used in computer graphics, especially in rendering, but we identify two key limitations. First, for each sample, we can often obtain rich auxiliary information, such as sample position, or geometric information. However, a classical Monte Carlo estimator cannot effectively use this information and only averages the function values. Second, the Monte Carlo formulation makes it difficult to adapt the sampling distribution toward truly informative regions, which can be critical for reconstructing the signal. To address these limitations, we argue that a sampler and integrator beyond the standard Monte Carlo methods is needed. We therefore propose an end-to-end sampling-integration approach that jointly learns both a sampler and an integrator using neural networks, enabling samples to be drawn and used in a more coupled and principled manner. By training on a dataset of integrands, the estimator can further use learned priors over integrand structure and specialize to a family of problems. We evaluate our method on diverse applications in lighting, transmittance, generalized winding number, and walk-on-spheres, spanning both linear and nonlinear cases, and a broad range of low- and high-dimensional settings. Even though the networks add computational overheads, in the equal-sample setting, our method achieves substantial improvements, providing a powerful alternative to traditional quadrature rules and sampling methods.<\/jats:p>","DOI":"10.1145\/3811318","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Neural Quadrature Rule and Autoregressive Adaptive Sampling"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2595-2493","authenticated-orcid":false,"given":"Haolin","family":"Lu","sequence":"first","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-2773-2032","authenticated-orcid":false,"given":"Liwen","family":"Wu","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8491-2502","authenticated-orcid":false,"given":"Zimo","family":"Wang","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5443-470X","authenticated-orcid":false,"given":"Tzu-Mao","family":"Li","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3993-5789","authenticated-orcid":false,"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459880"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2980218"},{"key":"e_1_2_1_3_1","unstructured":"Josh Bainbridge. 2022. OpenQMC sampling library for graphics applications. https:\/\/github.com\/AcademySoftwareFoundation\/openqmc"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13858"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3072959.3073708"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591562"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3618353"},{"key":"e_1_2_1_8_1","article-title":"Unbiased Warped-Area Sampling for Differentiable Rendering","volume":"39","author":"Bangaru Sai Praveen","year":"2020","unstructured":"Sai Praveen Bangaru, Tzu-Mao Li, and Fr\u00e9do Durand. 2020. Unbiased Warped-Area Sampling for Differentiable Rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 39, 6 (2020), 245:1\u2013245:18.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201337"},{"key":"e_1_2_1_10_1","volume-title":"Introduction to Symbolic Regression in the Physical Sciences. arXiv preprint arXiv:2512.15920","author":"Bartlett Deaglan J","year":"2025","unstructured":"Deaglan J Bartlett, Harry Desmond, Pedro G Ferreira, and Gabriel Kronberger. 2025. Introduction to Symbolic Regression in the Physical Sciences. arXiv preprint arXiv:2512.15920 (2025)."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/3658218"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459876"},{"key":"e_1_2_1_13_1","volume-title":"Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio.","author":"Cho Kyunghyun","year":"2014","unstructured":"Kyunghyun Cho, Bart Van Merri\u00ebnboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio. 2014. Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078 (2014)."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13472"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.13182\/NSE68-1"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/3233305"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450627"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/3084363.3085032"},{"key":"e_1_2_1_19_1","volume-title":"International Conference on Learning Representations (ICLR).","author":"Dao Tri","year":"2024","unstructured":"Tri Dao. 2024. FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning. In International Conference on Learning Representations (ICLR)."