├── imgs ├── theory.png ├── diagram.png ├── method1.png ├── method2.png └── application.png └── README.md /imgs/theory.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/YisiLuo/Continuous-Representation-Zoo/HEAD/imgs/theory.png -------------------------------------------------------------------------------- /imgs/diagram.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/YisiLuo/Continuous-Representation-Zoo/HEAD/imgs/diagram.png -------------------------------------------------------------------------------- /imgs/method1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/YisiLuo/Continuous-Representation-Zoo/HEAD/imgs/method1.png -------------------------------------------------------------------------------- /imgs/method2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/YisiLuo/Continuous-Representation-Zoo/HEAD/imgs/method2.png -------------------------------------------------------------------------------- /imgs/application.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/YisiLuo/Continuous-Representation-Zoo/HEAD/imgs/application.png -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Continuous-Representation-Zoo 2 | 3 | This project summarizes the papers and studies introduced in the review: Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives [arXiv] 📖 4 | 5 | # Abstract ✨ 6 | 7 | Recently, continuous representation methods emerge as novel paradigms that characterize the intrinsic structures of real-world data through function representations that map positional coordinates to their corresponding values in the continuous space. As compared with the traditional discrete framework, the continuous framework demonstrates inherent superiority for data representation and reconstruction (e.g., image restoration, novel view synthesis, and waveform inversion) by offering inherent advantages including resolution flexibility, cross-modal adaptability, inherent smoothness, and parameter efficiency. In this review, we systematically examine recent advancements in continuous representation frameworks, focusing on three aspects: (i) Continuous representation method designs such as basis function representation, statistical modeling, tensor function decomposition, and implicit neural representation; (ii) Theoretical foundations of continuous representations such as approximation error analysis, convergence property, and implicit regularization; (iii) Real-world applications of continuous representations derived from computer vision, graphics, bioinformatics, and remote sensing. Furthermore, we outline future directions and perspectives to inspire exploration and deepen insights to facilitate continuous representation methods, theories, and applications. 8 | 9 |

10 | 11 |

12 | 13 | bibtex: 14 | @article{arXiv2025Luo, 15 | author = {Yisi Luo, Xile Zhao, Deyu Meng}, 16 | title = {Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives}, 17 | journal = {arXiv:2505.15222}, 18 | year = {2025}, 19 | } 20 | 21 | 22 | # Continuous Methods (Parametric model) 23 | 24 |

25 | 26 |

27 | 28 | ## Basis Function Representation 29 | 30 | - Tatsuya Yokota, Rafal Zdunek, Andrzej Cichocki, and Yukihiko Yamashita. Smooth nonnegative matrix and tensor factorizations for robust multi-way data analysis. Signal Processing, 2015. 31 | 32 | - Otto Debals, Marc Van Barel, and Lieven De Lathauwer. Nonnegative matrix factorization using nonnegative polynomial approximations. IEEE Signal Processing Letters, 2017 33 | 34 | - Masaaki Imaizumi and Kohei Hayashi. Tensor decomposition with smoothness. In International Conference on Machine 35 | Learning, 2017. 36 | 37 | - Alex A. Gorodetsky and John D. Jakeman. Gradient-based optimization for regression in the functional tensor-train format. 38 | Journal of Computational Physics, 2018. 39 | 40 | - Nikos Kargas and Nicholas D. Sidiropoulos. Nonlinear system identification via tensor completion. In Proceedings of the 41 | AAAI Conference on Artificial Intelligence, 2020. 42 | 43 | - Nikos Kargas and Nicholas D. Sidiropoulos. Supervised learning and canonical decomposition of multivariate functions. IEEE Transactions on Signal Processing, 2021. 44 | 45 | - Lucas Sort, Laurent Le Brusquet, and Arthur Tenenhaus. Latent functional parafac for modeling multidimensional longitudinal 46 | data. arXiv, 2410.18696, 2024. 47 | 48 | - Peter Kunkel and Volker Mehrmann. Smooth factorizations of matrix-valued functions and their derivatives. Numerische Mathematik, 1991. 49 | 50 | - I. V. Oseledets. Constructive representation of functions in low-rank tensor formats. Constructive Approximation, 2013. 51 | 52 | - Petr Tichavsky and Ondrej Straka. Tensor train approximation of multivariate functions. In 2024 32nd European Signal 53 | Processing Conference, 2024. 54 | 55 | - Tianqi Chen, Hang Li, Qiang Yang, and Yong Yu. General functional matrix factorization using gradient boosting. In Proceedings of the 30th International Conference on International Conference on Machine Learning, 2013. 56 | 57 | - Behnam Hashemi and Lloyd N. Trefethen. Chebfun in three dimensions. SIAM Journal on Scientific Computing, 2017. 58 | 59 | - Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljacic, Thomas Y. Hou, and Max Tegmark. KAN: Kolmogorov-Arnold networks. In The Thirteenth International Conference on Learning Representations, 2025. 60 | 61 | - Tongle Wu and Jicong Fan. Smooth tensor product for tensor completion. IEEE Transactions on Image Processing, 2024. 62 | 63 | ## Implicit Neural Representation 64 | 65 | - Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. Fourier features let networks learn high-frequency functions in low-dimensional domains. In International Conference on Neural Information Processing Systems, 2020. 66 | 67 | - Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. Implicit neural representations 68 | with periodic activation functions. In International Conference on Neural Information Processing Systems, 2020. 69 | 70 | - Rizal Fathony, Anit Kumar Sahu, Devin Willmott, and J Zico Kolter. Multiplicative filter networks. In International 71 | Conference on Learning Representations, 2021. 72 | 73 | - Vishwanath Saragadam, Daniel LeJeune, Jasper Tan, Guha Balakrishnan, Ashok Veeraraghavan, and Richard G. Baraniuk. 74 | Wire: Wavelet implicit neural representations. In 2023 IEEE/CVF Conference on Computer Vision and Pattern 75 | Recognition, 2023. 76 | 77 | - Jason Chun Lok Li, Chang Liu, Binxiao Huang, and Ngai Wong. Learning spatially collaged fourier bases for implicit neural 78 | representation. In Proceedings of the AAAI Conference on Artificial Intelligence, 2024. 79 | 80 | - Zhen Liu, Hao Zhu, Qi Zhang, Jingde Fu, Weibing Deng, Zhan Ma, Yanwen Guo, and Xun Cao. Finer: Flexible spectral bias 81 | tuning in implicit neural representation by variable-periodic activation functions. In 2024 IEEE/CVF Conference on 82 | Computer Vision and Pattern Recognition, 2024. 83 | 84 | - Dhananjaya Jayasundara, Heng Zhao, Demetrio Labate, and Vishal M. Patel. PIN: Prolate spheroidal wave function-based 85 | implicit neural representations. In The Thirteenth International Conference on Learning Representations, 2025. 86 | 87 | - Sameera Ramasinghe and Simon Lucey. Beyond periodicity: Towards a unifying framework for activations in coordinatemlps. 88 | In 17th European Conference on Computer Vision, 2022. 89 | 90 | - Kexuan Shi, Xingyu Zhou, and Shuhang Gu. Improved implicit neural representation with Fourier reparameterized training. 91 | In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. 92 | 93 | - Zekun Hao, Arun Mallya, Serge Belongie, and Ming-Yu Liu. Implicit neural representations with levels-of-experts. In 94 | Advances in Neural Information Processing Systems, 2022. 95 | 96 | - Yizhak Ben-Shabat, Chamin Hewa Koneputugodage, Sameera Ramasinghe, and Stephen Gould. Neural experts: Mixture 97 | of experts for implicit neural representations. In Advances in Neural Information Processing Systems, 2024. 98 | 99 | - Kushal Vyas, Ahmed Imtiaz Humayun, Aniket Dashpute, Richard Baraniuk, Ashok Veeraraghavan, and Guha Balakrishnan. Learning transferable features for implicit neural representations. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. 