},{"key":"e_1_2_1_20_1","volume-title":"Objaverse: A Universe of Annotated 3D Objects. arXiv preprint arXiv:2212.08051","author":"Deitke Matt","year":"2022","unstructured":"Matt Deitke, Dustin Schwenk, Jordi Salvador, Luca Weihs, Oscar Michel, Eli Vander-Bilt, Ludwig Schmidt, Kiana Ehsani, Aniruddha Kembhavi, and Ali Farhadi. 2022. Objaverse: A Universe of Annotated 3D Objects. arXiv preprint arXiv:2212.08051 (2022)."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3610548.3618243"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/3687764"},{"key":"e_1_2_1_23_1","unstructured":"Fredo Durand. 2011. A frequency analysis of Monte-Carlo and other numerical integration schemes. (2011)."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073320"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721238.3730754"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3588432.3591537"},{"key":"e_1_2_1_27_1","article-title":"Light Transport Simulation with Vertex Connection and Merging","volume":"31","author":"Georgiev Iliyan","year":"2012","unstructured":"Iliyan Georgiev, Jaroslav K\u0159iv\u00e1nek, Tom\u00e1\u0161 Davidovi\u010d, and Philipp Slusallek. 2012. Light Transport Simulation with Vertex Connection and Merging. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 6 (2012), 192:1\u2013192:10.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_28_1","volume-title":"Advances in Neural Information Processing Systems","author":"Ghahramani Zoubin","year":"2002","unstructured":"Zoubin Ghahramani and Carl Rasmussen. 2002. Bayesian Monte Carlo. In Advances in Neural Information Processing Systems, S. Becker, S. Thrun, and K. Obermayer (Eds.), Vol. 15. MIT Press. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2002\/file\/24917db15c4e37e421866448c9ab23d8-Paper.pdf"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3322954"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-69-99647-1"},{"key":"e_1_2_1_31_1","article-title":"Variance-aware Multiple Importance Sampling","volume":"38","author":"Grittmann Pascal","year":"2019","unstructured":"Pascal Grittmann, Iliyan Georgiev, Philipp Slusallek, and Jaroslav K\u0159iv\u00e1nek. 2019. Variance-aware Multiple Importance Sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 38, 6 (2019), 152:1\u2013152:9.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530126"},{"key":"e_1_2_1_33_1","volume-title":"First conference on language modeling.","author":"Gu Albert","year":"2024","unstructured":"Albert Gu and Tri Dao. 2024. Mamba: Linear-time sequence modeling with selective state spaces. In First conference on language modeling."},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555496"},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1969-0260139-1"},{"key":"e_1_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360632"},{"key":"e_1_2_1_37_1","article-title":"A Path Space Extension for Robust Light Transport Simulation","volume":"31","author":"Hachisuka Toshiya","year":"2012","unstructured":"Toshiya Hachisuka, Jacopo Pantaleoni, and Henrik Wann Jensen. 2012. A Path Space Extension for Robust Light Transport Simulation. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 6 (2012), 191:1\u2013191:10.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201380"},{"key":"e_1_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/3730819"},{"key":"e_1_2_1_40_1","doi-asserted-by":"publisher","DOI":"10.1145\/3368313"},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461916"},{"key":"e_1_2_1_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-7484-5_3"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766977"},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459937"},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/3306346.3323009"},{"key":"e_1_2_1_46_1","volume-title":"Willems","author":"Lafortune Eric P.","year":"1993","unstructured":"Eric P. Lafortune and Yves D. Willems. 1993. Bi-Directional Path Tracing. In Compugraphics. 145\u2013153."},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-9430-0_2"},{"key":"e_1_2_1_48_1","volume-title":"International Conference on Machine Learning.","author":"Lehtinen Jaakko","year":"2018","unstructured":"Jaakko Lehtinen, Jacob Munkberg, Jon Hasselgren, Samuli Laine, Tero Karras, Miika Aittala, and Timo Aila. 2018. Noise2Noise: Learning Image Restoration without Clean Data. In International Conference on Machine Learning."