100 | 101 | - Chen Zhang, Steven Tin Sui Luo, Jason Chun Lok Li, Yik Chung Wu, and Ngai Wong. Nonparametric teaching of implicit neural representations. In Proceedings of the 41st International Conference on Machine Learning, 2024. 102 | 103 | - Wei Fang, Yuxing Tang, Heng Guo, Mingze Yuan, Tony C.W. Mok, Ke Yan, Jiawen Yao, Xin Chen, Zaiyi Liu, Le Lu, Ling Zhang, and Minfeng Xu. Cycleinr: Cycle implicit neural representation for arbitrary-scale volumetric super-resolution of medical data. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. 104 | 105 | - Vishwanath Saragadam, Jasper Tan, Guha Balakrishnan, Richard G. Baraniuk, and Ashok Veeraraghavan. Miner: Multiscale implicit neural representation. In 17th European Conference on Computer Vision, 2022. 106 | 107 | - Jiayi Li, Xile Zhao, Jianli Wang, Chao Wang, and Min Wang. Superpixel-informed implicit neural representation for multi-dimensional data. In 18th European Conference on Computer Vision, 2024. 108 | 109 | - Zhicheng Cai, Hao Zhu, Qiu Shen, Xinran Wang, and Xun Cao. Batch normalization alleviates the spectral bias in coordinate networks. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. 110 | 111 | - Chang Yu, Yisi Luo, Kai Ye, Xile Zhao, and Deyu Meng. Cross-frequency implicit neural representation with self-evolving 112 | parameters. arXiv:2504.10929, 2025. 113 | 114 | - Amirhossein Kazerouni, Reza Azad, Alireza Hosseini, Dorit Merhof, and Ulas Bagci. Incode: Implicit neural conditioning 115 | with prior knowledge embeddings. In 2024 IEEE/CVF Winter Conference on Applications of Computer Vision, 2024. 116 | 117 | - Yinbo Chen and Xiaolong Wang. Transformers as meta-learners for implicit neural representations. In European Conference 118 | on Computer Vision, 2022. 119 | 120 | - Matthew Tancik, Ben Mildenhall, Terrance Wang, Divi Schmidt, Pratul P. Srinivasan, Jonathan T. Barron, and Ren Ng. 121 | Learned initializations for optimizing coordinate-based neural representations. In Proceedings of the IEEE/CVF Conference 122 | on Computer Vision and Pattern Recognition, 2021. 123 | 124 | - Gizem Yuce, Guillermo Ortiz-Jimenez, Beril Besbinar, and Pascal Frossard. A structured dictionary perspective on implicit 125 | neural representations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. 126 | 127 | ## Grid Encoding Parametric Model 128 | 129 | - Thomas Muller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution 130 | hash encoding. ACM Transactions on Graphics, 2022. 131 | 132 | - Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In 17th European Conference on Computer Vision, 2022. 133 | 134 | - Cheng Sun, Min Sun, and Hwann-Tzong Chen. Direct voxel grid optimization: Super-fast convergence for radiance fields 135 | reconstruction. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. 136 | 137 | - Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural 138 | radiance fields. In 2021 IEEE/CVF International Conference on Computer Vision, 2021. 139 | 140 | - Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. 141 | 142 | - Hao Zhu, Shaowen Xie, Zhen Liu, Fengyi Liu, Qi Zhang, You Zhou, Yi Lin, Zhan Ma, and Xun Cao. Disorder-invariant 143 | implicit neural representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. 144 | 145 | - Hao Zhu, Fengyi Liu, Qi Zhang, Zhan Ma, and Xun Cao. RHINO: Regularizing the hash-based implicit neural representation. Science China Information Sciences, 2025. 146 | 147 | # Continuous Methods (Structural modeling) 148 | 149 |

150 | 151 |

152 | 153 | ## Matrix and Tensor Function Decomposition 154 | 155 | - Ruofan Liang, Hongyi Sun, and Nandita Vijaykumar. CoordX: Accelerating implicit neural representation with a split MLP architecture. In International Conference on Learning Representations, 2022. 156 | 157 | - Yisi Luo, Xile Zhao, Zhemin Li, Michael K. Ng, and Deyu Meng. Low-rank tensor function representation for multidimensional data recovery. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. 158 | 159 | - Jianli Wang and Xile Zhao. Functional transform-based low-rank tensor factorization for multi-dimensional data recovery. In 18th European Conference on Computer Vision, 2024. 160 | 161 | - Yanyi Li, Xi Zhang, Yisi Luo, and Deyu Meng. Deep rank-one tensor functional factorization for multi-dimensional data recovery. In Proceedings of the AAAI Conference on Artificial Intelligence, 2025. 162 | 163 | - Sai Karthikeya Vemuri, Tim Buchner, and Joachim Denzler. F-INR: Functional tensor decomposition for implicit neural representations. arXiv:2503.21507, 2025. 164 | 165 | - Tong Nie, Guoyang Qin, Wei Ma, and Jian Sun. Spatiotemporal implicit neural representation as a generalized traffic data learner. Transportation Research Part C: Emerging Technologies, 2024. 166 | 167 | ## Statistical and Bayesian Framework 168 | 169 | - Shikai Fang, Qingsong Wen, Yingtao Luo, Shandian Zhe, and Liang Sun. BayOTIDE: Bayesian online multivariate time series imputation with functional decomposition. In Proceedings of the 41st International Conference on Machine Learning, 2024. 170 | 171 | - Shikai Fang, Xin Yu, Shibo Li, Zheng Wang, Robert M. Kirby, and Shandian Zhe. Streaming factor trajectory learning for temporal tensor decomposition. In Proceedings of the 37th International Conference on Neural Information Processing 172 | Systems, 2023. 173 | 174 | - Shikai Fang, Xin Yu, Zheng Wang, Shibo Li, Mike Kirby, and Shandian Zhe. Functional Bayesian Tucker decomposition for continuous-indexed tensor data. In The Twelfth International Conference on Learning Representations, 2024. 175 | 176 | - Panqi Chen, Lei Cheng, Jianlong Li, Weichang Li, Weiqing Liu, Jiang Bian, and Shikai Fang. Generalized temporal tensor decomposition with rank-revealing latent-ODE. Arxiv: 2502.06164, 2025. 177 | 178 | ## Continuous Regularization for Structural Modeling 179 | 180 | - Jelmer M Wolterink, Jesse C Zwienenberg, and Christoph Brune. Implicit neural representations for deformable image registration. In Proceedings of The 5th International Conference on Medical Imaging with Deep Learning, 2022. 181 | 182 | - Zhemin Li, Hongxia Wang, and Deyu Meng. Regularize implicit neural representation by itself. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023. 183 | 184 | - Yisi Luo, Xile Zhao, and Deyu Meng. Revisiting nonlocal self-similarity from continuous representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2025. 185 | 186 | - Yisi Luo, Xile Zhao, Kai Ye, and Deyu Meng. Neurtv: Total variation on the neural domain. SIAM Journal on Imaging Sciences, 2025. 187 | 188 | - Hyeongjun Heo, Seonghun Oh, Jae Yong Lee, Young Min Kim, and Yonghyeon Lee. Isometric regularization for manifolds of functional data. In The Thirteenth International Conference on Learning Representations, 2025. 189 | 190 | # Theoretical Foundations 191 | 192 |

193 | 194 |

195 | 196 | ## Approximation and Representation Theory 197 | 198 | - Alex Gorodetsky, Sertac Karaman, and Youssef Marzouk. A continuous analogue of the tensor-train decomposition. Computer Methods in Applied Mechanics and Engineering, 2019. 199 | 200 | - Michael Griebel and Guanglian Li. On the decay rate of the singular values of bivariate functions. SIAM Journal on Numerical Analysis, 2018. 201 | 202 | - Rungang Han, Pixu Shi, and Anru R. Zhang and. Guaranteed functional tensor singular value decomposition. Journal of the American Statistical Association, 2024. 203 | 204 | - Behnam Hashemi and Lloyd N. Trefethen. Chebfun in three dimensions. SIAM Journal on Scientific Computing, 2017. 205 | 206 | - S.W. Ellacott. Aspects of the numerical analysis of neural networks. Acta Numerica, 1994. 207 | 208 | - Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Multilayer feedforward networks are universal approximators. Neural Networks, 1989. 209 | 210 | - Gerlind Plonka, Daniel Potts, Gabriele Steidl, and Manfred Tasche. Numerical Fourier Analysis, chapter 7, pages 235–259. John Wiley & Sons, Ltd, 2020. 211 | 212 | - Gizem Yu ̈ce, Guillermo Ortiz-Jim ́enez, Beril Besbinar, and Pascal Frossard. A structured dictionary perspective on implicit neural representations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. 213 | 214 | - T Mitchell Roddenberry, Vishwanath Saragadam, Maarten V. de Hoop, and Richard Baraniuk. Implicit neural representations and the algebra of complex wavelets. In The Twelfth International Conference on Learning Representations, 2024. 