},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1145\/3355089.3356562"},{"key":"e_1_2_1_50_1","article-title":"Differentiable Monte Carlo Ray Tracing through Edge Sampling","volume":"37","author":"Li Tzu-Mao","year":"2018","unstructured":"Tzu-Mao Li, Miika Aittala, Fr\u00e9do Durand, and Jaakko Lehtinen. 2018. Differentiable Monte Carlo Ray Tracing through Edge Sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 6 (2018), 222:1\u2013222:11.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_51_1","article-title":"SURE-based optimization for adaptive sampling and reconstruction","volume":"31","author":"Li Tzu-Mao","year":"2012","unstructured":"Tzu-Mao Li, Yu-Ting Wu, and Yung-Yu Chuang. 2012. SURE-based optimization for adaptive sampling and reconstruction. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 6 (2012), 194:1\u2013194:9.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_52_1","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657395"},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530158"},{"key":"e_1_2_1_54_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.14194"},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1145\/3658203"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731175"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530093"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","unstructured":"D. Meister and T. Harada. 2025. Geometric Integration for Neural Control Variates. Computer Graphics Forum 44 (10 2025). 10.1111\/cgf.70275","DOI":"10.1111\/cgf.70275"},{"key":"e_1_2_1_59_1","doi-asserted-by":"publisher","DOI":"10.1145\/3680528.3687636"},{"key":"e_1_2_1_60_1","doi-asserted-by":"crossref","unstructured":"Ben Mildenhall Pratul P. Srinivasan Matthew Tancik Jonathan T. Barron Ravi Ramamoorthi and Ren Ng. 2020. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In ECCV.","DOI":"10.1007\/978-3-030-58452-8_24"},{"key":"e_1_2_1_61_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897824.2925936"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.2312\/hpg.20191191"},{"key":"e_1_2_1_63_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13227"},{"key":"e_1_2_1_64_1","volume-title":"Neural Importance Sampling. arXiv:1808.03856","author":"M\u00fcller Thomas","year":"2018","unstructured":"Thomas M\u00fcller, Brian McWilliams, Fabrice Rousselle, Markus Gross, and Jan Nov\u00e1k. 2018. Neural Importance Sampling. arXiv:1808.03856 (2018)."},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1145\/3414685.3417804"},{"key":"e_1_2_1_66_1","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459812"},{"key":"e_1_2_1_67_1","doi-asserted-by":"crossref","unstructured":"Harald Niederreiter. 1992. Random number generation and quasi-Monte Carlo methods. SIAM.","DOI":"10.1137\/1.9781611970081"},{"key":"e_1_2_1_68_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13383"},{"key":"e_1_2_1_69_1","article-title":"Residual Ratio Tracking for Estimating Attenuation in Participating Media","volume":"33","author":"Nov\u00e1k Jan","year":"2014","unstructured":"Jan Nov\u00e1k, Andrew Selle, and Wojciech Jarosz. 2014. Residual Ratio Tracking for Estimating Attenuation in Participating Media. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 33, 6 (2014), 179:1\u2013179:11.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_70_1","first-page":"247","article-title":"Monte Carlo is Fundamentally Unsound. Journal of the Royal Statistical Society","volume":"36","author":"O'Hagan A.","year":"1987","unstructured":"A. O'Hagan. 1987. Monte Carlo is Fundamentally Unsound. Journal of the Royal Statistical Society. Series D (The Statistician) 36, 2\/3 (1987), 247\u2013249. http:\/\/www.jstor.org\/stable\/2348519","journal-title":"Series D (The Statistician)"},{"key":"e_1_2_1_71_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-3758(91)90002-V"},{"key":"e_1_2_1_72_1","volume-title":"Active learning of model evidence using Bayesian quadrature. Advances in neural information processing systems 25","author":"Osborne Michael","year":"2012","unstructured":"Michael Osborne, Roman Garnett, Zoubin Ghahramani, David K Duvenaud, Stephen J Roberts, and Carl Rasmussen. 2012. Active learning of model evidence using Bayesian quadrature. Advances in neural information processing systems 25 (2012)."