215 | 216 | - Yisi Luo, Xile Zhao, Zhemin Li, Michael K. Ng, and Deyu Meng. Low-rank tensor function representation for multi-dimensional data recovery. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. 217 | 218 | - Andong Wang, Yuning Qiu, Mingyuan Bai, Zhong Jin, Guoxu Zhou, and Qibin Zhao. Generalized tensor decomposition for understanding multi-output regression under combinatorial shifts. In Advances in Neural Information Processing Systems, 2024. 219 | 220 | - Rungang Han, Pixu Shi, and Anru R. Zhang and. Guaranteed functional tensor singular value decomposition. Journal of the American Statistical Association, 2024. 221 | 222 | - Alex A. Gorodetsky and John D. Jakeman. Gradient-based optimization for regression in the functional tensor-train format. Journal of Computational Physics, 2018. 223 | 224 | - Julien Fageot. Variational seasonal-trend decomposition with sparse continuous-domain regularization. arXiv:2505.10486, 2025. 225 | 226 | - Sourav Pal, Harshavardhan Adepu, Clinton Wang, Polina Golland, and Vikas Singh. Implicit representations via operator learning. In Forty-first International Conference on Machine Learning, 2024. 227 | 228 | - Dejia Xu, Peihao Wang, Yifan Jiang, Zhiwen Fan, and Zhangyang Wang. Signal processing for implicit neural representations. In Advances in Neural Information Processing Systems, 2022. 229 | 230 | ## Generalization and Convergence 231 | 232 | - Arthur Jacot, Franck Gabriel, and Cl´ement Hongler. Neural tangent kernel: convergence and generalization in neural networks. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, 2018. 233 | 234 | - Sanjeev Arora, Simon Du, Wei Hu, Zhiyuan Li, and Ruosong Wang. Fine-grained analysis of optimization and generalization for overparameterized two-layer neural networks. In Proceedings of the 36th International Conference on Machine Learning, 2019. 235 | 236 | - Sanjeev Arora, Simon S. Du, Wei Hu, Zhiyuan Li, Ruslan Salakhutdinov, and Ruosong Wang. On exact computation with an infinitely wide neural net. In Proceedings of the 33rd International Conference on Neural Information Processing 237 | Systems, 2019. 238 | 239 | - Colin Wei, Jason D. Lee, Qiang Liu, and Tengyu Ma. Regularization matters: generalization and optimization of neural nets v.s. their induced kernel. In Proceedings of the 33rd International Conference on Neural Information Processing Systems, 2019. 240 | 241 | - Zonghao Chen, Xupeng Shi, Tim G. J. Rudner, Qixuan Feng, Weizhong Zhang, and Tong Zhang. A neural tangent kernel perspective on function-space regularization in neural networks. In International Conference on Neural Information 242 | Processing Systems Workshop on Optimization for Machine Learning, 2022. 243 | 244 | - Zixiang Chen, Yuan Cao, Quanquan Gu, and Tong Zhang. A generalized neural tangent kernel analysis for two-layer neural networks. In Proceedings of the 34th International Conference on Neural Information Processing Systems, 2020. 245 | 246 | - Amnon Geifman, Daniel Barzilai, Ronen Basri, and Meirav Galun. Controlling the inductive bias of wide neural networks by modifying the kernel’s spectrum. Transactions on Machine Learning Research, 2024. 247 | 248 | - Shin-Fang Chng, Hemanth Saratchandran, and Simon Lucey. Preconditioners for the stochastic training of neural fields. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2025. 249 | 250 | - Ismail Alkhouri, Evan Bell, Avrajit Ghosh, Shijun Liang, Rongrong Wang, and Saiprasad Ravishankar. Understanding untrained deep models for inverse problems: Algorithms and theory. Arxiv: 2502.18612, 2025. 251 | 252 | - Samuel Audia, Soheil Feizi, Matthias Zwicker, and Dinesh Manocha. How learnable grids recover fine detail in low dimensions: A neural tangent kernel analysis of multigrid parametric encodings. In The Thirteenth International Conference on 253 | Learning Representations, 2025. 254 | 255 | - Andrea Bonfanti, Giuseppe Bruno, and Cristina Cipriani. The challenges of the nonlinear regime for physics-informed neural networks. In Advances in Neural Information Processing Systems, 2024. 256 | 257 | - Mike Nguyen and Nicole M¨ucke. Optimal convergence rates for neural operators. ArXiv:2412.17518, 2025. 