},{"key":"e_1_2_1_73_1","doi-asserted-by":"publisher","DOI":"10.5555\/3625834.3625985"},{"key":"e_1_2_1_74_1","doi-asserted-by":"crossref","unstructured":"Long Ouyang Jeffrey Wu Xu Jiang Diogo Almeida Carroll Wainwright Pamela Mishkin Chong Zhang Sandhini Agarwal Katarina Slama Alex Ray et al. 2022. Training language models to follow instructions with human feedback. Advances in neural information processing systems 35 (2022) 27730\u201327744.","DOI":"10.52202\/068431-2011"},{"key":"e_1_2_1_75_1","article-title":"Adaptive wavelet rendering","volume":"28","author":"Overbeck Ryan S","year":"2009","unstructured":"Ryan S Overbeck, Craig Donner, and Ravi Ramamoorthi. 2009. Adaptive wavelet rendering. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 28, 5 (2009), 140:1\u2013140:12.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_76_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142994277468"},{"key":"e_1_2_1_77_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1031594731"},{"key":"e_1_2_1_78_1","unstructured":"Art B Owen. 2013. Monte Carlo theory methods and examples."},{"key":"e_1_2_1_79_1","volume-title":"PyTorch: an imperative style, high-performance deep learning library","author":"Paszke Adam","unstructured":"Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas K\u00f6pf, Edward Yang, Zach DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. 2019. PyTorch: an imperative style, high-performance deep learning library. Curran Associates Inc., Red Hook, NY, USA."},{"key":"e_1_2_1_80_1","volume-title":"Rwkv: Reinventing rnns for the transformer era. arXiv preprint arXiv:2305.13048","author":"Peng Bo","year":"2023","unstructured":"Bo Peng, Eric Alcaide, Quentin Anthony, Alon Albalak, Samuel Arcadinho, Stella Biderman, Huanqi Cao, Xin Cheng, Michael Chung, Matteo Grella, et al. 2023. Rwkv: Reinventing rnns for the transformer era. arXiv preprint arXiv:2305.13048 (2023)."},{"key":"e_1_2_1_81_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.13366"},{"key":"e_1_2_1_82_1","doi-asserted-by":"publisher","DOI":"10.1145\/3763273"},{"key":"e_1_2_1_83_1","volume-title":"Numerical mathematics","author":"Quarteroni Alfio","unstructured":"Alfio Quarteroni, Riccardo Sacco, and Fausto Saleri. 2006. Numerical mathematics. Vol. 37. Springer Science & Business Media."},{"key":"e_1_2_1_84_1","unstructured":"Alec Radford Jeff Wu Rewon Child David Luan Dario Amodei and Ilya Sutskever. 2019. Language Models are Unsupervised Multitask Learners. (2019)."},{"key":"e_1_2_1_85_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530168"},{"key":"e_1_2_1_86_1","volume-title":"Monte Carlo statistical methods","author":"Robert Christian P","unstructured":"Christian P Robert, George Casella, and George Casella. 1999. Monte Carlo statistical methods. Vol. 2. Springer."},{"key":"e_1_2_1_87_1","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530095"},{"key":"e_1_2_1_88_1","doi-asserted-by":"publisher","DOI":"10.1145\/3550454.3555515"},{"key":"e_1_2_1_89_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721241.3734001"},{"key":"e_1_2_1_90_1","volume-title":"Proceedings of the 37th International Conference on Neural Information Processing Systems","author":"Scardigli Antoine","unstructured":"Antoine Scardigli, Lukas Cavigelli, and Lorenz K. M\u00fcller. 2023. RL-based stateful neural adaptive sampling and denoising for real-time path tracing. In Proceedings of the 37th International Conference on Neural Information Processing Systems (New Orleans, LA, USA) (NIPS '23). Curran Associates Inc., Red Hook, NY, USA, Article 2898, 18 pages."},{"key":"e_1_2_1_91_1","doi-asserted-by":"publisher","DOI":"10.1145\/3105762.3105770"},{"key":"e_1_2_1_92_1","volume-title":"Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347","author":"Schulman John","year":"2017","unstructured":"John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347 (2017)."},{"key":"e_1_2_1_93_1","article-title":"Practical Hessian-Based Error Control for Irradiance Caching","volume":"31","author":"Schwarzhaupt Jorge","year":"2012","unstructured":"Jorge Schwarzhaupt, Henrik Wann Jensen, and Wojciech Jarosz. 2012. Practical Hessian-Based Error Control for Irradiance Caching. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 31, 6 (2012), 193:1\u2013193:10.","journal-title":"ACM Trans. Graph. (Proc. SIGGRAPH Asia)"},{"key":"e_1_2_1_94_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-24870-2_7"},{"key":"e_1_2_1_95_1","doi-asserted-by":"publisher","DOI":"10.5555\/2354409.2354733"},{"key":"e_1_2_1_96_1","volume-title":"Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300","author":"Shao Zhihong","year":"2024","unstructured":"Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300 (2024)."},{"key":"e_1_2_1_97_1","doi-asserted-by":"publisher","DOI":"10.1145\/3731146"},{"key":"e_1_2_1_98_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2023.127063"},{"key":"e_1_2_1_99_1","unstructured":"Yu Sun Xinhao Li Karan Dalal Jiarui Xu Arjun Vikram Genghan Zhang Yann Dubois Xinlei Chen Xiaolong Wang Sanmi Koyejo et al. 2024. Learning to (learn at test time): Rnns with expressive hidden states. arXiv preprint arXiv:2407.04620 (2024)."},{"key":"e_1_2_1_100_1","volume-title":"\u0141 ukasz Kaiser, and Illia Polosukhin","author":"Vaswani Ashish","year":"2017","unstructured":"Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, \u0141 ukasz Kaiser, and Illia Polosukhin. 2017. Attention is All you Need. In Advances in Neural Information Processing Systems, I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Eds.), Vol. 30. Curran Associates, Inc. https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2017\/file\/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf"},{"key":"e_1_2_1_101_1","volume-title":"Robust Monte Carlo Methods for Light Transport Simulation. Ph. D. Dissertation","author":"Veach Eric","unstructured":"Eric Veach. 1998. Robust Monte Carlo Methods for Light Transport Simulation. Ph. D. Dissertation. Stanford University. Advisor(s) Guibas, Leonidas J."},{"key":"e_1_2_1_102_1","volume-title":"Guibas","author":"Veach Eric","year":"1995","unstructured":"Eric Veach and Leonidas J. Guibas. 1995. Optimally Combining Sampling Techniques for Monte Carlo Rendering. In SIGGRAPH. 419\u2013428."},{"key":"e_1_2_1_103_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201340"},{"key":"e_1_2_1_104_1","doi-asserted-by":"publisher","DOI":"10.1145\/3478513.3480561"},{"key":"e_1_2_1_105_1","volume-title":"Clear","author":"Ward Gregory J.","year":"1988","unstructured":"Gregory J. Ward, Francis M. Rubinstein, and Robert D. Clear. 1988. A Ray Tracing Solution for Diffuse Interreflection. Comput. Graph. (Proc. SIGGRAPH) (1988), 85\u201392."},{"key":"e_1_2_1_106_1","doi-asserted-by":"publisher","DOI":"10.1145\/3721238.3730679"},{"key":"e_1_2_1_107_1","unstructured":"Bing Xu Mukund Varma T Cheng Wang Tzumao Li Lifan Wu Bartlomiej Wronski Ravi Ramamoorthi and Marco Salvi. 2025. A Generalizable Light Transport 3D Embedding for Global Illumination. arXiv:2510.18189 [cs.GR] https:\/\/arxiv.org\/abs\/2510.18189"},{"key":"e_1_2_1_108_1","doi-asserted-by":"publisher","DOI":"10.2312\/sr.20251184"},{"key":"e_1_2_1_109_1","doi-asserted-by":"publisher","DOI":"10.1145\/3197517.3201313"},{"key":"e_1_2_1_110_1","volume-title":"RenderFormer: Transformer-based Neural Rendering of Triangle Meshes with Global Illumination. In ACM SIGGRAPH 2025 Conference Papers.","author":"Zeng Chong","year":"2025","unstructured":"Chong Zeng, Yue Dong, Pieter Peers, Hongzhi Wu, and Xin Tong. 2025a. RenderFormer: Transformer-based Neural Rendering of Triangle Meshes with Global Illumination. In ACM SIGGRAPH 2025 Conference Papers."},{"key":"e_1_2_1_111_1","doi-asserted-by":"publisher","unstructured":"Zheng Zeng Markus Kettunen Chris Wyman Lifan Wu Ravi Ramamoorthi Ling-Qi Yan and Daqi Lin. 2025b. ReSTIR PG: Path Guiding with Spatiotemporally Resampled Paths. SIGGRAPH Asia (Conference Track). 10.1145\/3757377.3763813","DOI":"10.1145\/3757377.3763813"},{"key":"e_1_2_1_112_1","doi-asserted-by":"publisher","DOI":"10.1145\/3763315"},{"key":"e_1_2_1_113_1","doi-asserted-by":"publisher","DOI":"10.5555\/2816723.2816781"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:37:28Z","timestamp":1783064248000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3811318"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,3]]},"references-count":113,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2026,7,3]]}},"alternative-id":["10.1145\/3811318"],"URL":"https:\/\/doi.org\/10.1145\/3811318","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,3]]},"assertion":[{"value":"2026-01-22","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-03-27","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-07-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}