258 | 259 | - Kexuan Shi, Hai Chen, Leheng Zhang, Shuhang Gu. Inductive Gradient Adjustment for Spectral Bias in Implicit Neural Representations, Forty-Second International Conference on Machine Learning, 2025. 260 | 261 | ## Implicit Regularization 262 | 263 | - Sanjeev Arora, Nadav Cohen, Wei Hu, and Yuping Luo. Implicit regularization in deep matrix factorization. In Proceedings 264 | of the 33rd International Conference on Neural Information Processing Systems, 2019. 265 | 266 | - Noam Razin, Asaf Maman, and Nadav Cohen. Implicit regularization in hierarchical tensor factorization and deep convolutional- 267 | tional neural networks. In Proceedings of the 39th International Conference on Machine Learning, 2022. 268 | 269 | - Suriya Gunasekar, Blake E Woodworth, Srinadh Bhojanapalli, Behnam Neyshabur, and Nati Srebro. Implicit regularization in matrix factorization. In Advances in Neural Information Processing Systems, 2017. 270 | 271 | - Noam Razin, Asaf Maman, and Nadav Cohen. Implicit regularization in hierarchical tensor factorization and deep convolutional neural networks. In Proceedings of the 39th International Conference on Machine Learning, 2022. 272 | 273 | - Kais Hariz, Hachem Kadri, Stephane Ayache, Maher Moakher, and Thierry Artieres. Implicit regularization with polynomial growth in deep tensor factorization. In Proceedings of the 39th International Conference on Machine Learning, 2022. 274 | 275 | - Kais Hariz, Hachem Kadri, St´ephane Ayache, Maher Moakher, and Thierry Arti`eres. Implicit regularization in deep Tucker factorization: Low-rankness via structured sparsity. In International Conference on Artificial Intelligence and Statistics, 2024. 276 | 277 | - Zhiwei Bai, Jiajie Zhao, and Yaoyu Zhang. Connectivity shapes implicit regularization in matrix factorization models for matrix completion. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. 278 | 279 | - Shuo Xie and Zhiyuan Li. Implicit bias of AdamW: $\ell_\infty$-norm constrained optimization. In Proceedings of the 41st International Conference on Machine Learning, 2024. 280 | 281 | # Applications 282 | 283 |

284 | 285 |

286 | 287 | ## Vision and Graphics 288 | 289 | - Alex Yu, Ruilong Li, Matthew Tancik, Hao Li, Ren Ng, and Angjoo Kanazawa. Plenoctrees for real-time rendering of neural radiance fields. In 2021 IEEE/CVF International Conference on Computer Vision, 2021. 290 | 291 | - Anpei Chen, Zexiang Xu, Andreas Geiger, Jingyi Yu, and Hao Su. Tensorf: Tensorial radiance fields. In 17th European Conference on Computer Vision, 2022. 292 | 293 | - Ben Mildenhall, Pratul P. Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing scenes as neural radiance fields for view synthesis. In European Conference on Computer Vision, 2020. 294 | 295 | - Chiyu Jiang, Avneesh Sud, Ameesh Makadia, Jingwei Huang, Matthias Nießner, and Thomas Funkhouser. Local implicit grid representations for 3d scenes. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020. 296 | 297 | - Daniele Grattarola and Pierre Vandergheynst. Generalised implicit neural representations. In Proceedings of the 36th International Conference on Neural Information Processing Systems, 2022. 298 | 299 | - Hao Chen, Bo He, Hanyu Wang, Yixuan Ren, Ser Nam Lim, and Abhinav Shrivastava. NeRV: Neural representations for videos. In Advances in Neural Information Processing Systems, 2021. 300 | 301 | - Hao Yan, Zhihui Ke, Xiaobo Zhou, Tie Qiu, Xidong Shi, and Dadong Jiang. DS-NeRV: Implicit neural video representation with decomposed static and dynamic codes. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. 302 | 303 | - Jeong Joon Park, Peter Florence, Julian Straub, Richard Newcombe, and Steven Lovegrove. Deepsdf: Learning continuous signed distance functions for shape representation. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019. 304 | 305 | - Jiaxiang Tang, Xiaokang Chen, Jingbo Wang, and Gang Zeng. Compressible-composable NeRF via rank-residual decomposition. In Advances in Neural Information Processing Systems, 2022. 306 | 307 | - Julian Chibane, Thiemo Alldieck, and Gerard Pons-Moll. Implicit functions in feature space for 3d shape reconstruction and completion. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020. 308 | 309 | - Kyle Genova, Forrester Cole, Daniel Vlasic, Aaron Sarna, William Freeman, and Thomas Funkhouser. Learning shape templates with structured implicit functions. In 2019 IEEE/CVF International Conference on Computer Vision, 2019. 310 | 311 | - Lars Mescheder, Michael Oechsle, Michael Niemeyer, Sebastian Nowozin, and Andreas Geiger. Occupancy networks: Learning 3d reconstruction in function space. In 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019. 312 | 313 | - Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. In Advances in Neural Information Processing Systems, 2021. 314 | 315 | - Luiz Schirmer, Tiago Novello, Vin ́ıcius da Silva, Guilherme Schardong, Daniel Perazzo, He ́lio Lopes, Nuno Gonc ̧alves, and Luiz Velho. Geometric implicit neural representations for signed distance functions. Computers & Graphics, 2024. 316 | 317 | - Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng. Fourier features let networks learn high frequency functions in low dimensional domains. In International Conference on Neural Information Processing Systems, 2020. 318 | 319 | - Michael Niemeyer, Lars Mescheder, Michael Oechsle, and Andreas Geiger. Differentiable volumetric rendering: Learning implicit 3d representations without 3d supervision. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020. 320 | 321 | - Mingyuan Yao, Yukang Huo, Yang Ran, Qingbin Tian, Ruifeng Wang, and Haihua Wang. Neural radiance field-based visual rendering: A comprehensive review. arXiv:2404.00714, 2024. 322 | 323 | - Sara Fridovich-Keil, Alex Yu, Matthew Tancik, Qinhong Chen, Benjamin Recht, and Angjoo Kanazawa. Plenoxels: Radiance fields without neural networks. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022. 324 | 325 | - Sara Fridovich-Keil, Giacomo Meanti, Frederik Rahbæk Warburg, Benjamin Recht, and Angjoo Kanazawa. K-planes: Explicit radiance fields in space, time, and appearance. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2023. 326 | 327 | - Seonghyeon Nam, Marcus A. Brubaker, and Michael S. Brown. Neural image representations for multi-image fusion and layer separation. In 17th European Conference on Computer Vision, 2022. 328 | 329 | - Shengxiang Hu, Huaijiang Sun, Dong Wei, Xiaoning Sun, and Jin Wang. Continuous heatmap regression for pose estimation via implicit neural representation. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. 330 | 331 | - Shuzhou Yang, Moxuan Ding, Yanmin Wu, Zihan Li, and Jian Zhang. Implicit neural representation for cooperative lowlight image enhancement. In 2023 IEEE/CVF International Conference on Computer Vision, 2023. 332 | 333 | - Thomas M ̈uller, Alex Evans, Christoph Schied, and Alexander Keller. Instant neural graphics primitives with a multiresolution hash encoding. ACM Transactions on Graphics, 2022. 334 | 335 | - Tianjing Zhang, Yuhui Quan, and Hui Ji. Cross-scale self-supervised blind image deblurring via implicit neural representation. In Advances in Neural Information Processing Systems, 2024. 336 | 337 | - Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein. Implicit neural representations with periodic activation functions. In International Conference on Neural Information Processing Systems, 2020. 338 | 339 | - Vincent Sitzmann, Michael Zollh¨ofer, and Gordon Wetzstein. Scene representation networks: continuous 3d-structure-aware neural scene representations. In Proceedings of the 33rd International Conference on Neural Information Processing Systems, 2019. 340 | 341 | - Wenbo Zhao, Xianming Liu, Deming Zhai, Junjun Jiang, and Xiangyang Ji. Self-supervised arbitrary-scale implicit point clouds upsampling. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2023. 342 | 343 | - Xiang Chen, Jinshan Pan, and Jiangxin Dong. Bidirectional multi-scale implicit neural representations for image deraining. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024. 344 | 345 | - Xinyue Xia, Gal Mishne, and Yusu Wang. Implicit graphon neural representation. 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